THE UNPARADOXICAL LIAR'S PARADOX
Prerequisite: Necessity Vs Truth, The Problem With Knowledge
One version of the liar's paradox is, "Every thing I say is a lie". A "lie" can be defined as, "intentionally claiming to believe something is true when actually believing it is false", or vice versa. "Lying" is incoherent when applied to necessities, as there is no coherent contrary to pass off as the case. A "lie" only applies to what we believe is a truth value, where there is a coherent contrary.
The "paradox", in order to be a paradox, relies on the statement (and every consequence of the statement) being true without fail, as opposed to being believed to be true. We can look at the conditional argument that follows from the "paradox", "If every thing I say is a lie, then every thing I say is not a lie". This asserts that if "Every thing I say is a lie" is true then "Every thing I say is not a lie" must be true as well. This is a contradiction, therefore incoherent. Only one of those two statements can be true. We can not go forward and say, "But, every thing I say is a lie, so every thing I say is not a lie is a lie". Much like zero times anything is zero, incoherence times anything is incoherent. We can call a "contradiction" anything we want, such as "a paradox", but it does not make it intelligible.
We can not presume that when someone says "Every thing I say is a lie", that it is true or it is false. We can only gather that "Every thing I say is a lie" is believed to be true or believed to be false. If we look at the first horn of the relevant dichotomy, we get "I believe it is true that (every thing I say is me intentionally claiming to believe something is true when I actually believe it is false) OR (every thing I say is me intentionally claiming to believe something is false when I actually believe it is true)". What we see here is that I claim to believe it is true that everything I says is a lie. Therefore, if it is the case that I am lying regarding what I claim in the first horn, then I actually do not believe it is true that everything I say is a lie. We can not logically move on and evaluate this new revelation against the OR condition, as it is made clear that the actual belief is that I believe it is false that "Every thing I say is a lie". That I believe it is false does not entail that I never lie, just that I do not believe I always lie. If it is the case that I am not attempting to lie when I say, "Every thing I say is a lie", then what I actually believe is that "Every thing I say is not a lie". My statement is in contradiction, but my belief and action is coherent.
That one believes or "says" something is true or false does not make it true or false. We can not assume in the "paradox" that one can not simply be mistaken, or deceptive in one's belief. Further, what one thinks, says, and does can be in opposition. One can "say" something that entails a contradiction, such as "I can draw a square circle", but that does not mean that they actually think that they can do it or that it is true that they can do it. In fact, it is demonstrably not the case, as by necessity one can not draw a "square circle".
Another example similar to the liar's paradox is, "This sentence is false". A "sentence" is normally understood as a container of an expression. Therefore, "This sentence" refers to the container of the expression, "This sentence is false". We now have, "The container of (This sentence is false.), is false", or simply, "The container is false". This truth value evaluation is unintelligible. It is no more intelligible as stating, "This tree is false". All truth value evaluations must contain a subject and a property to evaluate. Here, we are missing the property to evaluate. What about "The container" is false? What about "This tree" is false?
However, maybe the intended meaning of the expression "This sentence is false" is, "The expression contained within this sentence is false". Here we have, "(This sentence is false) is false". "(This sentence is false)" is unintelligible, as it is missing a property to evaluate. However, now we have added another truth value evaluation to an expression that is already unintelligible. Here again, incoherence times anything is still incoherent. Put another way, two incoherencies do not make a coherency.
August 2019
One version of the liar's paradox is, "Every thing I say is a lie". A "lie" can be defined as, "intentionally claiming to believe something is true when actually believing it is false", or vice versa. "Lying" is incoherent when applied to necessities, as there is no coherent contrary to pass off as the case. A "lie" only applies to what we believe is a truth value, where there is a coherent contrary.
The "paradox", in order to be a paradox, relies on the statement (and every consequence of the statement) being true without fail, as opposed to being believed to be true. We can look at the conditional argument that follows from the "paradox", "If every thing I say is a lie, then every thing I say is not a lie". This asserts that if "Every thing I say is a lie" is true then "Every thing I say is not a lie" must be true as well. This is a contradiction, therefore incoherent. Only one of those two statements can be true. We can not go forward and say, "But, every thing I say is a lie, so every thing I say is not a lie is a lie". Much like zero times anything is zero, incoherence times anything is incoherent. We can call a "contradiction" anything we want, such as "a paradox", but it does not make it intelligible.
We can not presume that when someone says "Every thing I say is a lie", that it is true or it is false. We can only gather that "Every thing I say is a lie" is believed to be true or believed to be false. If we look at the first horn of the relevant dichotomy, we get "I believe it is true that (every thing I say is me intentionally claiming to believe something is true when I actually believe it is false) OR (every thing I say is me intentionally claiming to believe something is false when I actually believe it is true)". What we see here is that I claim to believe it is true that everything I says is a lie. Therefore, if it is the case that I am lying regarding what I claim in the first horn, then I actually do not believe it is true that everything I say is a lie. We can not logically move on and evaluate this new revelation against the OR condition, as it is made clear that the actual belief is that I believe it is false that "Every thing I say is a lie". That I believe it is false does not entail that I never lie, just that I do not believe I always lie. If it is the case that I am not attempting to lie when I say, "Every thing I say is a lie", then what I actually believe is that "Every thing I say is not a lie". My statement is in contradiction, but my belief and action is coherent.
That one believes or "says" something is true or false does not make it true or false. We can not assume in the "paradox" that one can not simply be mistaken, or deceptive in one's belief. Further, what one thinks, says, and does can be in opposition. One can "say" something that entails a contradiction, such as "I can draw a square circle", but that does not mean that they actually think that they can do it or that it is true that they can do it. In fact, it is demonstrably not the case, as by necessity one can not draw a "square circle".
Another example similar to the liar's paradox is, "This sentence is false". A "sentence" is normally understood as a container of an expression. Therefore, "This sentence" refers to the container of the expression, "This sentence is false". We now have, "The container of (This sentence is false.), is false", or simply, "The container is false". This truth value evaluation is unintelligible. It is no more intelligible as stating, "This tree is false". All truth value evaluations must contain a subject and a property to evaluate. Here, we are missing the property to evaluate. What about "The container" is false? What about "This tree" is false?
However, maybe the intended meaning of the expression "This sentence is false" is, "The expression contained within this sentence is false". Here we have, "(This sentence is false) is false". "(This sentence is false)" is unintelligible, as it is missing a property to evaluate. However, now we have added another truth value evaluation to an expression that is already unintelligible. Here again, incoherence times anything is still incoherent. Put another way, two incoherencies do not make a coherency.
August 2019
Comments
Post a Comment