allzermalmer

Truth suffers from too much analysis

Posts Tagged ‘Empiricism’

Different Models of both Knowledge & Epistemology

Posted by allzermalmer on September 20, 2013

One of the differences in epistemology are different theories of knowledge. Renee Descartes helped to present one theory of knowledge, which followed a general form of Rationalism. There is another general form known as Empiricism.

We shall have two Categories and three Truth-values.

Category 1: Cognitive or Cognition
Truth Value: Either Cognition is always true or Cognition is sometimes true & sometimes false or Cognition is always false.

Category 2: Sensory or Senses
Truth Value: Either Senses are always true or Senses are sometimes true & sometimes false or Senses are always false.

Now we can combine both of these categories together to form Both Cognition & Senses, apply the Truth Values, and derive 9 different Models of Epistemology or Knowledge.

Hypothesis *1:
Both cognition is always true & senses are always true.
Both senses are always true & cognition is always true.

Hypothesis *2:
Both cognition is always true & senses are sometimes true and sometimes false.
Both senses are sometimes true and sometimes false & cognition is always true.

Hypothesis *3:
Both cognition is always true & senses are always false.
Both senses are always false & cognition is always true.

Hypothesis 1*:
Both cognition is sometimes true and sometimes false & senses are always true.
Both senses are always true & cognition is sometimes true and sometimes false.

Hypothesis 2*:
Both cognition is sometimes true and sometimes false & senses are sometimes true and sometimes false.
Both senses are sometimes true and sometimes false & cognition is sometimes true and sometimes false.

Hypothesis 3*:
Both cognition is sometimes true and sometimes false & senses are always false.
Both senses are always false & cognition is sometimes true and sometimes false.

Hypothesis *1*:
Both cognition is always false & senses are always true.
Both senses are always true & cognition is always false.

Hypothesis *2*:
Both cognition is always false & senses are sometimes true and sometimes false.
Both senses are sometimes true and sometimes false & cognition is always false.

Hypothesis *3*:
Both cognition is always false & senses are always false.
Both senses are always false & cognition is always false.

These models of knowledge, or epistemology, exhaust all logically possible positions given only these two categories and these three truth values. Some possible subdivisions could be made, especially when either categories, or both, take on the truth value of sometimes true and sometimes false.

One basic idea is that cognition, under Rationalism, would always be true & senses, under empiricism, would always be true.

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Hume and The Impossibility of Falsification

Posted by allzermalmer on May 5, 2013

Hume’s logical problem of induction as Hume presents it and Popper presents it, deals with contingent statements. The affirmation or the negation of the same contingent statement is possible. Take the contingent statement that “All Swans are White”: It is both possible that “All Swans are White” and it is also possible that  not “All Swans are White”. Logic alone cannot decide if “All Swans are White” is either true or false. So it would be decided by some other way as to wither its affirmation or negation to be true. Hume, and Popper, say that experience cannot show the truth of the contingent statement “All Swans are White”.

“Hume’s argument does not establish that we may not draw any inference from observation to theory: it merely establishes that we may not draw verifying inferences from observations to theories, leaving open the possibility that we may draw falsifying inferences: an inference from the truth of an observation statement (‘This is a black swan’) to the falsity of a theory (‘All swans are white’) can be deductively perfectly valid.” Realism and The Aim of Science

(H) Hypothesis: All Swans are White
(E) Evidence: This is a Black Swan

Hume, as Popper takes him in his problem of induction, showed that we cannot show that (H) is true, no matter how many individual swans that are white we have observed. To show that (H) is true, we must verify every case of (H). (H) is a Universal statement, its scope is that of all times and all places. The universal statement is both omnipresent and omnitemporal in its scope. It makes no restriction on temporal location and spatial location. (E) makes a Singular statement, its scope is of a particular time and a particular place. It makes a restriction on temporal location and spatial location. Popper held that we can know (E) is true, ‘This is a Black Swan’. Thus, we cannot know (H) All Swans are White but we can know (E) This is a Black Swan.

Hume’s logical problem of induction, as Popper takes it, goes something like this:

(i) Science proposes and uses laws everywhere and all the time; (ii) Only observation and experiment may decide upon the truth or falsity of scientific statements; (iii) It is impossible to justify the truth of a law by observation or experiment.

Or

(i*) Science proposes and uses the universal statement “all swans are white”; (ii*) Only singular observational statements may decide upon the truth or falsity of ‘all swans are white’; (iii*) It is impossible to justify the truth of the universal statement ‘all swans are white’ by singular observational statements.

It is taken as a fact that (i) or (i*) is true. So there is no question about either (i) or (i*). So the conflict of Hume’s logical contradiction arises between (ii) and (iii) or (ii*) and (iii*). Popper accepts (iii) or (iii*). So the only way out of Hume’s logical problem of induction is to modify or reject (ii) or (ii*) to solve the contradiction.

Popper thus solves Hume’s logical problem of induction by rejecting (ii) or (ii*) and replacing it with a new premise. This new premise is (~ii).

(~ii) Only observation and experiment may decide upon the falsity of scientific statements
Or
(~ii*) Only singular observation statements may decide upon the falsity of ‘all swans are white’.

Popper rejects (ii) or (ii*), which basically said that only singular observation statements can show that either universal statements are true or false. Popper rejects this because of (iii), and says that Singular observation statements can only show that universal statements are false. Popper believes, as the quote at the beginning of the blog says, that Hume’s logical problem of induction doesn’t show that we can’t show that a universal statement is false by a singular observational statements. But is this what Hume showed to be true?

It does not appear that Hume’s logical problem of induction even allows Popper to escape with the modification of (ii) to (~ii). It appears that Hume’s logical problem of induction does not allow Popper to escape from “fully decidable” to “partially decidable”, i.e.  decide both truth or falsity to cannot decide truth but only falsity.

Take the singular observational statement that Popper gives in the quote, i.e. ‘This is a black swan’. It is a singular statement, but the statement contains a universal within it, it contains “swan”. “Swan” are defined by their law-like behavior, which are their dispositional characteristics, and is a universal concept. These dispositions are law-like, and thus universal in scope as well. And by (iii) we cannot determine if something is a “swan” because of that. The concept “swan” is in the same position as “all swans are white”. They are both universal, and because of (iii) cannot be shown to be true.

“Alcohol” has the law-like behavior, or disposition, or being flammable. So if we were to say that ‘This is alcohol’. We would have to check all the alcohol that existed in the past, present, future, and all places in the universe in which it was located. We would have to light them to see if they catch fire, and thus flammable. Only than could we say that “This is alcohol”, and know that it is alcohol. But to do so would be to verify a universal through singulars, which is impossible by (iii).

In fact, Hume even talks about dispositions and law-like behavior in his talks about the problem of induction. For example, Hume says that “we always presume, when we see like sensible qualities, that they have like secret powers, and expect that effects, similar to those which we have experienced, will follow from them.” Hume is specifically attacking dispositions as well, which means he is attacking universal concepts and universal statements.

“Our senses inform us of the colour, weight, and consistence of bread; but neither sense nor reason can ever inform us of those qualities which fit it for the nourishment and support of a human body…The bread, which I formerly eat, nourished me; that is, a body of such sensible qualities was, at that time, endued with such secret powers: but does it follow, that other bread must also nourish me at another time, and that like sensible qualities must always be attended with like secret powers?” Enquiry’s Concerning Human Knowledge

From Popper’s point of view, science can only show the falsity of a universal statement through the truth of a singular statement. The singular statement would have to contradict the universal statement and the singular statement would have to be true.

(h) If it rained then wet ground.
(e) Not a wet ground
(c)Thus, it didn’t rain.

If we assume that both (h) and (e) are true, then we accept a contradiction. Contradictions can’t possibly be true. So we know that at least one of these two must be false. But which one is false and which one is true, (h) or (e).

But how can we show the truth of a singular observational statement when it relies on a universal concept, and universal concepts fall for (iii) just as much as universal statements? Hume’s position of the logical invalidity of of induction, i.e. (iii), also holds not only with universal statements but also universal concepts, i.e. law-like behavior/ dispositional characteristics. How does Popper respond to this?

Popper accepts the invalidity of reaching universal statements through experience, but takes it that we accept singular observational statements based on conventions. We conventionally accept the singular observation statement as true.

Hume’s logical problem of induction shows this:

(H) All Swans are White
(E) This swan is black

Now we may either accept (H) as a convention or accept (E) as a convention, or both as conventions. Popper rejects accept (H) as a convention, because you cannot show that a convention is false. Showing something false is what (~ii) was used to solve the original problem of induction. He wants to show that (H) is false, which is consistent with (~ii), but the only way to do that is if (E) can be shown true. But (E) contains a universal concept and (iii) prevents us from experiencing dispositions or law-like behaviors, i.e. Swan or Alcohol. (iii) applies just as much to universal statements as it does to universal concepts. (E) is based on universal concepts and so has to be accepted as a convention, to escape (iii), in order to show that (H) is false and be consistent with (i) and (~ii). (H) has to have the ability to be shown false to be falsifiable, and not being a convention means it has the ability to be shown false.

Contrary to what Popper thinks, Hume’s logical problem of induction doesn’t even allow you to show a falsifying instance. Thus, following full implications of Hume’s logical problem of induction, we can neither show the truth of a universal statement or show the falsify of a universal statement.

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George Berkeley’s on Immediate Perception & Mediated Perception Pt. II

Posted by allzermalmer on October 22, 2012

This is going to work off of a previous blog done on George Berkeley’s point about Immediate Perception and Mediated Perception.

All the human senses (sight, taste, sound, touch, and smell), are distinct from one another, like the sun is distinct from the moon. But these “naturally” distinct things are combined, connected, or associated, with one another. When they are combined, connected, or associated together, they bring forth new phenomena. One example is combining sight and touch together to form depth. We connect these two distinct senses together, and we get depth or three dimensions. This new phenomena is a human creation. It was not an immediate perception but was a mediated perception.

We connect each of the distinct senses together to help to form one “body” or “object”. You have a visual object, and this visual image happens to have color and shape. We also have tactical object, and this tactical feel happens to be hard, cold, and wet. We do this with taste, smell, and sound. We combine these distinct sensual immediate perceptions together to form one “object”, or “body”, and get the mediated perception of “the apple”.

Every sense is distinct from one another. Each distinct sense has their own immediate perceptions. So sight is distinct from touch, but touch has its own immediate perceptions and sight has its own immediate perception. Sight gives the immediate perception of red and touch gives the immediate perception of hot.

Now it appears that each sense would have its own “mediated perceptions” as well, or at least how the human mind has created somethings. Take this example, which is only dealing with sight. [**To speak clearly, these examples are not strictly immediate perceptions as Berkeley uses the term. But they are going to be called “immediate perceptions”, and what comes about from their combination becomes the “mediated perception”.**]

(1) You pick up a rock and look at it.
(2) You look at the rock with a magnifying glass. [(1) is not the same as (2)]
(3) You look at the rock with binoculars. [(2) is not the same as (3)]
(4) You look at the rock with a Light Microscope. [(3) is not the same as (4)]
(5) You look at the rock with an Electron Microscope. [(4) is not the same as (5)]
(6) You look at the rock with Infrared. [(5) is not the same as (6)]
(7) You look at the rock with X-Ray. [(6) is not the same as (7)]

Each of these visual “immediate perceptions” are distinct from one another. But similar to how we connect sight, touch, taste, smell, and sound, to form the “body” or “object” we call “the apple”, so too do we combine the different visual “immediate perceptions” to form the “mediated perception” of the visual “body, or “object”, we call “the rock”. This would hold with the other distinct senses, i.e. touch and taste, as well.

But the different “visual images” are obviously not of the same “body” or “object”. First, the “body” or “object” is a combination of different senses from one another. The rock is a combination of sight, touch, taste, smell, and sound. But each of these are “naturally” distinct from one another, and so the body that is the rock before us, is a creation of the human mind. Each of these senses presents a different aspect of the “same” object, (the object itself being a mediated perception and thus a creation of the human mind).

The senses themselves also have mediated perception, (in an analogical sense and not strictly). The rock has distinct visual aspects. And the human mind combines these distinct visual images and say they are different aspects of the “same” object, (the object itself being a mediated perception in a loose analogical sense, and thus a creation of the human mind). This would go on with the other senses as well, like touch.

Take the example of (1) and (5), or even (4). In these cases, when we look at (5), what we are looking at is something that we cannot touch. It is first of all the sense of sight, and the sense of sight is distinct from touch. Thus, we cannot touch what we see. But we have combined these two distinct senses to say that we can see what we touch. But now we have said that the sense of sight has shown us another “level” of the “body” or “object” that is “the rock” before us. And at the level of (5) or (4), what we see does not match up with what we touch. The rock feels smooth but image (5) or (4) does not feel smooth or even “look” smooth. So the image not only does not match up with the other images, it does not match up with the other senses or the minimum tangibly of touch.

 

 

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George Berkeley’s Immediate Perception and Mediated Perception

Posted by allzermalmer on October 7, 2012

George Berkeley makes two distinctions based on things presented to the human senses. There are those things immediately perceived those things that are mediately perceived. But it should be made clear, both things mediately and immediately perceied, only exist in a mind.

“Having of a long time experienced certain ideas, perceivable by touch – as distance, tangible figure, and solidity – to have been connected with certain ideas of sight, I do upon perceiving these ideas of sight forthwith conclude what tangible ideas are, by the wonted ordinary course of nature, like to follow. Looking at an object I perceive a certain visible figure and colour, with some degree of faintness and other circumstances, which from what I have formerly observed, determine me to think that if I advance forward so many paces or miles, I shall be affected with such and such ideas of touch. So that in truth and strictness of speech I neither see distance itself, nor anything that I take to be at a distance. I say, neither distance nor things placed at a distance are themselves, or their ideas, truly perceived by sight. This I am persuaded of, as to what concerns myself; and I believe whoever will look narrowly into his own thoughts and examine what he means by saying he sees this or that thing at a distance, will agree with me that what he sees only suggests to his understanding that, after having passed a certain distance, to be measured by the motion of his body, which is perceivable by touch, he shall come to perceive such and such tangible ideas which have been usually connected with such and such visible ideas. But that one might be deceived by these suggestions of sense, and that there is no necessary connexion between visible and tangible ideas suggested by them, we need go no farther than the next looking-glass or picture to be convinced…when I speak of tangible ideas, I take the word ‘idea’ for any the immediate object of sense or understanding, in which large signification it is commonly used by the moderns.

“But if we take a close and accurate view of things, it must be acknowledged that we never see and feel one and the same object. That which is seen is one thing, and that which is felt is another. If the visible figure and extension be not the same with the tangible figure and extension, we are not to infer that one and the same thing has divers extensions. The true consequence is that the objects of sight and touch are two distinct things.”

“In order therefore to treat accurately and unconfusedly of vision, we must bear in mind that there are two sorts of objects apprehended by the eye, the one primarily and immediately, the other secondarily and by intervention of the former. Those of the first sort neither are, nor appear to be, without the mind or at any distance off. They may indeed grow greater or smaller, more confused or more clear, or more faint, but they do not, cannot, approach or recede from us. Whenever we say an object is at a distance, whenever we say it draws near or goes farther off, we must always mean it of the latter sort, which properly belong to the touch, and are not so truly perceived as suggested by the eye in like manner as thoughts by the ear.”

“No sooner do we hear the words of a familiar language pronounced in our ears, but the ideas corresponding thereto present themselves to our minds. In the very same instant the sound and the meaning enter the understanding; so closely are they united that it is not in our power to keep out the one, except we exclude the other also. We even act in all respects as if we heard the very thoughts themselves. So likewise the secondary objects, or those which are only suggested by sight, do often more strongly affect us, and are more regarded than the proper objects of that sense, along with which they enter into the mind and with which they have a far more strict connexion than ideas have with words. Hence it is we find it so difficult to discriminate between the immediate and mediate objects of sight, and are so prone to attribute to the former what belongs only to the latter” An Essay Towards a New Theory of Vision (Italics are my own emphasis)

This is George Berkeley showing that each of the senses are distinct from one another, and they have no connection to one another. Sight is not sound, or taste, or tactile, or smell. So what we see by sight has no qualities of sound, taste, tactile, or smell. But we still immediately perceive something by sight, but we can mediate it with sound, taste, tactile, or smell. We can combine these two distinct things, and something new comes about, i.e. sight and touch forms distance or 3d vision.

We interweave one sense with another sense, and confound them together into the same “object”. This object can be a tower. We have a visual idea, or immediate perception of it, and we also have a tactile idea, or immediate perception of it. We connect these two distinct ideas together into the same “object” or “idea”. But each of these things are “naturally” distinct from one another and have no connection expect those that we make by connecting them. From all of these immediate perceptions, we mediate them by connecting them together with former connections we have made, and find that what we are experiencing “suggests” the tower getting closer or moving further away, or its height.

It becomes second nature to take the mediated for the immediate, even though it is not immediately given in by that sense (i.e. visual or tactile). It is something that the human mind creates itself, and takes it for being immediately given or suggested by experience. The immediate things are not done by the human mind, but the mediated things are done by the human mind. They are what the human mind adds on to what is immediately perceived by the senses.

One of Berkeley’s big points is that “sensible things are those only which are immediately perceived by sense.” So those things immediately perceived by the senses are ‘sensible things’, and those things that are mediately perceived by the senses are not sensible things. This would mean that depth or 3d are not sensible things. Like seeing someone’s face flush red, sensible thing, does not mean that it is sensible thing that the person had a passion arise in them. It might be “suggested”, but it is not by vision that the conclusion was reached, but because it was mediated by something else, which was itself not immediately perceived.

The example of written word is a great example. There are certain colors and shapes that are seen, and from these things seen one obtains some thoughts. But the thoughts were not themselves found in the visual experience itself. So one mediated what was immediately perceived through something else, which was thought. Vision was mediated with thoughts, which are two distinct things. This is sometimes closer to what is called theory-ladden observation.

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Difference Between Verification and Falsification

Posted by allzermalmer on September 30, 2012

Karl Popper developed the idea that the demarcation between empirical statements, which was mostly taken to be scientific statements, and metaphysical statements was based on the idea of falsification. Popper was speaking out, or presenting, a different criterion to differentiate between empirical statements and metaphysical statements.

“The problem of induction arises from an apparent contradiction between the basic empiricist requirement (only experience can decide the truth or falsity of a scientific statement) and Hume’s insight into the logical impermissibility of inductive decision (there is no empirical justification of universal statements). This contradiction exists only if we assume that empirical statements must be empirically “fully decidable”, that is, that experience must be able to decide not only their falsity, but also their truth. The contradiction is resolved once “partially decidable” empirical statements are admitted: Universal empirical statements are empirically falsifiable, they can be defeated by experience.” The Two Fundamental Problems of the Theory of Knowledge

Verification meant that empirical statements, or scientific statements, are those that it is possible be decided to be true or false by experience. You can fully decide that the statement is true because experience has shown the statement is true. Like experience can show that “this apple is red in color”, so too can experience show the statement that “all apples in the refrigerator are red in color”. The refrigerator is in a specific place, at a specific time, and logically possible to see if all the apples in the refrigeration  are red in color. It can be opened and found that all the apples are red in color, or that all but one of the apples in the refrigerator are red in color, like one can be yellow. Thus, it is both logically possible to empirically verify the statement or empirically falsify the statement. It is logically possible to either show it is true or show it is false.

However, the statement that “all apples in refrigerators are red in color” is logically impossible to empirically verify. This is because this universal statement applies to all times and all places, while the previous universal statement applies to a specific time and specific place.Thus, this universal statement cannot be verified, but it can still be empirically falsified. You might not be able to check all the refrigerators that will, or have, existed in all places or all times, but those that you have observed have the empirical possibility of showing the statement to be false. You might not be able to check all refrigerators in all places and times, but finding a specific refrigerator that has a yellow apple, shows that all refrigerators, in all times and place, do not have all red apples in them. One case has been found to run counter to the universal claim. Thus, we learn that some refrigerators have only red apples in color and some refrigerators have yellow apples in color.

The point becomes that science can introduce whatever universal statement it wants, so long as it is logically possible to make one empirical observation to show it is false. We do not have to show that what it introduces is true by experience, just that it can make predictions that are logically possible to show false by experience.

Let us imagine that there is a person who walks amongst us, and this person knows all the laws of nature. Let us also assume that it is a trickster like Loki. It mixes some truth with some falsity, knowingly. It decides to come up with a falsifiable statement, which means that it is not fully decidable, i.e. it is partially decidable. It knows that this universal statement is false, but it still makes predictions that are possible to be shown false by experience. This being that is like Loki knows that all attempted experiments to show that statement is false by experience will fail, which means it passes every single experimental test that can be presented. You would be justified in accepting a false statement because you cannot show it is true but you can show it is false.

 

 

 

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Whatever Is Conceivable Is Possible

Posted by allzermalmer on September 27, 2012

I am going to quote one little section in a book called Hume’s First Principles by Robert Fendel Anderson. This first part of the book is on Perceptions, and the first principle gone over on Perceptions is “Whatever is Conceivable is Possible”.

“The principle of the possible existence of whatever is conceivable is one which Hume finds both an evident principle and already an established maxim in metaphysics[1]. The application of the principle is frequently restricted to that which is clearly and distinctly conceivable: “…nothing of which we can form a clear and distinct idea is absurd and impossible.”[2] Again: “To form a clear idea of anything, is an undeniable argument for its possibility…”[3]. The possibility of existence, therefore, is of the essence of whatever is clearly and distinctly conceived; that is, its possibility is included or implied within it: “ ‘Tis an establish’d maxim in metaphysics, That whatever the mind clearly conceives includes the idea of possible existence…”[4] and: “Whatever can be conceiv’d by a clear and distinct idea necessarily implies the possibility of existence….”[5]

A clear and distinct idea, according to Hume’s doctrine, is one which neither contains nor implies a contradiction: “Now whatever is intelligible, and can be distinctly conceived, implies no contradiction…”[6] Again: “How any clear, and distinct idea can contain circumstances, contradictory to itself, or to any other clear, distinct idea, is absolutely incomprehensible….”[7] In saying that whatever is clearly and distinctly conceived is possible, therefore, it appears to be Hume’s intention also that whatever is self-consistent and noncontradictory is possible:

“Whatever can be conceiv’d by a clear and distinct idea necessarily implies the possibility of existence; and he who pretends to prove the impossibility of its existence by any argument deriv’d from the clear idea, in reality asserts, that we have no clear idea of it, because we have a clear idea. ‘Tis in vain to search for a contradiction in any thing that is distinctly conceiv’d by the mind.”[8]

The expression employed in the remarks thus far examined may lead the reader to suppose that there are some things clearly and distinctly conceived and some not- that some of our ideas are clear and distinct and some of them unclear and indistinct. Were this true, then it would follow that we have ideas of things the existence of which we must regard as impossible. There is evidence, however, that Hume considers all our ideas to be clear and distinct. He offers an argument to this conclusion, based on his doctrine that ideas are derived from impressions:

“…we need but reflect on that principle so oft insisted on, that all our ideas are copy’d from our impressions. For from thence we may immediately conclude, that since all impressions are clear and precise, the ideas, which are copy’d from them, must be of the same nature…”[9]

Since all perceptions are either impressions or ideas[10], we must conclude that there are no perceptions of any kind that are not clear and precise.

From the clarity and preciseness of all ideas, we may infer, moreover, that we possess no ideas of those things whose existence we must regard as impossible, but that any idea we may have is the idea of something the existence of which is possible. We find, indeed, that Hume does not always restrict the possibility of existence to that which is clearly and distinctly conceived, but extends it as well to everything that is conceived or imagined at all: “…whatever we conceive is possible.”[11] And: “…whatever we can imagine, is possible.”[12]Hume appears, indeed, to make no firm distinction between what is clearly and distinctly conceived and what is conceived or imagined merely, as is evidenced in his full statement of the metaphysical maxim: “ ‘Tis an establish’d maxim in metaphysics, That whatever the mind clearly conceives includes the idea of possible existence, or in other words, that nothing we imagine is absolutely impossible.”[13] We are thus again justified, apparently, in supposing that all our ideas are equally clear and distinct, and that all things conceived are possible. Things which are contradictory and therefore impossible, on the other hand, cannot be conceived or imagined at all: “We can form the idea of a golden mountain, and from thence conclude that such a mountain may actually exist. We can form no idea of a mountain without a valley, and therefore regard it as impossible.”[14] Again: “ ‘Tis in vain to search for a contradiction in any thing that is distinctly conceiv’d by the mind. Did it imply any contradiction, ‘tis impossible it cou’d ever be coneiv’d.”[15]

Knowing then that self-contradictory things are neither conceivable nor possible, and knowing that whatever is conceived or imagined is possible, we may next inquire what things are in fact conceived or imagined and hence possible. From certain of Hume’s remarks one might infer that we conceive only perceptions; for it is only perceptions that are “present to” the mind: “…nothing is ever really present with the mind but its perceptions or impressions and ideas…”[16] If this be true, then it is reasonable to suppose that we have clear and distinct ideas only of perceptions, as Hume sometimes appears to agree: “We have no perfect idea of any thing but of a perception.”[17] Now if we can conceive only of perceptions, then according to Hume’s principle it is only perceptions whose existence we may regard as possible. We may observe, moreover, that the remarks we have thus far examined do not imply that perceptions, as such, exist, but only that their existence is possible. Were there no further texts available to us from among Hume’s writings, we might justifiably conclude that what he calls “perceptions” are to be understood as a realm of mere essences which, taken together, comprehend all possibility, but which are not, of themselves, existence.”


[1] David Hume, A Treatise of Human Nature, ed. by L.A. Selby-Bigge (Oxford: Clarendon Press, 1888), pp. 32, 250, Hereafter cited as Treatise.

[2] Treatise, pp.19-20. Cf> David Hume, Dialogues Concerning Natural Religion, ed. and with an introduction by Henry D. Aiken(New York: Hafner Library of Classic, Hafner Publishing Company, 1948), p. 19, Philo speaking. Hereafter cited as Dialogues.

[3] Treatise, p. 89

[4] Treatise, p.32

[5] Treatise, p. 43

[6] David Hume, “An Enquiry Concerning the Human Understanding,” in An Enquiry Concerning the Human Understanding and an Enquiry Concerning the Principles of Morals, ed. and with an introduction by L.A. Selby-Bigge (2d ed.; Oxford: Clarendon Press, 1902), p. 35. Hereafter cited as “Understanding.” Cf. Dialogues, p. 58, Cleanthes speaking.

[7] “Understanding.” P. 157

[8] Treatise p. 43.

[9] Treatise, p. 72; cf. p. 366.

[10] Treatise, pp. 1, 96.

[11] Treatise, p. 236.

[12] Treatise, p. 250

[13] Treatise, p. 32.

[14] Treatise, p. 32.

[15] Treatise, p.43. Cf. “Understanding,” p. 164.

[16] Treatise, p. 67; cf. pp.197,212.

[17] Treatise, p. 234.

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Berkeley’s Immaterialism

Posted by allzermalmer on June 25, 2012

This blog is a paper that I had to do on George Berkeley. We had to talk about Berkeley’s “Immaterialism”. I received an A on this paper but this does not mean much.

George Berkeley was a Scottish philosopher who lived from 1685-1753. He was a philosopher of the empiricist type, which means that he believed knowledge of the world is based on experience, which is to say the human senses. He became famous for his stance of Immaterialism, which is the denial of a material substance and a mind-independent world. He is the philosopher who has become famous for the slogan of esse is percipi, or to be is to be perceived.

Berkeley starts out his book A Treatise Concerning the Principles of Human Knowledge by trying to go over a topic called Abstraction. It is from this that he believes that many problems have arisen and have misled people. One of the things he says in the introduction is “That we have first raised a dust, and then complain, we cannot see.”[1] Berkeley believes that abstraction has come about from an abuse of language, and he is going to try to rectify this problem. Berkeley does this by pointing out that when we come across a particular object, like an apple, we find that it has many qualities existing together. Abstraction is where we come to think of each of these qualities being separated from each other in this apple, and we come to hold that each quality can, or does, exist apart from the other qualities in which we originally found them. As Berkeley says, “the mind being able to consider each quality singly, or abstracted from those other qualities with which it is united, does by that means frame to itself abstract ideas.”[2]

We perceive particular objects by our senses, and we find that there is something alike, or different, between those particular things we experience when we make a comparison between them. We will find that there are certain qualities that these two objects have in common when we are comparing them, and find that they share the same quality, like the color red. We come to separate these qualities from those two objects and hold that they exist without the particular object itself.  Take an example of comparing Peter and James, two particular human beings. They are two particular human beings, and they have some different qualities and similar qualities. One of them is white in skin color and the other is black in skin color, but both have color; they both have different hair colors in that one is blond and one is black, but they both have colored hair; they both have hair but different styles of hair; they both have arms but different lengths; they both have legs but of different length; they both have a height but one is tall and the other is short. We can go on like this and find that the abstract idea of Human contains all of these qualities and none of these qualities. A Human is both white and not white, both 6 feet tall and not 6 feet all, both has two legs and no legs, and etc. Abstract ideas are not something that Berkeley can think of and does not find in experience. But we get caught up in taking abstract ideas as if they exist or represent something that exists.

When Berkeley is told to think of “human”, he thinks of something particular. He imagines that it is white in skin color, has red hair, has hair down to its shoulders, has long hairy forearms, is tall and has long legs, and etc. In other words, when he is asked to think about a human being he thinks of a particular human with particular qualities, not this “all and none” qualities that is found with an abstract idea of a human. This is the same when he does something like mathematics, which is supposed to be a very abstract science. He comes to think of a particular triangle, but a triangle in geometry can be either a right triangle, or acute triangle, or obtuse triangle, or equilateral triangle, or isosceles triangle, or a scalene triangle.

One thing about abstraction, which can be made a case and point with geometry, is that we do not find them in experience. One of the definitions for a line is a “breadthless length”. None of these things are found in experience. In fact, we cannot experience these things. When a line is drawn on a sheet of paper, it is not a line in geometry. We are calling something a line which is not a geometrical line. If triangles are built off of lines and lines are not experienced, then those triangles of geometry are not experienced either. But we apply this abstract idea to experience, or we apply something to its contradictory. We are applying a breadthless length to a line with breadth.

Once we clear up this problem with abstraction, Berkeley comes to deal with this idea that there is something that is primary qualities and secondary qualities. It was held by some people during Berkeley’s time, that we do not directly experience the “external world”. The position of perception was known as representational theory of perception. When the external world caused our perceptions, we indirectly had experiences of it. Primary qualities are said to be qualities of mind-independent objects, which are extension, figure, motion, rest, solidity, and number, and are the qualities that exist in the object itself. Secondary qualities are said to be mind-dependent objects, which are colors, sounds, tastes, and etc, and do not exist in the object itself. Matter, which is said to be mind-independent, has these primary qualities and when we have these mind-independent objects affect our senses to cause our perceptions, we only view a part of it that is the primary qualities and the secondary qualities are what our minds add on to the primary qualities. In other words, our perceptions both have something from the mind-independent world and something from the mind-dependent world. But what is key to keep in mind is that what we experience with our senses is not the external world itself. The experiences themselves are mind-dependent, which is our individual minds.

One way in it was said to be determined what qualities are from the external world, and those qualities from ourselves, was with the primary and secondary qualities distinction.  The primary qualities were supposed to be stable and did not change, much, if at all. It was to persist through change. And secondary qualities were said to change through time frequently, being in a sort of flux. There was one way to distinguish through primary and secondary qualities are with a simple argument. One of the things that was said to be a secondary quality was that of heat. Take the example of taking a bucket filled with water. “Suppose now one of your hands hot, and the other cold, and that they are both at once put into the same vessel of water, in an intermediate state; will not the water seem cold to one hand and warm to the other?…It will.”[3] But the heat of the water cannot both be hot and not hot, so heat is not part of the mind-independent world. These types of arguments were supposed to show that some of things we experience are not part of a mind-independent world, and arguments of the same kind were used to show what qualities were mind-independent and which qualities were mind-dependent.

What Berkeley does in this situation is to use the same type of arguments to show that even primary qualities are mind-dependent. Solidity, for example, is said to be mind-independent. Now take an example where an ant and a human come to touch a cherry. To the human, when they touch the cherry, they find that it gives way to them touching it, but when an ant touches it feels very hard. But the cherry, based on solidity, cannot both be hard and not hard. We also find extension is relative to different animals in that one animal will see one shape and another animal will see another shape, but one shape in a mind-independent world cannot be of two different shapes. This shows the relativity of different qualities that one human can experience from another, and the different qualities that one species experiences from that of another.

Berkeley shows that primary qualities fall to being mind-dependent as well, but he goes on to point out something else. Every time we experience a primary quality, it always is associated with secondary quality. So I may experience the primary quality of something with the shape of being round, but it will have a color of either being black or white, or blue or yellow. If it had no color, then I could not observe the object itself. When I pick up an object, I feel its shape in my hand but I also feel if it is hot or cold. Berkeley is pointing out that primary qualities are found to constantly have secondary qualities associated with them when we experience them. So not only are secondary qualities mind-dependent and so are primary qualities, but what we call secondary qualities and primary qualities are found to show up together and cannot separate one from the other without forming an abstract idea.

We find that primary qualities were of extension, shape, motion, rest, solidity and number. They were supposed to persist through change. These primary qualities were supposed to be of this substance called matter. Matter was supposed to be inert and a passive thing that was unthinking. Berkeley points out that this “matter” would be an abstraction. This is because the shape would be of neither a triangle, nor a square, nor polygon, or whatever else the mind can imagine, but all of them. Motion would be of one shape moving relative to another, and it would be at rest to another. It would be both at rest and moving. Matter turns out to be an abstraction, if not an outright contradiction. Now it is agreed that secondary qualities are mind-dependent, and Berkeley shows that arguments to show the mind-dependence of secondary qualities can also be used for primary qualities. Thus, all qualities that we experience are reduced to being mind-dependent.

Berkeley has left alternatives for matter, for it either is a contradiction, an abstraction, or something that we have no experience of. Being either an abstraction or having no experience of it is to make it meaningless by being a sign with no signification in experience, or being an empty term. So Berkeley believes that he has given enough ground to ignore matter as anything. He may ignore it if matter is meaningless and we have no experience of it, because one is just using words without anything signified by them. But Berkeley admits that even though it is meaningless in that no experience for it, it is still logically possible. But being logically possible is fine, but we cannot even think about it because it is an abstract idea. What is the point of using something that is possible that you cannot even think about it or experience it? He may also ignore it if it is a contradiction because it is a logical impossibility.

Now that Berkeley has dismissed of “matter”, he is going to go down a different route. One of the best ways to see where Berkeley is starting from, and part of what he is rejecting, deals with a certain passage from Renee Descartes Meditations on First Philosophy talks about particular bodies like a piece of wax. He says: “it has only just been removed from the honeycomb; it has not yet lost all the flavour of its honey; it retains some of the scent of the flowers among which it was gathered; its colour, shape, and size are clearly visible; it is hard, cold, easy to touch, and if you tap it with your knuckle, it makes a sound. In short, it has all the properties that seem to be required for a given body to be known as distinctly as possible. But wait—while I am speaking, it is brought close to the fire. The remains of its flavour evaporate; the smell fades; the colour is changed, the shape is taken away, it grows in size, becomes liquid, becomes warm, it can hardly be touched, and now, if you strike it, it will give off no sound. Does the same wax still remain? We must admit it does remain: no one would say or think it does not. So what was there in it that was so distinctly grasped? Certainly, none of those qualities I apprehended by the senses: for whatever came under taste, or smell, or sight, or touch, or hearing, has now changed: but the wax remains.”[4]

Berkeley holds the opposite. Descartes is holding that there is something that is this body below the sensible qualities that he just reviewed. Descartes said he did not find the “body” in the senses and moves on to the imagination, where he finds that a particular body does not derive from the imagination. Berkeley would say that anything beyond the sensible qualities that are supposed to be a particular body is an abstraction and not even possible to experience with the senses, or being in the imagination would need the sensible quality of color which is mind dependent. This particular body beyond the senses becomes meaningless, even if possible. When we use the sign of “apple”, it is meant to signify a pattern of sensible qualities found to be distinguished from other sensible qualities surrounding it, which happens to be red, have a certain shape, a certain smell, certain taste, and certain tactile sensations. In other words, a particular “body” is a specific pattern, and regularity, of sensible qualities found to go together, as distinguished from other sensible qualities.

Part of Berkeley’s position on experience is based on the Molyneux’s problem. This is based on a thought experiment of someone who is born blind and has tactile senses. This blind person has become accustomed with a tactile sensation that he calls a “cube”, and those with sight would understand to be a cube, and they are also accustomed to one of a “sphere”. Now imagine that the blind person has both objects before them on a table, and develop a sense known as sight. The person will not be able to pick out which object that he sees is associated with his tactile sensations that he knows as the “cube”. It shows that each sense is distinct from every other sense, but we eventually, through constant experience, begin associating one sense with another to form the idea of the “cube” or “bodies”.

When we are left with Descartes in some sort of solipsism, Berkeley has a way out. Berkeley finds that he has the ability to think and imagine things, like what he will do tomorrow. He also finds that when he wills to move his arm, his arm moves. He also finds that when he experiences sensible qualities, he is constantly associating one sense with another and associating sensory qualities in order to form what are known as “bodies”. He also makes connections to help form chains of cause and effect, as well as forming some understanding of what is going on to act. All of these things he finds to be a sign of activity or Mind. But he finds that when he closes his eyes, he cannot make whatever he wants to show up. It is against his will what he will see when he closes his eyes and then reopens them. These sensory qualities are forced upon him, or these flux of sensory qualities. He does not find the power for him to produce these sensory qualities, and so it means that there is something else besides Berkeley bringing about the experience he has. This shows a cause outside of Berkeley bringing about these experiences.

Now some might wonder how we can differentiate between reality and between dreams. Berkeley points out that “reality” is more vivid than that of a dream, and that dreams lack a coherence and vividness that we find with “reality”. This is, also, how we typically differentiate between “reality” and a “dream”. We find that what we are experiencing in a dream lacks a coherence from that which we have experienced when waking, and the experiences in reality are more vivid and stronger than what we find in dreams. We also find that we have a memory of things in the past while we have a tough time of remembering dreams and have a tough time fitting dreams into our experiences in a coherent way that we say that they are a dream. As Berkeley says, “The ideas formed by the imagination are faint and indistinct; they have, besides, an entire dependence on the will. But the ideas perceived by sense, that is, real things, are more vivid and clear, and being imprinted on the mind by a spirit distinct from us, have not a like dependence on our will. There is therefore no danger of confounding these with the foregoing; and there is as little of confounding them with the visions of a dream, which are dim, irregular, and confused. And though they should happen to be never so lively and natural, yet by their not being connected, and of a piece with the preceding and subsequent transactions of our lives, they might easily be distinguished from realities. In short, by whatever method you distinguish things from chimeras on your own scheme, the same, it is evident, will hold also upon mine.”[5]

The sensory qualities that he experiences as bodies, he observes them and finds that he does not see the power for one to move the other. He finds that those things he observes are passive, or that they are inert. Berkeley’s opinion of cause and effect is that we observe no necessary connection between these sensory qualities, but that we find one pattern of sensory qualities following another pattern of sensory qualities. There is no connection between these events or see one thing move another, and this makes them appear to be passive. One just follows the other, and do not see one making the other move or the other one to stop moving, or any necessary connection between them at all. Each event is distinct from one another and have no influence on one another.

From the position that he finds himself to be active and those sensory qualities that happen against his will to be passive, and that matter is either logically ruled out as being the cause or meaningless to assert it as the cause, so he finds that another mind to be the cause. This is because he cannot see how a passive thing can make itself show itself against his will or move one another, but he has found with himself that he can will his body to move and it moves. This shows that an active thing can move sensory qualities, and so another mind is the one that is giving Berkeley, and us, these sensory qualities. He finds that the active can move the passive with his own experience, and he is having experiences against his will and has ruled out “matter”, which leaves another mind moving and making these sensible qualities come against Berkeley’s will.

Berkeley finds that what he immediately perceives is from God, which means those sensory qualities that are forced upon him are from God. These are sight, touch, taste, sound, and smell which all come from God and giving them to Berkeley. Now Berkeley points out that we immediately perceive the sensible qualities, but we also mediate them. This mediation is a sign of activity, because we are making associations with our senses to form one “body” and observe a regularity in which “bodies” move amongst each other, and making judgments about them. We notice that when we come to predict these regularities that we can obtain food to nourish ourselves and predict when the water will flood to plant our food, and what to do to obtain pleasure and what not to do to escape pain. These regularities, by making the world predictable, show wisdom and providence of God to us and help show another mind.

Berkeley gives an example of mediation, or what he is talking about. “From what we have shown it is a manifest consequence that the ideas of space, outness, and things placed at a distance are not, strictly speaking, the object of sight. They are not otherwise perceived by the eye than by the ear. Sitting in my study I hear a coach drive along the street; I look through the casement and see it; I walk out and enter into it. Thus common speech would incline one to think I heard, saw, and touched the same thing, to wit, the coach. It is nevertheless certain, the ideas intromitted by each sense are widely different and distinct from each other; but having been observed constantly to go together, they are spoken of as one and the same thing. By the variation of the noise I perceive the different distances of the coach, and know that it approaches before I look out. Thus by the ear I perceive distance, just after the same manner as I do by the eye.”[6] He is pointing out that through constant association of different sensible qualities; we come to combine them into one thing called the “coach”. “Coach” becomes the sign for the sensible qualities signified by it. And the “Coach” is not in experience but something that we do with them. This helps form a basis for theory-laden observation, as the modern term goes, which shows a sign of activity of mind.

Now Berkeley has established an external world, which his that of God. He comes to discover other minds, or other finite minds like himself. Strictly speaking, we never experience other minds immediately by sensory qualities that we call “bodies”. That which is presented by immediate perception is passive and minds are active. So how does Berkeley come to other minds? Imagine that we are in a land that has “inanimate” objects. We find that these inanimate objects move in a regular fashion, like when I hold the rock in my hand and let go of it, it falls to the ground. We find that “inanimate” things in this world are works with regularity and move in a very predictable fashion. But in our experiences we find some “bodies” that do not move in a predictable and regular fashion.

“We experience certain ides of reality. These ideas exhibit a variety, order, and coherence far beyond anything that is within our ability to produce. Some other spirit must therefore produce them and this spirit must be supremely wise and benevolent. But among our ideas of reality there are some, those of the motions of animate bodies, which exhibit a degree of irregularity, inconsistency of purpose, greed, stupidity, and sheer perversity which is simply inconsistent with the notion that these ideas are produced by a wise and benevolent thing. One plausible way to deal with these phenomena is to postulate that there exist certain other spirits whose wills the divine spirit is disposed to indulge when moving animate bodies. Since the wills of these spirits are circumscribed to particular animate bodies and since their motions evidence a degree of reason and purpose, we may postulate further that they are finite, intelligent spirits, that is, beings “like ourselves”. It is in this way that we deduce the existence of other minds “from their operations, or the ideas by them excited in us.”[7]

The point becomes that when we notice certain sensory qualities known as “human bodies” and these do not move in the same way “inanimate” products. We notice a difference in their motions from one another. When we notice motion we come to infer a cause, and we notice that these motions do not match up with the regularities of “inanimate” objects, and these bodies appear to move with a purpose and greed. For only an active principle may move these “bodies” that we observe. We also notice that they look similar to our body and come to infer that there is another active agent besides that of us and God. The main point becomes that God’s actions are contingent, and we notice that the world works a certain way when there are no other finite minds. In other words, if it were not another finite mind, then those actions would have been different, which means it would have looked like a regularity of “inanimate” bodies.

Now Berkeley holds that all sensible qualities cannot exist without being perceived by a mind. This is because matter has already been eliminated and we are left with minds. So sensible objects are mind-dependent, which is that for them to exist, they must be perceived by a mind. This forms the slogan of “esse is percepi”, or “to be is to be perceived”. All unthinking things are dependent on being observed by some mind. This could either be myself, Berkeley, a group of humans/finite minds, or by God. This means that no sensible qualities exist outside of a mind. Now these sensible qualities may exist outside of human perception, but not that of another mind, like that of God. It may exist outside of the perception of all finite minds, but not that of the infinite mind of God. So the general rule of “esse is percepi” is true of sensible qualities known as “bodies”. For human being, sensible qualities are “esse is posse percepi”, also known as “to be is to be possibly perceived”. This means that for sensible qualities to exist for us finite minds known as humans, is that they be possible perceptions or actual perceptions. These possible perceptions might not be experienced by us, but they are at least experienced by God.

When Berkeley leaves a room with a desk and books, and no other finite minds perceive it, then the books and desk are still there because they are being perceived by God. But they are also a possible perception for finite minds, because if Berkeley were to enter the room, then he would perceive the desk and books. “The table I write on, I say, exists, that is, I see and feel it; and if I were out of my study I should say it existed, meaning thereby that if I was in my study I might perceive it, or that some other spirit actually does perceive it…so long [as “bodies” are] not actually perceived by me, or do not exist in my mind or that of any other created spirit, they must either have no existence at all, or else subsist in the mind of some eternal spirit: it being perfectly.”[8]

Berkeley was, it seems, a concurrentist when it comes to causality and finite minds willing their bodies to move. “First, concurrentists maintain that God’s activity is not merely required to create the world but also to conserve it in its existence…Second, concurrentists insist that creatures are endowed with genuine active and passive powers, and that they exercise their powers in ordinary causal interactions…Third, and most distinctively, concurrentists maintain that although creatures are endowed with genuine causal powers, no creaturely causal power could be efficacious in bringing about its appropriate effects without God’s active general assistance, or “concurrence”.”[9] The point is that God, being wise and disposed to humor us, God allows us to do, or will, to do certain actions. We may say that there is a certain law on what bodies are allowed to do, and anything within those laws that do not violate are allowable for us to do by goods kind disposition to us. God gives finite spirits what can be called an allowance, and may do whatever they want to do within that allowance. God humors us in allowing us to do it what we will to do.

 Bibliography

Berkeley, George, and Desmond M. Clarke. Berkeley: Philosophical Writings. Cambridge: Cambridge UP, 2009.

Descartes, René, and Michael Moriarty. Meditations on First Philosophy: With Selections from the Objections and Replies. Oxford: Oxford UP, 2008.

Luce, A. A. Berkeley’s Immaterialism; a Commentary on His “A Treatise concerning the Principles of Human Knowledge” London: T. Nelson and Sons, 1945. Print.

Bettcher, Talia Mae. Berkeley: A Guide for the Perplexed. London: Continuum, 2008. Print.

Foster, John, and Howard Robinson. Essays on Berkeley: A Tercentennial Celebration. Oxford: Clarendon, 1985. Print.

Falkenstein, Lorne. “Berkeley’s Argument for Other Minds.” History of Philosophy Quarterly 7.4 (1990): 431-40. Print.

Jeffrey K. McDonough. “Berkeley, Human Agency and Divine Concurrentism.” Journal of the History of Philosophy 46.4 (2008): 567-90.


[1] Berkeley, George, and Desmond M. Clarke. Berkeley: Philosophical Writings. Cambridge: Cambridge UP, 2009. Pg. 69

[2] Ibid. Pg. 70

[3] Ibid Pg. 162

[4] Descartes, René, and Michael Moriarty. Meditations on First Philosophy: With Selections from the Objections and Replies. Oxford: Oxford UP, 2008. Pg. 22

[5] Berkeley, George, and Desmond M. Clarke. Berkeley: Philosophical Writings. Cambridge: Cambridge UP, 2009. Pg. 216

[6]   Berkeley, George, and Desmond M. Clarke. Berkeley: Philosophical Writings. Cambridge: Cambridge UP, 2009. Pg. 23

[7] Falkenstein, Lorne. “Berkeley’s Argument for Other Minds.” History of Philosophy Quarterly 7.4 (1990): 431-40. Print. Pg. 438-439

[8] Berkeley, George, and Desmond M. Clarke. Berkeley: Philosophical Writings. Cambridge: Cambridge UP, 2009. Pg. 84-85

[9] Jeffrey K. McDonough. “Berkeley, Human Agency and Divine Concurrentism.” Journal of the History of Philosophy 46.4 (2008): 567-90. Pg. 568-569

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David Hume on Induction

Posted by allzermalmer on May 20, 2012

This is David Hume on the Problem of Induction, and this comes from Treatise of Human Nature: Book I (Of the Understandin), Part III (Of Knowledge & Probability), Sect. VI. Of the Inference from the Impression to the Idea

“It is easy to observe, that in tracing this relation, the inference we draw from cause to effect, is not derived merely from a survey of these particular objects, and from such a penetration into their essences as may discover the dependence of the one upon the other. There is no object, which implies the existence of any other if we consider these objects in themselves, and never look beyond the ideas which we form of them. Such an inference would amount to knowledge, and would imply the absolute contradiction and impossibility of conceiving any thing different. But as all distinct ideas are separable, it is evident there can be no impossibility of that kind. When we pass from a present impression to the idea of any object, we might possibly have separated the idea from the impression, and have substituted any other idea in its room.

It is therefore by EXPERIENCE only, that we can infer the existence of one object from that of another. The nature of experience is this. We remember to have had frequent instances of the existence of one species of objects; and also remember, that the individuals of another species of objects have always attended them, and have existed in a regular order of contiguity and succession with regard to them. Thus we remember, to have seen that species of object we call flame, and to have felt that species of sensation we call heat. We likewise call to mind their constant conjunction in all past instances. Without any farther ceremony, we call the one cause and the other effect, and infer the existence of the one from that of the other. In all those instances, from which we learn the conjunction of particular causes and effects, both the causes and effects have been perceived by the senses, and are remembered But in all cases, wherein we reason concerning them, there is only one perceived or remembered, and the other is supplyed in conformity to our past experience.

Thus in advancing we have insensibly discovered a new relation betwixt cause and effect, when we least expected it, and were entirely employed upon another subject. This relation is their CONSTANT CONJUNCTION. Contiguity and succession are not sufficient to make us pronounce any two objects to be cause and effect, unless we perceive, that these two relations are preserved in several instances. We may now see the advantage of quitting the direct survey of this relation, in order to discover the nature of that necessary connexion, which makes so essential a part of it. There are hopes, that by this means we may at last arrive at our proposed end; though to tell the truth, this new-discovered relation of a constant conjunction seems to advance us but very little in our way. For it implies no more than this, that like objects have always been placed in like relations of contiguity and succession; and it seems evident, at least at first sight, that by this means we can never discover any new idea, and can only multiply, but not enlarge the objects of our mind. It may be thought, that what we learn not from one object, we can never learn from a hundred, which are all of the same kind, and are perfectly resembling in every circumstance. As our senses shew us in one instance two bodies, or motions, or qualities in certain relations of success and contiguity; so our memory presents us only with a multitude of instances, wherein we always find like bodies, motions, or qualities in like relations. From the mere repetition of any past impression, even to infinity, there never will arise any new original idea, such as that of a necessary connexion; and the number of impressions has in this case no more effect than if we confined ourselves to one only. But though this reasoning seems just and obvious; yet as it would be folly to despair too soon, we shall continue the thread of our discourse; and having found, that after the discovery of the constant conjunction of any objects, we always draw an inference from one object to another, we shall now examine the nature of that inference, and of the transition from the impression to the idea. Perhaps it will appear in the end, that the necessary connexion depends on the inference, instead of the inference’s depending on the necessary connexion.

Since it appears, that the transition from an impression present to the memory or senses to the idea of an object, which we call cause or effect, is founded on past experience, and on our remembrance of their constant conjunction, the next question is, Whether experience produces the idea by means of the understanding or imagination; whether we are determined by reason to make the transition, or by a certain association and relation of perceptions. If reason determined us, it would proceed upon that principle, that instances, of which we have had no experience, must resemble those, of which we have had experience, and that the course of nature continues always uniformly the same. In order therefore to clear up this matter, let us consider all the arguments, upon which such a proposition may be supposed to be founded; and as these must be derived either from knowledge or probability, let us cast our eye on each of these degrees of evidence, and see whether they afford any just conclusion of this nature.

Our foregoing method of reasoning will easily convince us, that there can be no demonstrative arguments to prove, that those instances, of which we have, had no experience, resemble those, of which we have had experience. We can at least conceive a change in the course of nature; which sufficiently proves, that such a change is not absolutely impossible. To form a clear idea of any thing, is an undeniable argument for its possibility, and is alone a refutation of any pretended demonstration against it.

Probability, as it discovers not the relations of ideas, considered as such, but only those of objects, must in some respects be founded on the impressions of our memory and senses, and in some respects on our ideas. Were there no mixture of any impression in our probable reasonings, the conclusion would be entirely chimerical: And were there no mixture of ideas, the action of the mind, in observing the relation, would, properly speaking, be sensation, not reasoning. It is therefore necessary, that in all probable reasonings there be something present to the mind, either seen or remembered; and that from this we infer something connected with it, which is not seen nor remembered.

The only connexion or relation of objects, which can lead us beyond the immediate impressions of our memory and senses, is that of cause and effect; and that because it is the only one, on which we can found a just inference from one object to another. The idea of cause and effect is derived from experience, which informs us, that such particular objects, in all past instances, have been constantly conjoined with each other: And as an object similar to one of these is supposed to be immediately present in its impression, we thence presume on the existence of one similar to its usual attendant. According to this account of things, which is, I think, in every point unquestionable, probability is founded on the presumption of a resemblance betwixt those objects, of which we have had experience, and those, of which we have had none; and therefore it is impossible this presumption can arise from probability. The same principle cannot be both the cause and effect of another; and this is, perhaps, the only proposition concerning that relation, which is either intuitively or demonstratively certain.

Should any one think to elude this argument; and without determining whether our reasoning on this subject be derived from demonstration or probability, pretend that all conclusions from causes and effects are built on solid reasoning: I can only desire, that this reasoning may be produced, in order to be exposed to our examination. It may, perhaps, be said, that after experience of the constant conjunction of certain objects, we reason in the following manner. Such an object is always found to produce another. It is impossible it coued have this effect, if it was not endowed with a power of production. The power necessarily implies the effect; and therefore there is a just foundation for drawing a conclusion from the existence of one object to that of its usual attendant. The past production implies a power: The power implies a new production: And the new production is what we infer from the power and the past production.

It were easy for me to shew the weakness of this reasoning, were I willing to make use of those observations, I have already made, that the idea of production is the same with that of causation, and that no existence certainly and demonstratively implies a power in any other object; or were it proper to anticipate what I shall have occasion to remark afterwards concerning the idea we form of power and efficacy. But as such a method of proceeding may seem either to weaken my system, by resting one part of it on another, or to breed a confusion in my reasoning, I shall endeavour to maintain my present assertion without any such assistance.

It shall therefore be allowed for a moment, that the production of one object by another in any one instance implies a power; and that this power is connected with its effect. But it having been already proved, that the power lies not in the sensible qualities of the cause; and there being nothing but the sensible qualities present to us; I ask, why in other instances you presume that the same power still exists, merely upon the appearance of these qualities? Your appeal to past experience decides nothing in the present case; and at the utmost can only prove, that that very object, which produced any other, was at that very instant endowed with such a power; but can never prove, that the same power must continue in the same object or collection of sensible qualities; much less, that a like power is always conjoined with like sensible qualities, should it be said, that we have experience, that the same power continues united with the same object, and that like objects are endowed with like powers, I would renew my question, why from this experience we form any conclusion beyond those past instances, of which we have had experience. If you answer this question in, the same manner as the preceding, your answer gives still occasion to a new question of the same kind, even in infinitum; which clearly proves, that the foregoing reasoning had no just foundation.

Thus not only our reason fails us in the discovery of the ultimate connexion of causes and effects, but even after experience has informed us of their constant conjunction, it is impossible for us to satisfy ourselves by our reason, why we should extend that experience beyond those particular instances, which have fallen under our observation. We suppose, but are never able to prove, that there must be a resemblance betwixt those objects, of which we have had experience, and those which lie beyond the reach of our discovery.

We have already taken notice of certain relations, which make us pass from one object to another, even though there be no reason to determine us to that transition; and this we may establish for a general rule, that wherever the mind constantly and uniformly makes a transition without any reason, it is influenced by these relations. Now this is exactly the present case. Reason can never shew us the connexion of one object with another, though aided by experience, and the observation of their constant conjunction in all past instances. When the mind, therefore, passes from the idea or impression of one object to the idea or belief of another, it is not determined by reason, but by certain principles, which associate together the ideas of these objects, and unite them in the imagination. Had ideas no more union in the fancy than objects seem to have to the understanding, we could never draw any inference from causes to effects, nor repose belief in any matter of fact. The inference, therefore, depends solely on the union of ideas.

The principles of union among ideas, I have reduced to three general ones, and have asserted, that the idea or impression of any object naturally introduces the idea of any other object, that is resembling, contiguous to, or connected with it. These principles I allow to be neither the infallible nor the sole causes of an union among ideas. They are not the infallible causes. For one may fix his attention during Sometime on any one object without looking farther. They are not the sole causes. For the thought has evidently a very irregular motion in running along its objects, and may leap from the heavens to the earth, from one end of the creation to the other, without any certain method or order. But though I allow this weakness in these three relations, and this irregularity in the imagination; yet I assert that the only general principles, which associate ideas, are resemblance, contiguity and causation.

There is indeed a principle of union among ideas, which at first sight may be esteemed different from any of these, but will be found at the bottom to depend on the same origin. When every individual of any species of objects is found by experience to be constantly united with an individual of another species, the appearance of any new individual of either species naturally conveys the thought to its usual attendant. Thus because such a particular idea is commonly annexed to such a particular word, nothing is required but the hearing of that word to produce the correspondent idea; and it will scarce be possible for the mind, by its utmost efforts, to prevent that transition. In this case it is not absolutely necessary, that upon hearing such a particular sound we should reflect on any past experience, and consider what idea has been usually connected with the sound. The imagination of itself supplies the place of this reflection, and is so accustomed to pass from the word to the idea, that it interposes not a moment’s delay betwixt the hearing of the one, and the conception of the other.

But though I acknowledge this to be a true principle of association among ideas, I assert it to be the very same with that betwixt the ideas of cause and effects and to be an essential part in all our reasonings from that relation. We have no other notion of cause and effect, but that of certain objects, which have been always conjoined together, and which in all past instances have been found inseparable. We cannot penetrate into the reason of the conjunction. We only observe the thing itself, and always find that from the constant conjunction the objects acquire an union in the imagination. When the impression of one becomes present to us, we immediately form an idea of its usual attendant; and consequently we may establish this as one part of the definition of an opinion or belief, that it is an idea related to or associated with a present impression.

Thus though causation be a philosophical relation, as implying contiguity, succession, and constant conjunction, yet it is only so far as it is a natural relation, and produces an union among our ideas, that we are able to reason upon it, or draw any inference from it.”

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This is David Hume on the Problem of Induction from the Enquires Concerning Human Understanding: Section IV. Sceptical Doubts Concerning the Operations of the Understanding, Part II

“But we have not yet attained any tolerable satisfaction with regard to the question first proposed. Each solution still gives rise to a new question as difficult as the foregoing, and leads us on to farther enquiries. When it is asked, What is the nature of all our reasonings concerning matter of fact? the proper answer seems to be, that they are founded on the relation of cause and effect. When again it is asked, What is the foundation of all our reasonings and conclusions concerning that relation? it may be replied in one word, Experience. But if we still carry on our sifting humour, and ask, What is the foundation of all conclusions from experience? this implies a new question, which may be of more difficult solution and explication. Philosophers, that give themselves airs of superior wisdom and sufficiency, have a hard task when they encounter persons of inquisitive dispositions, who push them from every corner to which they retreat, and who are sure at last to bring them to some dangerous dilemma. The best expedient to prevent this confusion, is to be modest in our pretensions; and even to discover the difficulty ourselves before it is objected to us. By this means, we may make a kind of merit of our very ignorance.

I shall content myself, in this section, with an easy task, and shall pretend only to give a negative answer to the question here proposed. I say then, that, even after we have experience of the operations of cause and effect, our conclusions from that experience are not founded on reasoning, or any process of the understanding. This answer we must endeavour both to explain and to defend.

It must certainly be allowed, that nature has kept us at a great distance from all her secrets, and has afforded us only the knowledge of a few superficial qualities of objects; while she conceals from us those powers and principles on which the influence of those objects entirely depends. Our senses inform us of the colour, weight, and consistence of bread; but neither sense nor reason can ever inform us of those qualities which fit it for the nourishment and support of a human body. Sight or feeling conveys an idea of the actual motion of bodies; but as to that wonderful force or power, which would carry on a moving body for ever in a continued change of place, and which bodies never lose but by communicating it to others; of this we cannot form the most distant conception. But notwithstanding this ignorance of natural powers and principles, we always presume, when we see like sensible qualities, that they have like secret powers, and expect that effects, similar to those which we have experienced, will follow from them. If a body of like colour and consistence with that bread, which we have formerly eat, be presented to us, we make no scruple of repeating the experiment, and foresee, with certainty, like nourishment and support. Now this is a process of the mind or thought, of which I would willingly know the foundation. It is allowed on all hands that there is no known connexion between the sensible qualities and the secret powers; and consequently, that the mind is not led to form such a conclusion concerning their constant and regular conjunction, by anything which it knows of their nature. As to past Experience, it can be allowed to give direct and certain information of those precise objects only, and that precise period of time, which fell under its cognizance: but why this experience should be extended to future times, and to other objects, which for aught we know, may be only in appearance similar; this is the main question on which I would insist. The bread, which I formerly eat, nourished me; that is, a body of such sensible qualities was, at that time, endued with such secret powers: but does it follow, that other bread must also nourish me at another time, and that like sensible qualities must always be attended with like secret powers? The consequence seems nowise necessary. At least, it must be acknowledged that there is here a consequence drawn by the mind; that there is a certain step taken; a process of thought, and an inference, which wants to be explained. These two propositions are far from being the same, I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects. I shall allow, if you please, that the one proposition may justly be inferred from the other: I know, in fact, that it always is inferred. But if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. The connexion between these propositions is not intuitive. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact.

This negative argument must certainly, in process of time, become altogether convincing, if many penetrating and able philosophers shall turn their enquiries this way and no one be ever able to discover any connecting proposition or intermediate step, which supports the understanding in this conclusion. But as the question is yet new, every reader may not trust so far to his own penetration, as to conclude, because an argument escapes his enquiry, that therefore it does not really exist. For this reason it may be requisite to venture upon a more difficult task; and enumerating all the branches of human knowledge, endeavour to show that none of them can afford such an argument.

All reasonings may be divided into two kinds, namely, demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence. That there are no demonstrative arguments in the case seems evident; since it implies no contradiction that the course of nature may change, and that an object, seemingly like those which we have experienced, may be attended with different or contrary effects. May I not clearly and distinctly conceive that a body, falling from the clouds, and which, in all other respects, resembles snow, has yet the taste of salt or feeling of fire? Is there any more intelligible proposition than to affirm, that all the trees will flourish in December and January, and decay in May and June? Now whatever is intelligible, and can be distinctly conceived, implies no contradiction, and can never be proved false by any demonstrative argument or abstract reasoning priori.

If we be, therefore, engaged by arguments to put trust in past experience, and make it the standard of our future judgement, these arguments must be probable only, or such as regard matter of fact and real existence, according to the division above mentioned. But that there is no argument of this kind, must appear, if our explication of that species of reasoning be admitted as solid and satisfactory. We have said that all arguments concerning existence are founded on the relation of cause and effect; that our knowledge of that relation is derived entirely from experience; and that all our experimental conclusions proceed upon the supposition that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question.

In reality, all arguments from experience are founded on the similarity which we discover among natural objects, and by which we are induced to expect effects similar to those which we have found to follow from such objects. And though none but a fool or madman will ever pretend to dispute the authority of experience, or to reject that great guide of human life, it may surely be allowed a philosopher to have so much curiosity at least as to examine the principle of human nature, which gives this mighty authority to experience, and makes us draw advantage from that similarity which nature has placed among different objects. From causes which appear similar we expect similar effects. This is the sum of all our experimental conclusions. Now it seems evident that, if this conclusion were formed by reason, it would be as perfect at first, and upon one instance, as after ever so long a course of experience. But the case is far otherwise. Nothing so like as eggs; yet no one, on account of this appearing similarity, expects the same taste and relish in all of them. It is only after a long course of uniform experiments in any kind, that we attain a firm reliance and security with regard to a particular event. Now where is that process of reasoning which, from one instance, draws a conclusion, so different from that which it infers from a hundred instances that are nowise different from that single one? This question I propose as much for the sake of information, as with an intention of raising difficulties. I cannot find, I cannot imagine any such reasoning. But I keep my mind still open to instruction, if any one will vouchsafe to bestow it on me.

Should it be said that, from a number of uniform experiments, we infer a connexion between the sensible qualities and the secret powers; this, I must confess, seems the same difficulty, couched in different terms. The question still recurs, on what process of argument this inference is founded? Where is the medium, the interposing ideas, which join propositions so very wide of each other? It is confessed that the colour, consistence, and other sensible qualities of bread appear not, of themselves, to have any connexion with the secret powers of nourishment and support. For otherwise we could infer these secret powers from the first appearance of these sensible qualities, without the aid of experience; contrary to the sentiment of all philosophers, and contrary to plain matter of fact. Here, then, is our natural state of ignorance with regard to the powers and influence of all objects. How is this remedied by experience? It only shows us a number of uniform effects, resulting from certain objects, and teaches us that those particular objects, at that particular time, were endowed with such powers and forces. When a new object, endowed with similar sensible qualities, is produced, we expect similar powers and forces, and look for a like effect. From a body of like colour and consistence with bread we expect like nourishment and support. But this surely is a step or progress of the mind, which wants to be explained. When a man says, I have found, in all past instances, such sensible qualities conjoined with such secret powers: And when he says, Similar sensible qualities will always be conjoined with similar secret powers, he is not guilty of a tautology, nor are these propositions in any respect the same. You say that the one proposition is an inference from the other. But you must confess that the inference is not intuitive; neither is it demonstrative: Of what nature is it, then? To say it is experimental, is begging the question. For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities. If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance. Let the course of things be allowed hitherto ever so regular; that alone, without some new argument or inference, proves not that, for the future, it will continue so. In vain do you pretend to have learned the nature of bodies from your past experience. Their secret nature, and consequently all their effects and influence, may change, without any change in their sensible qualities. This happens sometimes, and with regard to some objects: Why may it not happen always, and with regard to all objects? What logic, what process of argument secures you against this supposition? My practice, you say, refutes my doubts. But you mistake the purport of my question. As an agent, I am quite satisfied in the point; but as a philosopher, who has some share of curiosity, I will not say scepticism, I want to learn the foundation of this inference. No reading, no enquiry has yet been able to remove my difficulty, or give me satisfaction in a matter of such importance. Can I do better than propose the difficulty to the public, even though, perhaps, I have small hopes of obtaining a solution? We shall at least, by this means, be sensible of our ignorance, if we do not augment our knowledge.

I must confess that a man is guilty of unpardonable arrogance who concludes, because an argument has escaped his own investigation, that therefore it does not really exist. I must also confess that, though all the learned, for several ages, should have employed themselves in fruitless search upon any subject, it may still, perhaps, be rash to conclude positively that the subject must, therefore, pass all human comprehension. Even though we examine all the sources of our knowledge, and conclude them unfit for such a subject, there may still remain a suspicion, that the enumeration is not complete, or the examination not accurate. But with regard to the present subject, there are some considerations which seem to remove all this accusation of arrogance or suspicion of mistake.

It is certain that the most ignorant and stupid peasants—nay infants, nay even brute beasts—improve by experience, and learn the qualities of natural objects, by observing the effects which result from them. When a child has felt the sensation of pain from touching the flame of a candle, he will be careful not to put his hand near any candle; but will expect a similar effect from a cause which is similar in its sensible qualities and appearance. If you assert, therefore, that the understanding of the child is led into this conclusion by any process of argument or ratiocination, I may justly require you to produce that argument; nor have you any pretence to refuse so equitable a demand. You cannot say that the argument is abstruse, and may possibly escape your enquiry; since you confess that it is obvious to the capacity of a mere infant. If you hesitate, therefore, a moment, or if, after reflection, you produce any intricate or profound argument, you, in a manner, give up the question, and confess that it is not reasoning which engages us to suppose the past resembling the future, and to expect similar effects from causes which are, to appearance, similar. This is the proposition which I intended to enforce in the present section. If I be right, I pretend not to have made any mighty discovery. And if I be wrong, I must acknowledge myself to be indeed a very backward scholar; since I cannot now discover an argument which, it seems, was perfectly familiar to me long before I was out of my cradle.”

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Positivism

Posted by allzermalmer on January 18, 2012

This blog will be based on a paper done by W.T. Stace. It was published in the philosophical journal Mind, New Series, Vol. 53, No. 211 (Jul., 1944), pp. 215-237. It was called Positivism.

During the time of writing this paper, there was a big movement in parts of Europe and eventually came to America, and it was Logical Positivism or Logical Empiricism. This group was known for the principle for which they became infamous and later collapsed. Stace says what he takes the principle to be, and calls it the Positivism Principle.

“A set of words purporting to express a factual proposition P is significant only if it is impossible to deduce or infer from it, in combination if necessary with other premises, some proposition or propositions (at least one) Q^1, Q^2, Q^3…etc., the truth or falsity of which it would be logically possible to verify by direct observation. If no such directly verifiable deductions from P are possible, then the set of words purporting to express P is non-significant, and P is not really a proposition at all, but a pseudo-proposition.”

Now there are some terms in that principle that would need to be clarified. These terms are “significant” and “meaning”. We, in our common speaking, talk of meaning of a sentence and meaning of a word. This will also deal with the difference between significant and meaning. The meaning of a sentence is called significance, because only a sentence can be true or false. The meaning of a word is called meaning, but words can’t be either true or false. This is because meaning of sentences is where the predicate of true or false apply, but those predicates don’t apply to single words like “red”. Sentences have significance, and words have meaning. This forms a big distinction from which the rest of the paper follows.

The difference between significance and meaning are based on a distinction within the genus of semantical meanings. So Stace shall be dealing with the semantical significance of sentences and the semantical meaning of words. And Stace will deal with “deduce or infer” as being a deduction or being a causal inference. So when we make the statement of “P”, it can hold the form of “P→Q”. This will help spell out some of the deduction and causal inference that is going on.

But Stace also quotes the Logical Positivist A.J. Ayer, as he states what is meant by the Positivist Principle.

“Let us call a proposition which records an actual or possible observation and experiential proposition. Then we may say that it is the mark of a genuine factual proposition…that some experiential proposition can be deduced from it in conjunction with certain other premises without being deducible from those other premises alone.”

There seems to be no clear distinction between A.J. Ayer and what W.T. Stace has said as well. And so what Stace would say would also seem to hold for the Positivism Principle.

The Positivism Principle seems to be of the same of the Verification principle, but there is some slight difference from when the original Verification principle was proposed. Schlick was one of the first to propose the Verification principle. Verification was meant to be direct and complete verification, which was the significance of a statement was the method of its verification. It had to be direct and complete verification. But such a principle makes universal statements to be insignificant. For to directly and completely verify a universal statement, you wold have to observe an infinite number of facts, which would have been of the past, present, and future, and all locations. And even singular statements about material objects would be insignificant sine the complete verification would also involve an infinite number of observations. Also, talk of the past wouldn’t be allowed for to be significant.

In order to escape some of these downfalls of what Schlick presented as the Verification principle, it was mean to soften it some, but keep some of the same points. Now, instead of complete and direct verification, the new principle allowed for indirect and partial verification. So we can verify the past occurrence of something by checking the present effect. And this is part of Carnap seems to mean with “testing” the proposition. Stace points out how we come to indirectly and partially verify something.

“What is now required in order to make a statement about the past significant is, not that the facts asserted in the statement should be themselves now observable, but that some of their effects should be observable (indirect verification). And what is required to make a universal proposition significant is not that all the facts which it asserts (an infinite number) should be observable, but that some of them should be observable (partial verification). These are the requirements which are embodied in the positivist principle as formulated in the first paragraph of this article.”

Now with the Positivist principle, and what was originally in the Verification principle which was later modified, seemed to be another principle. In other words, the Positivist Principle seems to be based on another principle. And now see what this other principle is would seem to help cast light on the Positivist Principle. This principle would be called The Principle of Observable Kinds:

“A sentence, in order to be significant, must assert or deny facts which are of a kind or class such that it is logically possible directly to observe some facts which are instances of that class or kind. And to observe some facts which are instances of that class or kind. And if a sentence purports to assert or deny facts which are a class or kind such that it would be logically impossible directly to observe any instance of that class or kinds, then the sentence is non-significant.”

Now let us use an example to see what this principle is trying to get across. Take “Napoleon crossed the Alps”. It is logically impossible for us to now directly observe this particular fact asserted in the sentence. This fact no longer exists, and so we can’t directly observe it. But this particular fact of Napoleon crossing the Alps is also part of the class of “men crossing mountains”, which we can experience. So the point becomes that we might not be able to logically observe all particular members of the class, but it is logically possible for us to observe some of the particular members of that class. Thus, the fact itself might not be observable but it is of the observable kind. This means that if the kind of thing said is unobservable, then we definitely can’t observe the particulars.

So the point becomes, “A sentence is significant if what it asserts or denies is the sort of thing which it is logically possible to observe, even if the particular instance in the sentence is such that it would not be logically possible to observe it.”

Now Stace will maintain that the Positivist Principle implies the Principle of Observable Kinds. But the Positivist Principle might not directly say it. But the Principle of Observable Kinds doesn’t seem to be what the Positivist Principle is saying, or what the Logical Positivist themselves maintain. There seem to be two differences between the two principles: 1. The principle of observable kinds introduces the notion of classes, while, on the other hand, the positivist principle says nothing about classes. 2. The Positivist principle makes use of the concept of indirect verification while the principle of observable kinds contains only concepts of direct verification or observation.

Now the Principle of Observable Kind is based on direct verification, and would seem to go back to that of the Verification principle that was given by Shclick. But this wouldn’t be correct to think that it goes back to the Verification principle. But the Principle of Observable Kinds does make a distinction from that of the Verifiability principle, which is based on that of classes.

“Suppose the proposition to be examined for its significance is P. Then according to the original principle of verifiability the facts asserted or denied in P must themselves be capable of being observed. What the new positivist principle says is that the facts asserted or denied in Q (the proposition or propositions deduced from P), must themselves be capable of being observed. It does not say anything at all about the observability or non-observability of the facts asserted or denied in P. It entirely ignores that question.

Now as was pointed out earlier, P can be replaced with P→Q. So P of the P→Q might not be directly verifiable by experience, or direct experience. But the consequence of it, which is Q, would be of the observable kinds. But now there is a divide between both principles, the original formulation and the later formulation that deals with indirect verification. And this divide is filled with the Principle of Observable Kinds. This is because the original formulation doesn’t state whether the facts stated in P must be observable. Nothing is said on this.

So what is the Positivist to say with this divide? “He ought to say, not that the particular facts asserted in P must be observable (this is what he wished quite rightly to avoid), nor yet that they may be of a wholly unobservable kind; but rather that the particular facts asserted in P, although they cannot be themselves be observed, must yet be of a kind of facts which other instances can be observed. And this is what the principle of observable kinds does say.” Thus, the Principle of Observable Kinds is implied by the new Positivist Principle.

The Principle of Observable Kinds seems to carry some of the same meaning of the Positivist Principle, but would seem to give more gain than that of the Positivist Principle. One of the reasons is that the Positivist Principle is based on the way of the propositions logical consequences, while the Principle of Observable kinds don’t seem to be worried too much about that.

Now A.J. Ayer makes a point in his book The Foundation of Empirical Knowledge, that we can have two different philosophers disagree over a certain point. So take that Philosopher A said that “We do not perceive the table or the chair, we only perceive sense-data which we believe to belong to a  table and a chair.” But Philosopher B says, “No, what we perceive is the actual table and the actual chair”. What Ayer says is that both philosophers disagree with the language, but they agree with the observations. They agree about the color, shape, weight, and about every fat which could possibly be observed. They agree about all possible observable facts, and there is no disagreement between these two philosophers on the facts. Thus, they both disagree over the language and not the facts.

But what do we say, in this position, when they disagree over unobservable facts? This seems to be something that Ayer might have overlooked, and is overlooked by the Positivist Principle.

“For instance, Philosopher A may hold the view that there is a “physical object”, X, which possesses intrinsic qualities which correspond to the perceived qualities of shape, size, color, smell, etc, but which are forever hidden fro us, so that we can never know anything about these intrinsic qualities except the fact of their correspondence to perceived qualities; and that this physical object X stands in a causal relation to our sense-data…Philosopher B may deny that any such object as X exists. He may say that the table or the chair simply is the collection of all the sense-data which (according to A) are caused by it. Thus both of them may admit the existence of the sense-data, and may entirely agree about all their characteristics, which means that they will agree about all the observable facts. But they will assert that they are in disagreement whether x exists or not. X, if it is a fat, is a fact forever unobservable These philosophers will therefore say that they are in disagreement about whether or not there exists an alleged unobservable fact. Mr. Ayer appears to have overlooked this in his argument.”

This seems to be one reason why the Positivist Principle would have many things listed as insignificant. It is more of a difference over language than it is over some actual fact. And thus, for the Positivist, it is only about a way of speaking than some actual facts. For they both contain the same observable kinds.

But now maybe the Positivist principle doesn’t rely on the principle of observable kinds. What might be the case if this isn’t so? Than although the facts stated in Q of P→Q are logically capable of being directly verified, then P itself might states facts which would be logically impossible to observe. And the Positivist principle seems to tell us that this might be the case. For Q tells us that it is observable, but it doesn’t say anything about the observability of P. And there seem to be two cases: (1.) Where P→Q is a deductive argument, and (2.) where P→Q is a cause and effect inference.

Case 1: If P→Q is a deductive argument, then either (A.) Q states some facts as P, either in whole or in part or (B.) Q states some facts or elements of fact which are not asserted in P. (A.) is the view that logical rules are rules of linguistic transformations. (B.) is the view that in the conclusion of a deductive argument there may be some element of fact that may be “new”, i.e. not “contained” in the premises.

If we accept (A.), then it is clear that if Q is of the observable kind then P will be of the observable kind as well. This is because Q states the same thing as P, but in different words. Thus, if Q is observable, then P would also be observable since P is just another way of saying Q. This means P is another way of saying observable kind, which is what Q did as well. Thus, the Positivist principle implies the Principle of Observable Kind.

If we accept (B.) then it doesn’t seem that we can rigorously prove that if Q states observables P must state observables. For p might conceivably be of a different kind from the facts stated in Q. But, what seems to be enough, is that the Logical Positivist themselves held to the linguistic transformations.

Case 2: If P→Q is a cause and effect inference, then it’s certain that facts stated in P cannot be unobservable if the facts stated in Q are observables. This is because inference must rest on a causal law. “The cause C will be the fact stated in P, while the effect E will be the fact stated in Q. For instance, P any state the fact that it rained five minutes ago, while Q states in effect of this rain, namely, that the ground will be wet now. But it is impossible that the causal connection between C and E can have been established except on the basis that E has been observed to follow C. Therefore C, the fact stated in P, must be an observable.”

Thus, from these considerations, it appears obvious that the Positivist Principle does rely on the Principle of Observable Kinds. And the Positivist Principle, if adopted because that is the definition for significance that they choose, it carries no real force. This is because they just freely choose this criterion while someone else can pick whatever else criterion they wish to use for significance. But if they wish for it to carry some meaning about it based on experience, it would have to be shown through some sort of experience. This would be be based on inductive generalizations.

Now we might wonder how did we arrive at this Positivist Principle. Stace has an answer on how he thinks that the Positivist derived their principle.

“I think it is almost certain that positivists believe that their principles are a development of the general principle of empiricism. They call themselves “empiricists”. And thus by implications they claim that, whatever evidence there is to support the general principle of empiricism is also evidence which supports them. They think that,although their position is in some way different from that of the other empiricists (such as Hume)- more “advanced” no doubt- yet it grows out of the same root as does the tree of empiricism., and that therefore the sap which nourishes that tree will also nourish them. This is a very interesting and also a very important claim. And I propose to examine it. the question is: Is positivism a legitimate development of empiricism, and are the grounds which support empiricism also grounds which support positivism?”

Now the Logical Positivist claim that they’re “empiricists”, but we might wonder what type of empiricist they are. They’re seems, in history, to be different types of empiricist, but they haven’t, as Stace says, made it clear what type of empiricists they are. But there does seem to be two different types of Empiricism. (1.) the doctrine that all knowledge is “based upon ” or “derived from” experience, and (2.) the doctrine that all “ideas” are “based upon” or “derived from” experience.

With the first kind, the meaning of the phrase “based upon” or “derived from” seem to be different in (1.) and (2.). With (1.) is that if any proposition is known to be true, it can only be so known because there is empirical evidence for it, or must be empirical grounds for it. John Stuart Mill brought this up and tried to use it to support that 2+2=4 is an empirical generalization and illustrates this kind of empiricism. The (2.) kind is based upon ideas, like that of a “centaur”. The idea is neither true or false. What happens is that we can break down our ides into some basic parts, or that our experiences are built up off of some basic parts like “blue”, “horse”, “human head”, and etc. This is like Hume saying that “complex ideas” are based on “simple ideas”.

It appears that the Principle of Observable Kinds isn’t based on the first type of empiricism. As Stace says, “For the principle of observable kinds professes to be a criterion, not of the truth of propositions, nor of ways of knowing them to be true, but of whether they have significance. But the first kind of empiricism has nothing to do with significance at all, and cannot so far as I can see have any bearing on that subject.”

For whatever the relaations between “being known to be true” and “being significant” may be, they are certainly not the same thing, since a proposition may be significant and yet not known to be true. A significant proposition may in fact be known to be false. The long and short of it is that the first kind of empiricism is a theory about the truth of propositions (more correctly about how their truth can be known) while the principle of observable kinds is a theory about the significance of propositions. And since the two theories are “about” different subjects, one cannot possibly follow from, or be legitimately developed out of, the other.”

Of the first kind of empiricism, which is about the truth of propositions, the Logical Positivist would have seemed to hold this position as well. And the position that they state is that a priori statements are analytic statements, which means they’re not “derived from” experience. This stance follows from the first kind of empiricism, but we’ve also noticed that the significance of a proposition isn’t based on the first kind of empiricism. And all a priori propositions being analytic would follow from the first principle.

Now take the second kind of empiricism. We might wonder if the Principle of Observable Kinds comes from the second kind of empiricism. David Hume, after all, does bring up something that would be similar to that of the second kind of empiricism, “from what impression is that supposed idea derived.” But the Principle of Observable Kinds doesn’t follow from the second kind of empiricism.

The second kind of empiricism dealt with “ideas” being derived from experience. But as was pointed out earlier, the Principle of Observable Kinds is based on sentence significance, and not word significance. The second kind of empiricism is worried about the ideas, like that of “red”. But it is only the sentences that make significance and not the words itself. The second kind of empiricism is strictly concerned from what those experiences come from, like “red”, “sweater”, “blue-jeans”, “tennis shoes”, and etc, but isn’t concerned with whole sentences. The Principle of Observable Kinds is concerned with only whole sentences, like “James wore a red sweater while also having some blue-jeans to match their tennis shoes.” That sentence carries significance.

So it doesn’t look like the Principle of Observable Kinds follows from empiricism as well, in either kind. Thus, since the Positivist Principle seems to be implied by the Principle of Observable Kinds, the Positivist Principle seems to carry no weight when it comes to empiricism. Thus, those who call themselves empiricists and support the Positivist Principle don’t seem to have such a right.

The reason is that the principle of empiricism was stated by David Hume. The idea can be listed as the mind cannot spontaneously generate “simple ideas”, nor create them out of nothing, but has to derive them from “impressions”. These simple ideas would be those things that you can’t break down any further from your experience. For example, you have “red, “hot”, “cold”, “round”, “soft”, “sweet”, “loud”. From these unanalyzable, simple, building blocks, we can create different things from them by combining them in different ways. Giving some basic material, you can combine it in many different ways. But the basic idea is that you can’t create these simple ideas out of nothing, which means that you needed some impression of them.

The principle of empiricism implies nothing on how we form these simple ideas are to be combined into complex ideas. It provides no rules for combination. This means that we are free to combine the simple ideas in any way we would like, at least we have no rules on how to combine them, or at least according to the principle of empiricism. But there could be some laws, like the law of non-contradiction, or incompatible characters cannot be combined in the mode of spatio-temporal coincidence, though they can in the mode of spatial juxtaposition. This second idea is the Principle of Incompatibles. It basically states that the surface of a ball may be red and blue simultaneously if juxtaposed over one another. Also, we might have the laws of syntax to deal with how to combine our ideas. But the point is that none of these ideas follow from the principle of empiricism.

“The principle of empiricism concerns only the origination of simple ideas, nothing else. It tells us: no impressions,then no simple ideas. We may add as part of the principle, if we wish, the fact that certain of our ideas are not simple but are compounded out of simple ideas.”

But sentences are based on some ideas being placed in relation to one another in a certain way, or whatever way since the principle of empiricism does not care. Sentences, it seems, deals with complex ideas. So take a word to be symbolized like “F”. This word is composed of different simple ideas, like a certain color, shape, smell, taste, or sound, to go along with it. So all these different, simple ideas, can be symbolized as m,n,o,p,q. Thus, F=m,n,o,p,q. And sentences are composed of complex ideas which talk about the relations between something like A being B or A being related to B.

Thus, when empiricism isn’t concerned on how we form complex sentences, which is how we form our simple ideas together, it doesn’t imply the Principle of Observable Kinds because that principle relies on sentences or how complex ideas are to be put together. And this would also mean that the Positivist Principle isn’t implied by the principle of empiricism.

“What [the principle of empiricism] tells us is that if a sentence asserts or denies a fact F, which is a complex of a,b,c,d…, then each of these simples, a,b,c,d,…, must be an observable. But what the principle of observable kinds does is to assert that the total complex fact F, or abcd, must as a whole, be an observable. But for this there is not the slightest warrant in the principle of empiricism.”

The main point is that the Positivist have no right to claim to their principle of significance follows from empiricism. And that they’re constriction on propositions is arbitrary on it’s own, and has no standing in the principle of empiricism.

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Are All Empirical Statements Merely Hypotheses?

Posted by allzermalmer on December 19, 2011

This blog will be based on an article done by W.T. Stace. It is called, Are All Empirical Statements Merely Hypotheses? It appeared in the philosophical journal known as The Journal of Philosophy Vol. 44, No. 2 (Jan. 16, 1947), pp. 29-38.

It is sometimes stated that all empirical statements are only probable. This was stated by those like, and especially by, Rudolph Carnap. One philosopher who disagreed, and said that some empirical statements are certain, was G.E. Moore. Stace shall agree with Moore, but with some qualifications. The statement that will be the exemplar of what is being talked about will be the statement of “This key is made of iron”. Now this statement is a singular statement like x is Y.

“To say that this proposition can never be more than probable means, I assume, that there must always be some doubt as to its truth. The question we have to get clear about is: what is the doubt, or what are the doubts, which those philosophers who say that such a statement can never be more than probable, have in mind?”

Some of the doubts could be as follows for what makes this empirical statement probable: the laws of nature are statistical, we could be deceived by some sort of demons or might be dreaming, or statements that we make rely on memory and our memory could be wrong. None of these things seems to be what has lead some to think that all empirical statements are probable. That is because these doubts are arising from practical doubt because of the frailty of human faculties.

The philosophers, like Carnap, seem to be relying on theoretical/logical doubt. This seems to be based on the logic at which we arrive at empirical truths, regardless of the frailties of particular human beings. They seem to be saying that we arrive at these empirical statements, like “this key is made of iron”, are arrived at by means of induction. And, through the means of induction, we never arrive at certainty by by means of probability.

Stace quotes Carnap on the basic idea of which is to lead to all empirical statements are merely probable. Take the statement that “This key is made of iron”. This proposition will be known as P1. We can test P1 by seeing if it is attracted by a magnet, if it is then we have partial verification of P1. So here is what Rudolph Carnap says, which leads him to state that all empirical statements are merely probable in his book Philosophy and Logical Syntax:

“After that, or instead of that, we may make an examination by electrical tests, or by mechanical, chemical, or optical tests, etc. If in these further investigations all instances turn out to be positive, the certainty of the proposition P1 gradually grows…but absolute certainty we can never attain. the number of instances deducible from P1 is infinite. Therefore there is always the possibility of finding in the future a negative instance.”

Now this is the logical problem that we face. Anytime we perform a new test, and the test is passed, it only adds a degree of probability to the statement that “this key is made of iron”. And the problem, further, is that we can’t completely verify the statement, or be certain of it, because we would have to complete an infinite number of observations. But this is not only practically impossible, it is also logically impossible.

But there is some ambiguity of what Carnap means, because there are two ways that this can be taken. The first thing could be about the different kinds of tests. For we noticed that he brought up the tests that could be done, like magnetic, electrical, chemical, and etc. So the it could be meant that the number of different kinds of test is infinite, which means we would have to make an infinite number of kinds of tests in order to achieve complete verification of the statements truth. But Stace has an objection to this position.

“If an infinite number of kinds of tests of the key were possible, this would imply that the key must have an infinite number of different characteristics or properties to be tested for. But even if an object can have an infinite number of characteristics, it would not be necessary to test for them all in order to identify the object as iron. All we need is to verify the defining characteristics of iron, which are certainly finite in number. and there is, of course, no logical difficulty about doing that.”

Now there is a second possible meaning for which Carnap has in mind. We could do a single test of a defining characteristic like “being attracted by a magnet”, or what other defining characteristics there might be. These tests only make the statement probable because we may find that the key is attracted one time and perform many of the same tests a thousand times in succession and find the same results as the first test. But we can never be sure that an instance will not turn up in the future in which the object will not be attracted by a magnet (problem of induction). “If the same thing happens in the same circumstances in a vast number of times, each time it happens makes it a little more probable that it will happen again, but it can never be quite certain.”

It is true that scientists perform the same experiments, this is the repeatably of the scientific tests. What one scientist is able to do in a test, it has to be reproducible by other scientists around the world. The same experiment can be repeated by the same experimenter over and over, or can be done by other experimenters around the world. But why are experiments repeated? Is it because each fresh instance of a positive result of the same test adds to the probability of the conclusion? It seems not.

Let us assume that we have an object that is to be tested. We want to test whether it is composed of a certain substance, which we can call X. Now let us suppose that there is only one defining characteristic of X which we call A. The scientist is testing for Y. If Y is found it is a sign that the substance is X. Now, is it true that A may be repeated many times. But why?

“It is not because he supposes that a barren repetition of instances of A makes it more probable that the substance is X. It is always, on the contrary, because he has doubts whether he has satisfactorily established by his observations of the presence of A. It is not the validity of the inductive inference from A to X that he is doubting, but whether A is really present…the doubt which the experimenter is trying to exclude is not any logical doubt about induction, but practical doubts arising from difficulties of observation, possible deficiencies in apparatus, difficulty in ensuring that the experiment is made in the exact conditions required, and so on. He is not doubting that the inductive premises will lead to an absolutely certain conclusion. He is doubting whether he has satisfactorily established the inductive premises.”

What is going on is that the scientist procedure is that a single observation is sufficient to establish an inductive conclusion with certainty. But this is only the case provided that the premises have been established. So it is not the inductive conclusion that is being questioned, but it is the premises that are being questioned. As Stace says, “What is implied by the scientist’s procedure is that a single observation or experiment is sufficient to establish an inductive conclusion with certainty, provided the premises have been established. I hold that the scientist is right.”

Stace locates the problem at three points. And this is the problem of how some philosophers have reached the conclusion that all empirical statements are merely probable.

(1.) One of the problems was how philosophers thought that scientists were repeating experiments to try to dispel logical doubts about the validity of induction. What the scientists were doing, in fact, was trying to dispel practical errors in observing or establishing the premises on which an induction rests. The question of probability doesn’t fall within the inductive argument, but outside of the inductive argument.

“That is to say, what is only probable is not that, if A is once associated with B, it will always be associated with B, but that A has actually been found associated with B; not that if a substance has a certain specific gravity it is gold, but that the substance now before me actually has that specific gravity…a natural mistake located the question of probability within the inductive argument instead of outside of it; have extrapolated it from the practical sphere of observation, measurement, and so on, where it actually belongs, to the logical sphere of the inductive inference in which in reality it has no place.”

So the problem is not in the inductive argument itself, but outside of the argument. What is outside of the argument is making sure that you have made an observation that meets with the premises of the argument. This is what constant testing is about, to make sure that the observations are in line with the premises. It is not the argument being questioned, but something outside of the argument that is being questioned.

(2.) Another reason that it seems that it is brought up that empirical statements are probable deals with the view of induction where an application of the inductive principle to a type of cases different from that of the Iron key. This other application is based on generalizing from observations. For example, we generalize from observations of a number from a certain class to the whole class. This means, from observing some white swans, we go on to generalize to the class of swans. From seeing a certain number of swans being white, and not observing any black swans, we go on to say that All swans are white. This will be dealt with a little later on.

(3.) This view seems to follow, as some philosophers think, from what David Hume had to say on the problem of Induction. Hume showed that we can’t “prove” a conclusion in an inductive argument. Because of this, some seem to have imagine that because we can’t prove it, we can at least make it probable. But it doesn’t seem that this follows from what Hume said on the problem of Induction. But Stace does think that something follows from what Hume said on this problem.

Imagine that we have a single instance of A being associated with B, and we’ve ruled out all practical doubts from possible errors of observation or experiment. We now have, logically, two positions that we can take up.

The first is that we can assume the validity of the principle of Induction. So, in this single instance, we can conclude that A is always associated with B, and our conclusion follows with absolute certainer from our two premises of single observed association of A with B and the principle of induction. With these two premises, the conclusion is certain to start with, and so there is no increasing probability or probability at all.

The second is that you may not assume that validity of the inductive principle. Now this means that we follow Hume, which means that there’s no logical connection between the premises and the conclusion of induction. This means, nothing follows from induction, neither certainty nor probability. No matter how many single instances that support our inductive conclusion, the probability never arises above zero. (Karl Popper would agree with this point). There is no connection to say that because the conclusion obtained, that we can say that the probability of the premises rises some more. They are disconnected. It is like having three dots on a sheet of paper. They are disconnected from each other. So when we affirm one, we can’t affirm any of the others because they’re not connected with one another.

“I have affirmed that, given the inductive principle, a single case will prove the inductive conclusion with certainty, I ought to give a formulation to the inductive principle which embodies this…”If in even a single instance, we have observed that a thing of the sort A is associated with a thing of the sort B, then on any other appearance of A, provided the other factors present along with A are the same on both occasions, it is certain that A will be associated with B.””

There is the clause of “provided the other factors present along with A are the same on both occasions.” This forms part of the principle, which comes down to “Same cause, same effect”. There is an example to help make this point clear. If the bell is struck in air then it produces sound. But it doesn’t follow that a bell struck in a vacuum will produce sound. This is because of the clause that was inserted into the principle. The factors aren’t the same, and so they’re not the same type of thing. But it does introduce a new inductive discovery.

There is one obvious objection that one could make to this principle. It could be said that this new interpretation is merely an assumption that is incapable of proof. So if this is a matter of being arbitrary choice of how to formulate it in terms of certainty and probability, then we ought not to assume more than is necessary to justify our sciences and our practice. So someone could say, “it will be quite sufficient for these purposes to assume that, if A is associated with B now, it will probably be associated with B at other times and places. On this ground the probability formulation should be preferred.”

But putting the term certainty in there is not meant to be arbitrary, but it is mean to represent a formulation of the assumption which has been the basis of science and practice. But maybe Stace should be more clear, which is what he tries to do like as follows:

“If you have one case of a set of circumstances A associated with B, and you are quite sure you have correctly established this one association, then, assuming the uniformity of nature, or the reign of law, or the principle of induction-call it what you will- a repetition of identically the same set of circumstances A is bound to be associated with B. For if not, you would have a capricious world, a world in which A sometimes produces B, and sometimes it does not, a world in which the kettle put on the fire may boil today, but freeze tomorrow. And this would clearly be a violation of the principle of induction which you have assumed.”

Now, if you assume the principle of induction, then a single case validates an induction. But now Stace will try to prove his second contention that if you don’t assume the principle of induction, your inductive conclusion aren’t probable at all and there’s no repetition of instances, so no matter how great the number, then the probability is never raised above zero.

To establish this position, Stace will assume that Hume is right. This means, between the premises and the conclusion of an inductive argument there is absolutely no logical connection at all. This means that there is nothing to establish the slightest probability because they’re is no connection between them. So if we affirm one part, it has no connection to another to raise the probability of this part that is connected to what we affirmed. They are so completely disconnected that there’s no logical connection to even bring up probability.

For example, here is what Al-Ghazali said about causality, which is the same position that David Hume took up, and this is based in some ways on the principle of induction. “The affirmation of one does not imply the affirmation of the other; nor does its denial imply the denial of the other. The existence of one is not necessitated by the existence of the other; nor its non-existence by the non-existence of the other.” So when we affirm one thing with induction, like a correct experiment, this in no way can increase any probability when the affirmation of one doesn’t imply the affirmation of the other. How can you raise the probability when what you affirm has no connection to anything else to raise the probability of this other thing? You can’t.

Stace goes on to try to examine the types of cases in which generalize a whole class from a number of instances that are smaller than the whole class. Try to generalize about a whole class of swans from observing a few of the swans that are suppose to make up the whole class. If we observe one swan and it is white,nto conclude that all swans are white, we might be accused of generalizing from one instance. But if we make 10,000 observations, we might think we have a degree of probability to support the generalization. We go on to make observe 1 billion swans and they were white. This might lead us to go on to admit that the hypothesis has become even more probable. So, someone might say to defend the probability view, that how can we deny that we probability and use the probability view of induction?

“But the inductive principle only holds with the proviso, “if the factors present along with A are the same” in subsequent repitition of A. And this case of the swans is simply a case in which it is extremely difficult to be sure that this is so. A in this case means the defining characteristics of the class swan, and B means whiteness. Now different swans will have, along with the defining characteristics A, a number of other characteristics. and these will differ with different individual swans, not to mention circumambient differences of environment. Thus the first case of A you observed was really ACDE, and this was associated with B. The second case was APQR, the third AXYZ. Now, of course, it does not follow from the principle of induction that because ACDE was associated with B, therefore APQR and AXYZ must be associated with B. For we do not have there that exact repetition of the same sets of circumstances which the inductive principle requires.”

To try to remedy the situation that we are in, we constantly repeat observations of this class of swans. Now if we keep making these observations of A, and they’re found to have B, then we think it becomes more and more likely that we have eliminated other certain possibilities, and raise the probability. We want to eliminate some of the accidental characteristics of certain swans. This would be something like they’re size. food they eat, and the climates that they live in. When we rule out sets of circumstances as irrelevant, they become more probable.

The fundamental reason why there is constant repetition of observation on new members of class is that although in theory the association of A with B, once it is observed must always hold, is because in practice we never get our cases of pure A. “We can not isolate the system. It is always mixed up with extraneous circumstances. Thus the doubt which we are trying to dispel by repeated observations has nothing at all to do with Hume’s doubt about the validity of induction…” That doubt can’t be dispelled, no matter now many numerous observations we make. But the doubt that we are trying to get rid of isn’t the logical doubt. The doubt we are trying to get rid of is the practical doubt from the enormous complexity of nature, our frailty of our intellects which are unequal with the task to disentangle the complexities, or the inadequacy of the instruments that we have at our disposal to isolate the system present.

Some, like Carnap, have divided knowledge into empirical knowledge and necessary propositions. Necessary propositions would be those like mathematics and logic. Now the empirical propositions could be considered doubtful because the practical doubts that arise from our human infirmities. But this means that we ought to have the same doubts in concern with mathematics. This is why we have people that check our work in mathematics, to make sure that we made no practical doubts in the process that we followed.

“There is one sense in which mathematical, or, in general, deductive conclusions are certain this may be called the logical or theoretical sense. And there is another sense, which may be called the practical sense, in which they are only probable, since the mathematician or the syllogizer may err in his reasoning. The mathematician may miscalculate, and the syllogizer may make any one of a hundred mistakes. And if practical doubts are not a ground for denying that, in an appropriate sense, mathematics is certain, then practical doubts can not be a ground for denying that, in an appropriate sense, empirical conclusions are uncertain.”

“As it is with mathematical truths, so precisely it is with empirical truths. There is one sense in which an inductive conclusion is certain, namely, the theoretical sense that it follows with certainity from a single observation plus the inductive principle. And there is another sense, the practical one, in which it is probable only, because there may be errors in observation, experimentation, and the like.”

“The statement that empiricial knowledge may be theoretically certain is, of course, subject to the proviso that we accept the inductive principle. If we don’t accept it, then, of course, empirical knowledge is not even probable. It has no validity at all. In no case does any question of probability enter into the matter.”

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