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Truth suffers from too much analysis

Posts Tagged ‘Knowledge’

Defense of Skepticism

Posted by allzermalmer on December 28, 2013

This post is based on a paper that was done for a class on epistemology. The paper was about a paper called “A Defense of Skepticism“, authored by Peter Unger, and appeared in the philosophical journal A Philosophical Review, Vol. 80, No. 2 (Apr., 1971), pp. 198-219.

“Both propositions of “Forty-five  plus fifty-six is the same as one hundred and one” and “45+56=101” are propositions that hardly anyone knows, under Peter Unger’s skeptical thesis. Under the skeptical thesis presented by Unger, most people don’t know those propositions are true, though some might, & those people that don’t know those propositions are true typically talk as if those propositions are true. In fact, it will be given that there are a great many propositions that we may reasonably believe or a great many propositions that we may suppose to be true, while never knowing them to be true.

Unger’s skepticism wants to deals within common idea of language and knowledge. Skepticism presented by Unger deals with language, since that is the background in which some philosophers believe that they have solved some skeptical problems about knowledge. For example, the common idea of language and knowledge that Unger is working under is that the language we speak is adequate at expressing truths. From this common idea, Unger presents idea of how our language habits possibly serve us well in practical ways, while these language habits have us saying what’s false rather than true.

Our language habits that involve positive assertions contain special features that Unger want’s to point out, and which also motivates his skeptical thesis. There are absolute terms within our languages or language habits, and some of these absolute terms are basic. From these basic absolute terms, we may build up other absolute terms. Examples of absolute terms are both “flat” and “certain”. The proposition “That is a cube” involves the basic absolute term of “flat”, since a cube’s surface is flat. If we don’t know a basic absolute term of “flat”, then we can’t know what is built up from those basic absolute terms, which is “That is a cube”.

“That is a cube” is a proposition that many people might reasonably believe, or “The road is flat”. But the basic absolute term of “flat” generally fails to apply to the world. A cube is a geometrical object which has no width or depth. However, those objects that we generally come across do have width or depth. So those objects that we call “cubes” aren’t something that applies to the world. We may talk as if “That is a cube” or “The road is flat”. It is reasonable to suppose or believe that they are true. From whatever is built, or has any part of, of that basic absolute term would also generally be false.

The skepticism presented by Unger implies some things that might be deemed impossible to accept, since it would imply something about the functioning of our language. It would attack a common idea about language being adequate to express truth. Unger’s thesis would have it that common terms of language involve the use of error systematically in expressing truth. Two common terms that would be found to use error systematically would be “know” and “knowledge”. While we believe what we say is true, what we believe is actually false.

Suppose that an individual believes that “this region of space is a vacuum” is true. Now further suppose that contrary to the individual’s belief, “this region of space isn’t a vacuum” since “this region of space has the slightest trace elements of gaseous stuff”. Now further suppose that for practical purposes principle, there isn’t an important difference whether you falsely believe the first supposition or truly believes the second supposition, i.e. “this region of space has the slightest trace elements of gaseous stuff”.

One might think that the first supposition implies the practical purpose principle, since there is no important difference. Things would go on as we practically expected with the region of space being a vacuum, since if the region is a vacuum then whatever gaseous content it has is none. Even giving such a thought, there is still something that is unique. The second supposition doesn’t imply the practical purpose principle. The principle may be derived from the first supposition and can’t be derived from the second supposition. In other words, from “this region of space is a vacuum” we can derive that the region of space doesn’t contain any gaseous elements or doesn’t practically contain any gaseous elements. The practical result of the first supposition would show that there aren’t any gaseous elements, so the practical result would have been no gaseous elements. However, by the second supposition, wouldn’t practically show up as a result. So our belief can still be reasonably supposed true, even though false.

The example given above is to help point out that we can have false beliefs, even though the beliefs are reasonable, and they don’t clash with experiences of life, or way we experience the world. We can have many false beliefs, based on some of the account that was given above. The practical purpose would come from positive assertions, since the first supposition was a positive assertion and the second assertion was a negative assertion. From the positive assertion we were able to derive the practical purpose principle, and we couldn’t derive the practical purpose principle from the negative assertion. The individual isn’t in position to determine if the region of space contains gaseous elements, given the practical limitation that was given from the derived principle from first supposition.

Those terms of knowledge belong to a class of terms in our language, and these are those absolute terms. “Flat” is an absolute term, so saying that “a surface is flat” is also saying that matters of degree are not instanced in the surface to any degree. Being flat means no degrees of being bumpy or having a curve, i.e. perfectly flat. “Bumpy” and “curve” are taken as examples of relative terms, and so we notice that there is some connection between absolute terms and relative terms.

Relative terms and some absolute terms, specifically those of basic absolute terms, have the special ability of being modified by many different terms. We can take a term such as “very”, can be applied to either relative terms or basic absolute terms, and we can obtain something like “the table is very bumpy” or “the table is very flat”. These modifications of either the relative term or basic absolute term are one based on matters or degree, or indicate matters of degree.

“Cube” is an absolute term, even though it isn’t a basic absolute term. This is because “Cube” is built up off of the absolute term of “flat” & “straight”. “Cube” doesn’t admit of matter of degree, even though the basic absolute terms used to build up the term do admit to matter of degree. In other words, it takes two basic absolute terms of “flat” and “straight” to build up the absolute term of “cube” & “cube” doesn’t allow for matter of degree while “straight” and “flat” do allow for matter of degree. Not all absolute terms can be modified by matters of degree, but some like “flat” or “straight” can be, and all relative terms can be modified by matters of degrees.

Some might think to take basic absolute terms as the same relative terms, but this won’t do. There is a special distinction between both types of terms when it comes to matter of degrees. When we say that “a surface is very flat” or “a surface is very bumpy”, we are saying how flat the surface is or how bumpy the surface is. Intuitively, there is a difference between these two. Flat being an absolute term, it has an ultimate location in which we may judge things. We are saying how close the surface is to being flat. We have perfectly flat, which is what the absolute term of flat means, and saying it is very flat allows us to say how close it is being perfectly flat since we have the index of perfectly flat to compare it with.

When it comes to relative terms, like “a surface is very bumpy”, since “a surface is bumpy” implies “a surface is very bumpy”. However, from “a surface is very bumpy” we can’t derive that “a surface is bumpy” because might be that the surface isn’t bumpy at all. We notice an asymmetry, and this comes from an intuitive level. Something would seem strange in our common language to express “a surface is bumpy” and deny that “a surface is very bumpy” is implied, or “a surface is very bumpy” and affirm that “a surface is bumpy”.

Either both the first surface is flat and the second surface is not flat or both the first surface is closer to being flat than the second surface. This is a more complex way in which Unger deals with the matter of degrees when they are applied to basic absolute terms. This helps to change things so that when we deal with relative terms and matter of degree, the same interpretation of common language doesn’t hold.

Basic absolute terms can at least be partially defined by relative terms, or the matter of degree terms. And since absolute terms are defined by basic absolute terms, this in turn means that absolute terms that aren’t basic absolute terms are also partially defined by relative terms. These relative terms help to point out the negative accept of the skeptical thesis presented by Unger. For supposing that “flat” is a basic absolute term, which is defined in part by a relative term, means that something isn’t flat at all, or not in the least, bumpy. This is the negative relative requirement that basic absolute terms have to meet when partially defined by relative terms.

Absolute terms and Relative terms are both part of our language, but we also have things that are part of our language that are neither absolute terms nor relative terms. Some of these terms are unmarried or married, true and false, or right and wrong. But Unger points out that some of these terms can be taken as “absolute” in some language.

Some terms of our language are followed by propositional clauses, and we may call these terms propositional terms. So one might wonder, are these propositional terms, like “certain”, absolute or relative terms. A term like “certain” has two things that need to be made clear about them, or interpretations that may be given to it. (1) Certain in which certain is not certain of anything, or (2) certain in which certain is certain of something. An example of (1) is “It is certain that it is raining”, since the term “it” doesn’t appear to have any reference. This is the impersonal context, which is the impersonal idea of certainty. An example of (2) is “He is certain that it is raining”, since the term “he” does appear to have a reference. This is the personal context, which is the personal idea of certainty.

Unger believes that certainty has to contain both of those conditions; it is both impersonal certainty and personal certainty. What comes from each of these on their own is that certainty involves no doubt. So we get that “If certain that p then isn’t doubtful that p” with impersonal certainty. With personal certainty we get that, “In his mind, if he’s certain that p then isn’t doubtful that p.” All doubt is absent in his mind.

Certain are now connected negative definitions of certainty, which is an absolute term. Certainty or Certain are common concepts with language, and they are built on absolute term which has a negative definition.

When an individual says that he is certain that p, they are saying they aren’t confident of p & more than confident of p. If they say they are confident that p then they are saying they are confident that p. So there is a difference between an individual being certain and being confident. So you can be as confident as you want because of the highest reasonable belief.

Take these two propositions, either (1) “He’s (really) very certain of p” or (2) “he’s very certain of p”. The second proposition says more about certainty than the first proposition. The second proposition gets ride of one matter of degree. Each of these modifiers is saying that they aren’t certain, but one less degree of modifiers saying that they aren’t certain. This might seem implausible at first, but there has been a pattern in which to place our languages of language to express truth.

Someone saying that “I’m more certain that p than I am that q” is the same as “I am either certain that p while not certain that q or I’m more nearly certain that p than I am that q”. The first part of the disjunction tells us that either p or q is certain and it was proposition p. The second disjunction tells us that aren’t certain of either proposition and one is of a higher degree that the other. However, someone saying that I’m more confident that p than I am that q” isn’t the same as “I’m either both confident that p and not confident that q or I’m more nearly confident that p than q.”, since confident of both.

Given these expositions of propositional terms, absolute terms v. relative terms, basic absolute terms, impersonal certainty v. personal certainty, we can come to skepticism about many things that we reasonably believe. It can be taken that “lots of surfaces of physical things are flat” is a reasonable belief. But this comes to contradict the experience of life. We take a microscope and we start to examine those objects that we commonly come upon, and we start to notice that they aren’t flat. They take on the form of being bumpy. So now the absolute term is one that is false and yet for practical purposes it is true. The absolute term was even a reasonable belief that is or was held.

One of the basic problems of absolute terms is that there are counter-examples to them, and the absolute terms are part of language to express truth. These absolute terms, at least basic ones, are shown to be false by experiences of life. However, these terms are very useful and they do express some truth. Absolute terms have reason to doubt, since we do have a counter-example. Most absolute terms would have counter-examples, but that doesn’t mean that all absolute terms have counter-examples.

Going back to previous example, experience of life presents what seems to be a smooth stone & look through a microscope at the smooth stone. The smooth stone is found to actually be bumpy, which means that it isn’t smooth. To account for the stone being bumpy, an inference to the best explanation could be used. It could be that the smoothness is built up from the finer part of the stone which has small bumps. It can further be better explained that the bumps are made of something even smaller, like atoms, which combine in a certain way in which smooth stone is final outcome, while there are no smooth stones in the combination to begin with, i.e. neither atoms are smooth nor atoms are stones. This belief would have plenty of evidence, and be a reasonable belief. However, the degrees of “deeper” explanations to account for the counter-example can eventually end in an absolute matter where there is no counter-example to be found. So we eventually come to the point that we should suspend judgment on this issue. We don’t know either.

The real sting of Unger’s skepticism comes down to this form: If person is certain of p, then not anything of which the person is more certain. So the individual can be certain of p, which means that person isn’t as certain, i.e. isn’t certain, of q. This comes back to this point, if more certain of another thing, then either certain of other while and not being certain of first or more nearly certain of other thing than of the first. Suppose that it is logically possible that there’s something an individual might be more certain of than they are now of a given thing, then the person wasn’t really certain to begin with.

Is it reasonable to believe that there are automobiles? It would seem to be an experience of life. However, a dilemma can be presented to them. Either more certain that there are automobiles or aren’t. This can be because someone is more certain that they exist than certain automobiles are an experience of life. Since they are more certain that they exist, then certain that they exist and aren’t certain that automobiles exist. So when someone is presented with something that they think they are more certain of than another, they are saying that they aren’t certain of second. If they hold open that what they hold to be more certain can possibly be false, then they aren’t certain of it to begin with, either.

So from this, we can know one thing, but most everything else that we think we are certain of isn’t certain of. So we can hold that we are more certain of our own existence than of 45+56=101. For practical purposes though, we are certain that 45+56=101. This would be us having a reasonable belief without it being true, i.e. certain that 45+56=101. Even something like some basic arithmetic can fall for skepticism, even though it is not a universal skepticism in which no one knows anything.

The skepticism that Unger presents deals with knowledge being certain, which has also been a common idea of epistemology. However, some suppose that knowledge requires just belief, or at least reasonable belief such that, if both believe that p implies know that p & believe that p implies p then p implies know that p. This would appear to lead to omniscience, which seems to contradict experience of life. So such a supposition would be an absolute term which is false but practically useful. This belief is reasonable is because it meets certain conditions, which helps allow us to say that we have knowledge. However, these conditions don’t exclude having a false belief.

So Unger’s skepticism is an attack on language is capable of expressing truth. Unger holds that language is capable of expressing truth, but that it also systematically expresses error as well. Language relies on positive assertions, which require negative definitions. These definitions are based on absolute terms that are basic, while there are absolute terms that aren’t basic and there are relative terms. The basic absolute terms help to define absolute terms that aren’t basic. These basic absolute terms end up having counter-examples. Our common way of expressing language would have error.

One of the words that we use for knowledge is “certain”, which is an absolute term. However, based on the definition of being certain, there can only be one thing that we are certain about. So we may use the knowledge term of certain, or that we have knowledge, but we truly don’t have knowledge. The skepticism that Unger presents show there isn’t much of knowledge that we have, since there isn’t much that we are certain about, but that doesn’t mean we don’t have any knowledge. Unger’s skeptical thesis is consistent that we don’t know anything, but it doesn’t imply that we don’t know anything. We just know less than we say that we know or we are more certain of one thing than we are of another, or we aren’t certain at all.”

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Source of Knowledge and Epistemology

Posted by allzermalmer on September 23, 2013

It will be assumed that there are only two sources for knowledge. These sources are both Cognition and Senses.

It will be assumed that each source of knowledge has three possible truth values to be attached to it. The truth values are always true, sometimes true, and never true.

From these two assumptions we are able to derive different epistemological systems that can take on any of these sources or truth values.

1. For all sources of knowledge, if knowledge source is Cognition then knowledge source is always true & if knowledge source is Senses then knowledge source is always true.

2. For all sources of knowledge, if knowledge source is Cognition then knowledge source is always true & if knowledge source is Senses then knowledge source is sometimes true.

3. For all sources of knowledge, if knowledge source is Cognition then knowledge source is always true & if knowledge source is Senses then knowledge source is never true.

4. For all sources of knowledge, if knowledge source is Cognition then knowledge source is sometimes true & if knowledge source is Senses then knowledge source is always true.

5. For all sources of knowledge, if knowledge source is Cognition then knowledge source is sometimes true & if knowledge source is Senses then knowledge source is sometimes true.

6. For all sources of knowledge, if knowledge source is Cognition then knowledge source is sometimes true & if knowledge source is Senses then knowledge source is never true.

7. For all sources of knowledge, if knowledge source is Cognition then knowledge source is never true & if knowledge source is Senses then knowledge source is always true.

8. For all sources of knowledge, if knowledge source is Cognition then knowledge source is never true & if knowledge source is Senses then knowledge source is sometimes true.

9. For all sources of knowledge, if knowledge source is Cognition then knowledge source is never true & if knowledge source is Senses then knowledge source is never true.

It should be made immediately clear that (2) and (4), and (3) and (7), and (6) and (8), are the converse of one another.

It should be made immediately clear that (1) and (9) are contrary to one another, since both may be false but both can’t be true.

It should be made clear that (1) and (5), and (5) and (9) are both contradictory, since both can’t be false but one can be true.  Either (1) or (5) or (9) are true.

Those epistemological hypothesis, like those of (2)-(8), all are fallible. They are sometimes true. It can be supposed that there are different degrees contained within those epistemological hypothesis.

For example, it may be supposed that since some truth comes one of the two sources and that 99% is true or that 1% is true from one of the two sources.

Here is an example of fallibility, i.e. sometimes true, and different degrees of truth contained within it.  Suppose that X stands for Cognition or Senses but not both together.

For all knowledge, if knowledge source is X then knowledge source is 99% true
For all knowledge, if knowledge source is X then knowledge source is 89% true
For all knowledge, if knowledge source is X then knowledge source is 79% true
For all knowledge, if knowledge source is X then knowledge source is 69% true
For all knowledge, if knowledge source is X then knowledge source is 59% true
For all knowledge, If knowledge source is X then knowledge source is 49% true
For all knowledge, if knowledge source is X then knowledge source is 39% true
For all knowledge, if knowledge source is X then knowledge source is 29% true
For all knowledge, if knowledge source is X then knowledge source is 19% true
For all knowledge, if knowledge source is X then knowledge source is 9% true
For all knowledge, if knowledge source is X then knowledge source is 1% true.

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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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Fallacy of Evidentialism

Posted by allzermalmer on August 18, 2013

There are two philosophers, who are taken to be generally representative of Evidentialism. These two philosophers are David Hume and C.K. Clifford. These two philosophers have two quotes that are examplars of their Evidentialism thesis. They are, respectively, as follows.

“A wise man, therefore, proportions his belief to the evidence…when at last [a wise man] fixes his judgement, the evidence exceeds not what we properly call probability.” – David Hume in “Of Miracles” (Italics are Hume’s)

“We may believe what goes beyond our experience, only when it is inferred from that experience by the assumption that what we do not know is like what we know…It is wrong in all cases to believe on insufficient evidence” – W.K. Clifford in “The Ethics of Belief

Thomas Huxley,

Huxluy Evidence

Those quotes from these three writers are taken as representative of Evidentialism, and thus the Evidentialist Principle. The statements they make might appear to carry some validity & they might even seem to be sound.

However, Karl Popper holds that they are not valid. He also doesn’t hold that they are sound. They even contradict all empirical systems or all empirical propositions. They forbid us from ever believing or holding to any empirical system or empirical proposition, they forbid us from ever believing or holding to any scientific hypothesis or scientific proposition. But the problem of Induction applies to both the truth of this matter of fact assertion and the probability of the truth of this matter of fact assertion.

Both of the propositions contain signs of being based on Induction. Hume points out that a wise man will fix their judgements on a proposition when the evidence indicates that it is probable. Clifford points out that we may infer from experience what goes beyond our experience, but this is based on hypothesis that unknown is similar to the known.

Both of the propositions show that Evidentialism is founded on Induction, or inductive inferences.

Hume, supposedly, showed that it is logically impossible to infer the unknown from the known. It is logically impossible to derive the unknown from the known. Thus, Evidentialism is founded on a logical impossibility.

“The problem of the source of our knowledge has recently been restated as follows. If we make an assertion, we must justify it; but this means that we must be able to answer the following questions.

How do you know? What are the sources of your assertion?’ This, the empiricist holds, amounts in its turn to the question,

‘What observations (or memories of observations) underlie your assertion?’ I find this string of questions quite unsatisfactory.” – Karl Popper in “The Sources of Knowledge and Ignorance

Popper presents the Evidentialist Principle, in that quote, as saying that “If we make an assertion, we must justify it“. If you make an assertion, then you must justify it, or making an assertion implies must justify the assertion. You would have to answer one question, ‘How do you know? What are the sources of your assertion?’, and have to answer another question, ‘What observations (or memories of observations) underlie your assertion?’. 

As Popper points out, the Evidentialist Principle is an answer to The Problem of Source of Knowledge. So we may suppose that Evidentialism and Induction are to be based on the Source of a proposition or an empirical proposition. It seeks that the source of a proposition to be justified.

Criticizing or discrediting a proposition because of the source has some similarity to the Genetic Fallacy: “if the critic attempts to discredit or support a claim or an argument because of its origin (genesis) when such an appeal to origins is irrelevant.”

With the Genetic Fallacy, a proposition is being discredited, or supported, because it is “paying too much attention to the genesis of the idea rather than to the reasons offered for it”. The origin, or source, of the proposition is used to discredit, or support, the proposition.

Evidentialism would discredit a proposition because the source of the proposition is without justification.

We also find that David Hume presents an example of the questions that Popper finds to be unsatisfactory.

“All reasonings concerning matter of fact seem to be founded on the relation of cause and effect. By means of that relation alone we can go beyond the evidence of our memory and senses. If you were to ask a man, why he believes any matter of fact, which is absent; for instance, that his friend is in the country, or in France; he would give you a reason; and this reason would be some other fact; as a letter received from him, or the knowledge of his former resolutions and promises…All our reasonings concerning fact are of the same nature. And here it is constantly supposed that there is a connexion between the present fact and that which is inferred from it. Were there nothing to bind them together, the inference would be entirely precarious.

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.” – David Hume in “Sceptical doubts concerning the operations of the understanding” (Italics are Hume’s)

David Hume himself goes down the line of questioning that Popper brings up. For example, suppose that some assertion is made like “all ravens are black”. This assertion is what Hume calls a Matter of Fact, i.e. Synthetic proposition or Contingent proposition. It is Possible that it is true that “all ravens are black” and it is possible that it isn’t true that “all ravens are black”. This starts a line of questioning once this assertion is presented.

Question: What is the nature of reasoning concerning that matter of fact?
Evidence: The assertion is founded on the relation of cause and effect.
Question: What is the foundation of reasoning and conclusion concerning that relation of cause and effect?
Evidence: The relation of cause and effect of that assertion is founded on Experience.

These two questions follow a basic form that Popper is bringing up, and the type of basic form that Popper finds unsuitable, or the type of basic form of Evidentialism that is unsuitable. The basic reason for this is because another question follows from the answer to the previous two questions.

Question: What is the foundation of that conclusion drawn from experience?

This new question is where the Problem of Induction arises, or what Popper calls The Logical Problem of Induction.

If all Ravens are Black then justified in the relation of cause and effect. If justified in the relation of cause and effect then justified by experience. If justified by experience then experience is justified by Induction. So if all ravens are black then justified by Induction. But, Induction isn’t justified. So assertion all ravens are black isn’t justified. Therefore, Evidentialism would make it so that the assertion all Ravens are Black isn’t justified. This applies to all matters of fact, and thus all empirical and scientific assertions.

“It is usual to call an inference ‘inductive’ if it passes from singular statements (sometimes called ‘particular’ statements), such as accounts of the results of observations or experiments, to universal statements, such as hypotheses or theories. Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusions drawn in this way may always turn out to be false: no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white. The question whether inductive inferences are justified, or under what conditions, is known as the problem of induction.” – Karl Popper in “The Logic of Scientific Discovery” (Italics are Popper’s)

The Problem of Induction comes about because Induction relies on statement that is a matter of fact assertion, but this matter of fact assertion cannot, in principle, be inductively justified. So either all reasonings concerning matter of fact seem to be founded on experience or not all reasonings concerning matter of fact seem to be founded on experience.

This is a logical problem because either Induction relies on a statement that is either a contingent proposition or necessary proposition. We can call this the “Principle of Induction”. But the Principle of Induction can’t be a necessary proposition because the negation of the Principle of Induction is possible to be false. A necessary proposition can’t be possible to be false. So it is possible that Principle of Induction is true and it is possible that isn’t true that Principle of Induction is true. Therefore, the Principle of Induction is a contingent proposition.

Hume points out that matter of facts about dispositions and universal propositions are matters of facts. Thus dispositional propositions and universal propositions are contingent propositions. Dispositional propositions describe law-like behavior and universal propositions describe lawful behavior or law-like behavior. These would both be contingent propositions, and so we wouldn’t be justified, based on Induction, in asserting those dispositional propositions or universal propositions.

We wouldn’t be justified, based on Evidentialism, when it came to assertions about dispositional propositions or universal propositions. Science wouldn’t be justified, based on Evidentialism, when it came to assertions about dispositional propositions or universal propositions. But science is full of assertions about dispositional propositions and universal propositions. Therefore, science wouldn’t be justified in asserting dispositional propositions and universal propositions.

“[Hume] tried to show that any inductive inference- any reasoning from singular and observable cases (and their repeated occurrence) to anything like regularities or laws- must be invalid. Any such inference, he tried to show, could not even be approximately or partially valid. It could not even be a probable inference: it must, rather, be completely baseless, and must always remain so, however great the number of the observed instances might be. Thus he tried to show that we cannot validly reason from the known to the unknown, or from what has been experienced to what has not been experienced (and thus, for example, from the past to the future): no matter how often the sun has been observed regularly to rise and set, even the greatest number of observed instances does not constitute what I have called a positive reason for the regularity, or the law, of the sun’s rising and setting. Thus it can neither establish this law nor make it probable.” Karl Popper in “Realism and the Aim of Science” (Italics are Popper’s)

The assertion “all ravens are black” isn’t justified as true under Evidentialism and “all ravens are black” isn’t jusified as probably true under Evidentialism. Hume himself points out that the wise man doesn’t fixate his judgement on an assertion in which the evidence exceeds what we properly call probability. In other words, the Evidentialist doesn’t hold to assertions in which the evidence exceeds what we properly call probability. So Evidentialist only hold to assertion in which evidence shows it is true or probably true. So “all ravens are black” is only held by an Evidentialist if evidence shows it is true or at least probably true.

Popper presents a solution to the Problem of Induction, and thus treats assertions differently from Evidentialism. Popper rejects Induction, and thus rejects Evidentialism. The source of an assertion has nothing to do with either discrediting the truth of a proposition or supporting the truth of a proposition.

Matter of fact propositions, or scientific propositions, don’t discredit or support the source of an assertion. Science doesn’t support the truth of a proposition or support the probability of a proposition. It, basically, seeks to discredit the truth of a proposition. Science seeks to show that the proposition is false, not that the proposition is true or probably true. Science always seeks to discredit it’s proposition and not to support it’s propositions. So scientific propositions are, in principle, possible to show they are false and never show they are true or probably true. This includes both dispositional propositions and universal propositions.

In other words, Evidentialism seeks both positive justifications for assertion and negative justifications for assertion. Evidentialism would be based on “full decidability”. Falsifiability, or Falsification, seeks only negative justifications for assertions. Falsifiability would be based on “partial decidability” . These negative justifications, for Falsifiability, basically state that scientific assertion hasn’t been demonstrated false as of yet. This never indicates a positive justification for the assertion being true or probably true.

“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.” – Karl Popper in “The Two Problems of The Theory of Knowledge” (Italics are Popper’s)

For Falsifiability, the source of an assertion is irrelevant when judging whether the assertion is either true or false, and the source of an assertion is irrelevant when judging whether justified in believing that assertion is true or probably true. The source of an assertion is irrelevant for the justification of the assertion. Would have to rely on Induction, and Induction isn’t justified itself. The only justification of an assertion, specifically an empirical assertion, is that it is possible to show that assertion is false. An empirical assertion has the possibility to be shown false, but it doesn’t have the possibility to be shown true (or probably true).

Science, thus, doesn’t care of the source of an assertion. Science is justified in believing, or holding to, an empirical proposition because that empirical proposition allows for the possibility that can be shown that it is false, but hasn’t been shown that it is false yet. For example, science would be justified in believing the empirical proposition that “all ravens are orange” if wasn’t for “some ravens are black”. It would be a negative justification, since don’t have another empirical proposition that contradicts it, or shows that it is false.

One of the basic mechanisms of Falsifiability is that works by deductive inference. Modus Tollens forms an example of deductive inference that Falsifiability uses. Given the conditional claim that the consequent is true if the antecedent is true, and given that the consequent is false, we can infer that the antecedent is also false.

If an empirical assertion is true implies another empirical assertion is true & the other empirical assertion is false, then original empirical assertion is false.

Principle of Modus Tollens:If all ravens are orange implies no ravens are not orange & some ravens are black, then not all ravens are orange. This is how the negative justification of empirical assertions works, which is deductive inference of modus tollens. It wouldn’t be possible for “not all ravens are orange” to be false. So it must be true.

The Principle of Modus Tollens is a necessary truth, which is different from the Principle of Induction. The Principle of Induction isn’t a necessary truth. It is possible that the Principle of Induction is false. So it might be true.

An assertion that is the conclusion of the Principle of Induction, or the assertion of a wise man that reviewed the Evidence, might be true. An assertion that is the conclusion of the Principle of Modus Tollens, or the assertion of a foolish man that never reviewed the Evidence, must be true.

The truth that the Principle of Modus Tollens always produces truth. It is similar to negative theology. It isn’t true that “all ravens are orange” & it isn’t true that “no ravens are not orange”. Each time saying what is true because true isn’t those false statements, since it is true that “not all ravens are black”.

The contradiction between “all ravens are orange” and “not all ravens are orange” are exclusive, they both can’t be true and no intermediary empirical propositions between them. If know that “all ravens are orange” is false then know that “not all ravens are orange” is true. All ravens are orange implied no ravens are not orange & some ravens are black. Therefore, it is necessarily true that not all ravens are orange. If Know that “not all ravens are orange” is true then “not all ravens are orange” is true. “Not all ravens are orange” is true.

Both the Principle of Modus Tollens are dealing with scientific propositions. The scientific propositions are possibly true or possibly false. If combine scientific propositions with the Principle of Induction, then scientific proposition infered might be true. If combine scientific propositions with Principle of Modus Tollens, then scientific proposition infered must be true. The negative justification allows for things that aren’t possibly not true & hold to statements that are only true, while positive justification allows for things that are only possibly true & hold to some statements that aren’t only true.

So Evidentialist like David Hume, or C.K. Clifford, would be justified in holding some scientific propositions that aren’t only true. Evidentialist would hold to both true statements and false statements. While the Non-Evidentialist, which follows Falsifiability or negative justification, would hold only to true statements. The Non-evidentialist wouldn’t be justified in asserting a scientific statement, even though conclusions drawn from it must be true.

Thus, Evidentialism is fallacious because the assertions that it concludes to be justified in holding, based on the evidence, aren’t truth-preserving. It’s conclusions of justified scientific propositions aren’t based on the evidence or derived by positive support it receives from the evidence. However, it is completely opposite with Non-Evidentialism of Falsification, or it isn’t fallacious.

The Evidentialist would be acting irrationally by seeking their justification, while the Falsifiabilist, which is necessarily a Non-Evidentialist, would be acting rationally by not seeking the Evidentialist justification.

Huxley’s assertion, in his examplar of Evidentialism, mentions that “merciless to fallacy in logic.” But we later find out that Evidentialism isn’t “merciless to fallacy in logic”, but is founded on a fallacy in logic itself. David Hume recognized this, even though exemplar of Evidentialism. Instead, he went about acting irrationally by seeking a (positive) justification of proposition by evidence & the rest of Evidentialism followed, like C.K. Clifford and Thomas Huxley. They would all go about by searching for evidence that proposition is true and end right back in the same place.

Finding Evidence

So we finally come full circle with the fallacy of Evidentialism, and find the source of the Evidentialist fallacy.

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Gnostic and Agnostic Breakdown

Posted by allzermalmer on August 2, 2013

The main interest is of Agnosticism, and this by default can have some implication with Atheism and Theism.

It will be supposed that Agnosticism is about lack of knowledge or not knowing. Gnosticism will be about having knowledge or knowing. It will be supposed that to have knowledge of a claim, then that claim is Justified, True, and it is Believed.

(Gnostic) K=JTB
(Agnostic) ~K= (A1) NJTB v (A2) JNTB v (A3) JTNB v (A4) NJNTNB

There are four ways to agnosticism, but there is only one way to gnosticism.

(A1) Claim isn’t Justified & Claim is True & Claim is Believed.
(A2) Claim is Justified & Claim isn’t True & Claim is Believed.
(A3) Claim is Justified & Claim is True & Claim isn’t Believed.
(A4) Claim isn’t Justified & Claim isn’t True & Claim isn’t Believed.

(Gnostic Socrates) If Socratesl knows the claim p, then Socrates claim is Justified, True, and Believed by the Socrates.

(Agnostic Socrates) If Socrates doesn’t know the claim p, then…
(A1) Socrates claim isn’t Justified, but Socrates believes the claim and it’s True.
(A2) Socrates claim isn’t True, but Socrates claim is Justified and Believed.
(A3) Socrates claim isn’t Believed, but Socrates claim is Justified and it’s True.
(A4) Socrates claim isn’t Justified, isn’t Believed, and isn’t True.

Suppose that p is “there exists a deity”. So ~p stands for “there doesn’t exist a deity”.

(i)Kp= Socrates knows there exists a deity.
(ii) K~p= Socrates knows that there doesn’t exist a deity.

(iii) ~Kp= Socrates doesn’t know that there exists a deity.
(iv) ~K~p= Socrates doesn’t know that there doesn’t exist a deity.

Assume Socrates doesn’t know that the earth is flat. This is because Socrates knows that the earth isn’t flat. Socrates knowing that the earth isn’t flat implies that it is true that the earth isn’t flat. Socrates can’t know false things (but can believe false things), so Socrates doesn’t know that the earth is flat, especially because Socrates knows that the earth isn’t flat.

So it becomes obvious that:

(i) Kp doesn’t forbid ~K~p:: Socrates knows that there exists a deity doesn’t forbid Socrates doesn’t know there doesn’t exist a deity.

(ii) K~p doesn’t forbid ~Kp:: Socrates knows that there doesn’t exist a deity doesn’t forbid Socrates doesn’t know that there exists a deity.

(iii) ~Kp doesn’t forbid (ii) K~p :: Socrates doesn’t know there exists a deity doesn’t forbid Socrates knows there doesn’t exist a deity.

(iv) ~K~p doesn’t forbid (i) Kp :: Socrates doesn’t know there doesn’t exist a deity doesn’t forbid Socrates knows there does exist a deity.

(iii) or (iv) doesn’t imply that Gnostic, but can be Gnostic. (A1)-(A4) show some reasons on why (iii) and (iv) don’t necessarily imply, but don’t forbid, being Gnostic.

When it comes specifically to “there exists a deity”, it would mean that in order to be Agnostic on that claim, Socrates would have to take part of (iii) and (iv).

In order to be Agnostic, then Socrates doesn’t know there exists a deity and Socrates doesn’t know there doesn’t exist a deity.

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Lack of Knowledge implies Knowledge

Posted by allzermalmer on July 28, 2013

Socrates was once opined to have said that all he knows is that he doesn’t know anything, or I know that I don’t know.

There is a formal system known as epistemic logic. It deals with an epistemic operator, K. One of the epistemic logic is known as negative knowledge, in some sense.

Negative Knowledge: ~Kp –> K~Kp or CNKpKNKp

If I don’t know p then I know that I don’t know P. Not knowing p implies knowing that don’t know p.

If I don’t know what it looks like down at the center of the Earth (or Sun), then I know that I don’t know what it looks like down at the center of the Earth (or Sun).

Furthermore, from this Axiom, we may easily show that not knowing something implies knowing something.

All we need is our axiom of negative knowledge, CNKpKNKp, and the law of contraposition. This law, basically, states that we switch the antecedent (i.e. NKp) with the consequent (i.e. KNKp), and we negate both of those propositions when we switch their places.

By the law of contraposition and negative knowledge, we obtain CNKNKpNNKp.
Now we use the law of double negation to the consequent (i.e. NNKp), and we obtain CNKNKpKp.

We obtain that if we don’t know that we don’t something then we know something.

 

 

 

 

 

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Desiring, Believing, Knowing, Obligation, and Fitch’s Paradox

Posted by allzermalmer on April 26, 2013

Assume that Striving, Doing, Believing, & Knowing (SDBK) have some fairly simple properties.
Assume that (SDBK) Striving, Doing, Believing, & Knowing are two-termed relations between an Agent and a Possible State of Affairs.

It shall be a convention to treat Possible State of Affairs as Propositions. So, Φ is assumed to be an agent and  p is assumed to be a proposition.
(i) “Φ strives for p” is equivalent to saying “Φ strives to bring about or realize the (possible) state of affairs expressed by the proposition p.”
(ii) “Φ does p” is equivalent to saying “Φ brings about the (possible) state of affairs expressed by the proposition p.”
(iii) “Φ believes p” is equivalent to saying “Φ believes about or realize the (possible) state of affairs expressed by the proposition p.”
(iv) “Φ knows p” is equivalent to saying “Φ knows about or realize the (possible) state of affairs expressed by the proposition p.”

It shall be a convention to ignore the Agent and treat concepts to be considered, i.e. Striving, Doing, Believing, & Knowing (SDBK), as a “Class of Propositions” instead of Two-Termed relation.
(i) ‘Striving’ means the Class of Propositions striven for (that is striven to be realized).
(ii) ‘Believing’ means the Class of Propositions believed.
(iii) ‘Doing’ means the Class of Propositions doing (that is doing to be realized).
(iv) ‘Knows’ means the Class of Propositions known.

Simplification and Adjunction

Here are two basic rules of Logical Inference in propositional logic. They are known, respectively, as Simplification and Adjunction.

Simplification: Because both components of a conjunctive argument are true, it is permissible to infer that either of it conjuncts is true.
(Premise): Germany Lost World War One & Germany Lost World War Two
(Conclusion): Germany Lost World War One

(Premise): Germany Lost World War One & Germany Lost World War Two
(Conclusion): Germany Lost World War Two

Adjunction: Because both premises are presumed true, we can infer their conjunction.
(Premise): Germany Lost World War One
(Premise): Germany Lost World War Two
(Conclusion): Germany Lost World War One & Germany Lost World War Two

Assume p and q are variables for two different propositions. Assume Ω stand for Class of Propositions, which can be either Striving, Believing, Obligation, and Knowing, or etc. Assume → stands for Strict Implication, Logical Entailment, Entailment, Logical Consequence.

Closed with Respect to Conjunction Elimination

Class of Propositions are Closed with Respect to Conjunction Elimination whenever a conjunctive proposition is in the Class, then those two propositions themselves are in that Class. Closed with Respect to Conjunction Elimination follows the logical inference of Simplification, but it uses one the relation of (SDBK).

Class of Propositions Closed with Respect to Conjunction Elimination:
(p)(q)[(Ω[p & q]) → [(Ωp) & (Ωq)]]

Assume that Ω stands for the Class of Propositions “know”. So the Class of Propositions (know) Closed with Respect to Conjunction Elimination means that “If (know both p & q) then logically entails (know p) & (know q)”. We can replace Ω with “Believe”, “Striving”, “Doing”, or the others listed.

Class of Propositions covered by Closed with Respect to Conjunction Elimination are: Striving (for), Doing, Believing, Knowing, Proving, Truth, Causal Necessity (in the sense of Burks), Causal Possibility ( in the sense of Burks), (Logical) Necessity, (Logical) Possibility, Obligation (Deontic Necessity), Permission (Deontic Possibility), Desire (for),

Closed with Respect to Conjunction Elimination

Class of Propositions Closed with Respect to Conjunction Introduction whenever two propositions are in the class, then so is the conjunction of the two propositions. Closed with Respect to Conjunction Introduction follows the logical inference of Adjunction, but it uses one of the relations of (SDBK).

Class of Propositions Closed with Respect to Conjunction Introduction:
(p)(q)[[(Ωp) & (Ωq)] → (Ω[p & q])]

Assume Ω stands for the Class of Propositions “know”. So the Class of Propositions (know) Closed with Respect to Conjunction Introduction means that “If (know p) and (know q), then logically entails (Know both p & q).” We can replace Ω with “Believe”, “Strive”, “Doing”, or others listed.

Class of Propositions covered by Closed with Respect to Conjunction Introduction are:
Truth, Causal Necessity (in the sense of Burks), Logical Necessity, Obligation (Deontic Necessity).

Class of Propositions possibly covered by Closed with Respect to Conjunction Introduction are: Striving (for), Doing, Believing, Knowing, Proving, Desire (for).

Class of Propositions not covered by Closed with Respect to Conjunction Introduction are: Causal possibility (in the sense of Burks), Logical Possibility, and Permission (Deontic Possibility).

Truth Class

Class of Propositions are a Truth Class if every member of it is true.

Class of Propositions Truth Class:
(p)[(Ωp) → p]

Assume Ω stands for Class of Propositions Truth Class “knows”. So the Class of Propositions Truth Class (knows) means “If (knows p) then logical entails p.”

Class of Propositions Truth Class are: Truth, Causal Necessity (in the sense of Burks), Logical Necessity, Knowing, Done, and Proving.

Theorems about Truth Classes

Theorem 1: If (Class of Propositions) is a Truth Class which is Closed with Respect to Conjunction Elimination, then the proposition, [p & ~(Ωp)], which asserts that p is true but not a member of (Class of Propositions) (where p is any proposition), is itself necessarily not a member of (Class of Propositions).

Proof: Suppose the contrary, [p & ~(Ωp)], is a member of (Class of Propositions), i.e. suppose that (Ω[p & ~(Ωp)]) is a member of (Class of Propositions). Since (Class of Propositions) are Closed with Respect to Conjunction Elimination, the propositions p and ~(Ωp) must both be members of (Class of Propositions), so that the propositions (Ωp) and (Ω(~(Ωp))) must both be true. But the fact that (Class of Propositions) is a truth class and has ~(Ωp) is true, and this contradicts the result that (Ωp) is true. Thus from the assumption that [p & ~(Ωp)] is a member of (Class of Propositions) we have derived contradictory results. Hence, that assumption is necessarily false.

Theorem 2: If (Class of Propositions) is a Truth Class which is Closed with Respect to Conjunction Elimination, and if p is a true proposition which is not a member of (Class of Proposition), then the proposition, [p & ~(Ωp)], is a true proposition which is necessarily not a member of (Class of Propositions).

Proof: The proposition [p & ~(Ωp)] is clearly true, and by Theorem 1 it is necessarily not a member of (Class of Propositions).

Omnipotent and Fallibility

Theorem 3: If an Agent is all-powerful in the sense that for each situation that is the case, it is logically possible that that situation was brought about by that Agent, then whatever is the case was brought about (done) by that Agent.

Proof: Suppose that p is the case but was not brought about by the agent in question. Then, since (doing) is a Truth Class Closed with Respect to Conjunction Elimination, we conclude from Theorem 2 that there is some actual situation which could not have been brought about by that Agent, and hence that Agent is not all-powerful in the sense described. Hence, that assumption is necessarily false.

Theorem 4: For each Agent who is not omniscient, there is a true proposition which that Agent cannot know.

Proof: Suppose that p is true but not known by the Agent. Then, since (knowing) is a Truth Class Closed with Respect to Conjunction Elimination, we conclude from Theorem 2 that there is some true proposition which cannot be known by the Agent.

Knowability Paradox

Theorem 5: If there is some true proposition which nobody knows (or has known or will know) to be true, then there is a true proposition which nobody can know to be true.

Proof: Similar to proof in Theorem 4.

Proved True Never Proved

Theorem 6: If there is some true proposition about proving that nobody has ever proved or ever will prove, then there is some true proposition about proving that nobody can prove.

Proof: Similar to the proof in Theorem 4, using the fact that if p is a proposition about proving, so is [p & ~(Ωp)].

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Paradox of Knowability

Posted by allzermalmer on April 12, 2013

Theorem 5: If there is some true proposition which nobody knows (or has known or will know) to be true, then there is a true proposition which nobody can know to be true

“There are truths that cannot be known. For suppose that all truths can be known. Then all truths actually are known. Otherwise, we may suppose for some p that p but it is not known that p. Then it can be known that p but it is not known that p. But when it is known that thus and such, it is known that thus and it is known that such. So it could be known that p and known that it is not known that p. But what is known is true. So it could be known that p and not known that p. But that is a contradiction, and no contradiction can be true. So all truths are actually known.” W.D. Hart

(1) Assume that if X is true then possible to know that X is true. (2) Then, if X is true & do not know that X is true, then possible to know that both X is true & do not know X is true. (3) But, not possible to know that both X is true & do not know X is true. (4) Not both X is true & do not know X is true. (5)  If X is true then do not not know that X is true. (6) If X is true then know that X is true.

What if the World is non-omniscient? This would mean that nobody knows all truths, and nobody ever will. Therefore, there are unknowable truths. If some truth is unknown, then that it is unknown is itself unknowable; Because the world is non-omniscient, there is some unknowable truth. If there at exists at least one Truth, such that Truth is true and Truth is unknown, then there exists at least one Truth, such that Truth is unknown and Truth is unknowable. If there does not exist at least one Truth, such that Truth is unknown and Truth is unknowable, then there does not exist at least one Truth, such that Truth is true and Truth is unknown.

It is possible that it is known by someone at some time that both X is true & It is not known by someone at some time that X is true. It is possible that both It is known by someone at some time that X is true & It is not known by someone at some time that X is true (reduction ad absurdum)

Non-Omniscience: X is true & It is not known by someone at some time that X is true.

Verdicality (KV): If it is known by someone at some time that X is true, then X is true.

Distribution (KC): If it is known by someone at some time that both X is true & Y is true, then both it is known by someone at some time that X is true & It is known by someone at some time that Y is true.

Non-Contradiction (LNC): It is not possible that both X is true & X is not true.

Clousure (CP): If X is true implies Y is true & it is possible that X is true, then it is possible that Y is true.

Knowability (KP): If X is true then it is possible that it is known by someone at some time that X is true.

(1) Assume that X is true & It is not known by someone at some time that X is true

(2) It is possible that it is known by someone at some time that both X is true & It is not known by someone at some time that X is true. (By KP & (1).

(3) It is known by someone at some time that both X is true & It is not known by someone at some time that X is true. It is known by someone at some time that X is true & It is known by someone at some time that it is not known by someone at some time that X is true.

(4) It is known by someone at some time that both X is true & it is not known by someone at some time that X is true. It is known by someone at some time that X is true & It is not known by someone at some time that X is true. (By Simp, VK, and Adjunction (and Transitivity implication))

(5) It is possible that both It is known by someone at some time that X is true & It is not known by someone at some time that X is true. (by CP)

(6) It is not possible that both It is known by someone at some time that X is true & It is not known by someone at some time that X is true. (by LNC)

(7) It is necessary that not both X is true & X is not true.

*(8) X is true & It is known by someone at some time that X is true. (by Reduction Ad Absurdim)

Thus, If X is true, then it is known by someone at some time that X is true:: If it is not known by someone at some time that X is true, then X is not true.

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Meno’s Paradox

Posted by allzermalmer on April 11, 2013

Meno: But how will you look for something when you don’t in the least know what it is? How on earth are you going to set up something you don’t know as the object of your search? To put it another way, even if you come right up against it, how will you know that what you have found is the thing you didn’t know?

Socrates: I understand what you mean, Meno. Do you see that an eristic argument you’re introducing, that it isn’t possible for one to inquire either into what one knows, or into what one doesn’t know? For one wouldn’t inquire into what one knows- for one knows it, and there’s no need to inquire into such a thing; nor into what one doesn’t know- for one doesn’t know what one is inquiring into.

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Truth of Reasoning and Truth of Fact

Posted by allzermalmer on October 26, 2012

“All that which implies contradiction is impossible, and all that which implies no contradiction is possible.” G.W. Leibniz

“I assume that every judgement (i.e. affirmation or negation) is either true or false and that if the affirmation is true the negation is false, and if the negation is true the affirmation is false; that what is denied to be true-truly, of course- is false, and what is denied to be false is true; that what is denied to be affirmed, or affirmed to be denied, is to be denied; and what is affirmed to be affirmed and denied to be denied is to be affirmed. Similarly, that it is false that what is false should be true or that what is true should be false; that it is true that what is true is true, and what is false, false. All these are usually included in one designation, the principle of contradiction.” G.W. Leibniz

“There are . . . two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible; truths of fact are contingent and their opposite is possible. When a truth is necessary, its truth can be found by analysis, resolving it into more simple ideas and truths, until we come to those which are primary. It is thus, that in Mathematics speculative Theorems and practical Canons are reduced by analysis to Definitions, Axioms, and Postulates. In short, there are simple ideas, of which no definition can be given; there are also axioms and postulates, in a word primary principles, which cannot be proved, and indeed have no need of proof, and these are identical propositions, whose opposite involves an express contradiction.” G.W. Leibniz

 So Leibniz obtains all knowable propositions or statements to be divided based on the principle of contradiction. The truth of statements is divided into two realms. This also deals with what people can know, or knowability. It basically says that
“For each statement, if statement is knowable, then statement is either truth of reasoning or truth of fact. For each statement, if statement is truth of reasoning, then statements affirmation is logically possible and statements negation is logically impossible. For each statement, if statement is truth of fact, then statements affirmation is logically possible and statements negation is logically possible.”

A truth of reasoning is always true and not possible it is false. It is logically impossible that it is false. The negation of a truth of reasoning is an impossible statement or impossible proposition. It is self-contradictory. A truth of fact is not always true and possible it is false. It is logically possible that it is true or logically possible it is false. Truth of Reasoning is Logically Necessary and Truth of Fact is Logically Contingent.

“For each statement, if statement is Truth of Fact, then statement is an empirical claim. For each statement, if statement is Truth of Reasoning, then statement is not an empirical claim. For each statement, if statement is Truth of Reasoning, then statement is non-empirical claim. For each statement, if statement is Truth of Fact, then statement is not non-empirical claim.”

What also happens to come from this is that Truth of Facts do not entail or lead to Truth of Reasoning, and Truth of Reasoning do not entail or lead to Truth of Fact. This means that Truth of Facts do not imply or entail non-empirical claims and Truth of Reasoning do not imply or entail empirical claims. This means that statements of experience are not non-empirical claims and means statements of experience are empirical claims.

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