The Mechanism of Paradoxes
I am a liar.
This sentence can be interpreted in various ways depending on the time and situation. It could be taken as a confession that I skipped work yesterday by feigning illness, or as a statement of one facet of my multifaceted nature—that I am 'basically honest but often tell harmless lies'—or as a statement of the law that 'no one can live their life speaking only true propositions.' In any case, from the perspective of everyday linguistic sense, this is a perfectly normal sentence with no sense of discomfort.
However, in logic, this sentence is called a paradox. In other words, it goes like this: If I am a liar, then this sentence is telling the truth, which contradicts the act of lying. Also, if I am an honest person, then this sentence is saying something contrary to fact, which contradicts being an honest person. Whether I am considered a liar or an honest person, it leads to a contradiction either way, so it is a paradox.
Why does something that is normal in everyday life become a paradox when handled by logic? The answer is 'time.' Logic is built upon the exclusion of time. And excluding time in logic also means not acknowledging 'change.'
Conversely, if you include time and change in your thinking, the sentence is not a paradox at all. For example, 'I told a lie yesterday. I am now honestly stating that fact.' There is no problem with this.
(Note: In another article, I discussed how 'going to a restaurant and eating a meal' and 'eating a meal and going to a restaurant' are both equivalent as 'P∧Q'.)
This sentence is not correct.
'This sentence' refers to the sentence 'This sentence is not correct,' that is, it refers to itself. This is also considered a paradox because, logically, 'whether it is correct or not correct, it leads to a contradiction either way.'
However, if you include time in your thinking, the true nature of the paradox becomes visible. This is because there must be a temporal sequence where 'first there is a sentence, and then its truth or falsehood is judged.'
Let us consider the process of creating the sentence 'This sentence is not correct.' When we do, the temporal sequence is strange. It becomes something absurd, like 'judging the truth or falsehood of an incomplete sentence while it is still being written.'
In other words, it is like this: A paradox arises in logic because it does not include time, but if you include time, this sentence is an 'impossible sentence' because such a thing could never happen.
There is no rule without an exception.
If you try to create a 'rule' that says 'you must not create a rule without an exception,' this also becomes a paradox. If you try to apply this rule to all other rules, it means there is no exception to this rule, which is a contradiction. If you allow an exception to this rule, it means some other rule has no exception, which is a contradiction. Therefore, this rule is self-contradictory when treated logically.
And the reason why it becomes a paradox is that 'logic does not allow for exceptions.' If it did, logic itself could become a paradox. ... Hmm, this is getting complicated.
In other words, the mechanism is this: Logic judges things in a binary choice of 'true or false' and does not allow for anything in between. That is, logic is built upon the exclusion of 'degree.' Logic treats everything uniformly and does not allow for exceptions or possibilities. That is why the rule mentioned earlier becomes a paradox, but if you allow for degrees, exceptions, and possibilities, the paradox is resolved. For example, by saying 'exceptions may (or may not) be allowed,' or (as in defining laws in a constitution) by 'treating itself as an exception.'
The mechanism of paradoxes
Let us return to the first sentence, 'I am a liar.' The mechanism by which it becomes a paradox can also be attributed to the fact that 'logic excludes degree.' When thinking logically, we assume that 'a liar = someone who only says things that are not true and never says anything true' and 'an honest person = someone who only says things that are true and never says anything that is not true.' These are very unnatural assumptions when considered realistically, but it is only by assuming them that a paradox arises. If you grasp it with some breadth without going to such extremes, it does not become a paradox.
Logic is useful, but it has several weaknesses. Because of those weaknesses, things that are not paradoxes when thought about normally become paradoxes logically.
<Weakness No. 1> is that it cannot handle time. Therefore, it cannot handle change, sequence, or process. Logic is a temporally static system.
<Weakness No. 2> is that it cannot handle degree. Therefore, it cannot handle possibilities or exceptions. Logic is a system specialized for truth-value judgment and does not evaluate degrees.
The range that can be handled by logic is quite narrow.
◇ ◇ ◇
~ The mask of logical correctness ~
▷ There are four types of logic
▷ The mechanism of paradoxes
▷ Correct arguments are meaningless