On what can be true and false

Statements can be true or false, because there are false statements. For example, if I state that “I went to a shop yesterday”, but actually didn’t, then this statement is false.

Things of a kind can’t, however, be true or false, because there are no false things of a kind. For example, there are no false bears, false trees of life or false Higgs particles.

The reason for this difference is that the number of statements is infinite, since the number of words is infinite, whereas the number of things of a kind is finite, since the number of things is finite, meaning that all things must be either true things of a kind or false things of a kind if “finiteness” is different from “infinity”. There simply can’t be both true and false things of a kind, because it would mean that there is one thing that is both a true thing of a kind and a false thing of this kind at the same time, since it would conflate “finiteness” and “infinity” (see Russell’s paradox). (Instead, there are actually different kinds of infinity: countable and uncountable.)

It means that a search for “the true tree of life” and “Higgs particle” is vain per definition. If such things indeed could be found, then the definitional foundation for the search for them would instead be wrong. A simpler expression of this paradox is that the logical basis for the search conflates the concepts “finiteness” and “infinity”, or simpler that it searches for what it, itself, decides.

Only statements can thus be true or false, BUT excluding statements asserting that a certain thing is a true or false thing of a kind, because such statements are inconsistently self-confirming (ie, both self-contradictory and untestable).


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