allzermalmer

Truth suffers from too much analysis

Posts Tagged ‘Dispositions’

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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Descartes Wax

Posted by allzermalmer on March 19, 2012

This blog is based on Meditation Two of Descartes Meditations on First Philosophy. This will deal specifically with Descartes analogy, or problem, with this pesky piece of wax of his.

“Let us consider the things which people commonly think they understand most distinctly of all; that is, the bodies which we touch and see. I do not mean bodies in general- for general perceptions are apt to be somewhat more confused- but one particular body. Let us take, for example, this piece of wax. It has just been taken from the honeycomb; it has not yet quite lost the taste of honey; it retains some of the scent of the flowers from which it as gathered; its colour, shape and size are plain to see; it is hard, cold and can be handled without difficulty; if you rap it with your knuckle it makes a sound. In short, it has everything which appears necessary to enable a body to be known as distinctly as possible. But even as I speak, I put the wax by the fire, and look: the residual taste is eliminated, the smell goes away, the colour changes, the shape is lost, the size increases; it becomes liquid and hot; you can hardly touch it, and if yous trike it, it no longer makes a sound. But does the same wax remain? It must be admitted that it does; no one denies it, no one thinks otherwise. So what was it in the wax that I understood with such distinctness? Evidently none of the features which I arrived at by means of the senses; for whatever came under states, smell, sight, touch or hearing has now altered- yet the wax remains.”

[As a side note, there was, supposedly, an auction of some of Descartes personal belonging. Some philosophers wanted to buy Descartes’ wax that is mentioned in this passage. And what was said was that it was a foot in height, and had been molded into a hat.]

So what is going on here in this passage? Descarte is going over what his senses presented to him, which happens to be this piece of wax. Now what is this wax that he knows by his senses? This is a particular body, as Descartes says. It has the property of  “tast[ing] of honey…the scent of the flowers…colour, shape and size…hard, cold and…handled without difficulty…it makes a sound.” All these things that were just listed “appears necessary to enable a body to be known as distinctly as possible.”Not only are these properties necessary to know them as distinctly as possible, it’s how we come to know of this body he calls wax. Remember, Descartes says “Let us consider the things which people commonly think they understand most distinctly of all; that is, the bodies which we touch and see. I do not mean bodies in general… but one particular body.”

He thinks that people typically think they understand, distinctly, bodies that they touch and see. He lists some of these properties that we think we understand, distinctly. We have one thing with all of these properties. Now he does something interesting, which is to put the piece of wax in a fire and pull it out. What do we notice about this thing that we thought we understood distinctly? Now the “taste is eliminated, the smell goes away, the colour changes, the shape is lost, the size increases; it becomes liquid and hot; you can hardly touch it, and if you strike it, it no longer makes a sound.” In other words, the piece of wax that we originally had is all of a sudden different. It no longer holds the properties that it just had, it changed. One and the same thing can be different at times.

Descartes comes to ask “[b]ut does the same wax remain?”. We notice the qualities change through time, but is there something that contains these qualities that remains through these changes in properties present to our senses?He says, ” It must be admitted that it does; no one denies it, no one thinks otherwise.” Now we seem to be in a predicament. We hold that something changes through time, yet remains the same in some sense, and that we don’t come to know of this thing from what our senses present to us. Either we have to give up the idea of things beneath what the senses present or there is something beneath what the senses present. He obviously decides to go with things beneath what the senses present. He is basically saying that experience doesn’t show us what lies beneath the appearances of the senses. He comes to ask and say,  “So what was it in the wax that I understood with such distinctness? Evidently none of the features which I arrived at by means of the senses.” This means we come up with the idea of “bodies” not through the senses, because the senses change when the bodies don’t really change, but through some other source than the senses.

“Perhaps the answer lies in the thought which now comes to my mind; namely, the wax was not after all the sweetness of the honey, or the fragrance of the flowers, or the whiteness, or shape, or the sound, but was rather a body which presented itself to me in these varies forms a little while ago, but which now exhibits different ones. But what exactly is it that I am now imagining? Let us concentrate, take away everything which does not belong to the wax, and see what is left: merely something extended, flexible and changeable. But what is meant here by ‘flexible’ and ‘changeable’? Is it what I picture in my imagination: that this piece of wax is capable of changing from a round shape to a square shape, or from a square shape to a triangular shape? Not at all; for I can grasp that the wax is capable of countless changes of this kind, yet I am unable to run through this immeasurable number of changes in my imagination, form which it follows that it is not the faculty of imagination that gives me my grasp of the wax as flexible and changeable. And what is meant by ‘extended’? Is the extension of the wax also unknown? For it increases if the wax melts, increases again if it boils, and is greater still of the heat is increased. I would not be making a correct judgement about the nature of wax unless I believed it capable of being extended in many more different ways than I will ever encompass in my imagination, I must therefore admit that the nature of this piece of wax is in no way revealed by my imagination, but is perceived by the mind alone. (I am speaking of this particular piece of wax; the point is even clearer with regard to wax in general.) But what is this wax which is perceived by the mind alone? It is of course the same wax which I see, which I touch, which I picture in my imagination, in short the same wax which I thought it to be from the start. And yet, and here is the point, the perception I have of it is a case not of vision or touch or imagination- nor has it ever been, despite previous appearances- but of purely mental scrutiny; and this can be imperfect and confused, as it was before, or clear and distinct as it is now, depending on how carefully I concentrate on what the wax consists in.”

He breaks down the piece of wax even further. He used his senses and found that the idea of the wax, this thing that is the wax, wasn’t derived from the senses. He now decides to change what else, besides these other qualities he listed before, made up this wax. He comes to find that it is based on being changeable, flexible, and extended. Now he wants to see if he derived these three main characteristics of the wax, since he discarded the senses because they don’t indicate anything to support the idea of the particular body of wax. Maybe it being changeable, flexible, and extended, can indicate anything to support the particular body of wax.

He comes to question what is meant by ‘changeable’ and ‘flexible’, because these are now the three things helps us come to the idea of this particular body known as wax. He doesn’t come to this idea based on his imagination, because he finds that there are many ways he can change or it flex it so that it takes different shapes. Yet his imagination is limited and could be changed even further than he can imagine. Thus, it doesn’t come through is imagination that he comes to the idea of this wax as changeable and flexible, nor through his senses since he just got rid of them previously.As he says, ” I am unable to run through this immeasurable number of changes in my imagination, form which it follows that it is not the faculty of imagination that gives me my grasp of the wax as flexible and changeable.”

He comes to question what is meant by ‘extension’, since this is the third idea of this particular body known as wax. He comes to think that ‘extension’ does not even help him come to the idea of this body known as wax, the particular one he has before him. He has seen the extension of the object change as well. For example, he has seen it melt and decrease, he has seen it boiled and it increases, and the extension goes even further when heated. He comes on to say, “I would not be making a correct judgement about the nature of wax unless I believed it capable of being extended in many more different ways than I will ever encompass in my imagination…” he eventually comes to say that his imagination does not give him the idea of this extension which he said was part of the three things that make up this particular body he knows as the wax. It was also not given to him by his senses.

His final conclusion comes down to, “I must therefore admit that the nature of this piece of wax is in no way revealed by my imagination, but is perceived by the mind alone. (I am speaking of this particular piece of wax; the point is even clearer with regard to wax in general.)” The conclusion is that the body of wax is something that we don’t derive from our senses or imagination. His conclusion is that ” the bodies which we touch and see…[have] none of the features  arrived at by means of the senses…[or] is in no way revealed by my imagination.” The imagination and senses don’t allow us to comprehend this thing that lies beneath what is present to our senses or imagination, but that we come to know of them through “mental scrutiny”, as Descartes says.

“But as I reach this conclusion I am amazed at how to error my mind is. For although I am thinking about these matters within myself, silently and without speaking, nonetheless the actual words bring me up short, and I am almost tricked by ordinary ways of talking. We say that we see the wax itself, if it is there before us, not that we judge it to be there from its colour or shape; and this might lead me to conclude without more ado that knowledge of the wax comes from what the eye sees, and not from the scrutiny of the mind alone. But then if I look out of the window and see men crossing the square, as I just happen to have done, I normally say that I see the men themselves, just as I say that I see the wax. Yet do I see any more than hats and coats which could conceal automatons? I judge that they are men. And so something which I thought I was seeing with my eyes is in fact grasped solely by the faculty of judgement which is in my mind.”

Descartes comes to point out that we are often lead to error by trusting what the senses and imagination present to us. This is because we believe that there is something that holds to all these qualities that we experienced with the senses. We also think that it also holds these other qualities of changeable, flexible, and extension. However, through mental scrutiny of this particular object of wax, he finds that he comes to no idea of a body beneath all of these qualities. But we have this idea of it, and he finds that we come to this conclusion based on “mental scrutiny”, which he also calls “Innate Ideas”.

He thought, as was previously pointed out, that there are some perplexing, if not out right contradictions, in holding to this idea of body based on the imagination and senses. Thus, to have this idea, it is not derived from the senses or imagination. But when we talk about these things, in our ordinary language, we come to think that there is something beneath what we experience, and that we come to know of it through the senses and imagination. We are “tricked” into ordinary ways of talking to hold this view. As he says, “We say that we see the wax itself, if it is there before us, not that we judge it to be there from its colour or shape; and this might lead me to conclude without more ado that knowledge of the wax comes from what the eye sees, and not from the scrutiny of the mind alone.”

Descartes comes to conclude that we judge there to that particular piece of wax with those properties because of the senses and imagination. He concludes that these people are wrong, if we hold to belief of some particular body known through senses and imagination. They ignore that we come to know of it through mental scrutiny, because neither the senses or imagination give us this idea. He also brings this up nicely through the example of the people he sees walking in the street. This is a clear example of the problem of other minds. The senses and imagination don’t give him the idea that there are people there, he judges them to be people and not automatons. He knows this through “Innate Ideas”, like he does about something being the body of particular wax, even though not know through senses or imaginations.

Review:

We believe there is a particular body, which is expressed by this wax Descartes has in his hand. The wax is expressed with taste, scent, color, shape, size, hard, cold, and makes sounds, by the human senses. He finds that these things change, they exist at one time and cease to exist at another. So don’t come to the idea of particular body, as expressed by this wax, through the human senses. The wax is expressed with ‘extension’, ‘changeable’, and ‘flexible’, by the imagination. He finds that these things change, and come and go as well. So don’t come to the idea of a particular body, as expressed by this wax, through the human imagination. But we believe that there is some particular body, and it doesn’t come from the senses or imagination. Thus, Descartes comes to say that we come to know of a particular body because of “mental scrutiny”.

There is someone who holds a different position than Descartes, drastically different, and that is George Berkeley. Descartes has his piece of wax and Berkeley has his apple.

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