Consider the statement, "There exists at least one true statement." Is a demonstration of the truth of this statement possible, which does not assume the statement's truth? If so, what is that demonstration? If not, does it then follow that certain knowledge - that is, knowledge that is conscious of itself as knowledge - is impossible?

Comments

The truth of "There is at least one true statement" (*) follows logically from the claim that "S is a true statement" (**), where S is some particular statement. So if we could establish (**) without presupposing the truth of (*), we would have answered your first question affirmatively. Let S be the statement "There is a pen on my desk now." Observation tells me that S is true. It seems that I can know that S is true, i.e., that (**) is the case, without the need to assume that (*) is the case. Hence, I can establish the truth of (*) in a non-circular fashion.

It's important to avoid a certain confusion here. One might say, about Alex's argument, that if there does not exist at least one true statement, then of course "There is a pen on my desk now" is not itself a true statement; hence the argument is circular. Of course, the first part is true; but the conclusion does not follow. For the argument to be circular, the claim "There is at least one true statement" would need to be used in that argument, but it is not. What is used in the argument are simply (analogues of) the following two premises: (i) snow is white; (ii) if snow is white, then "snow is white" is true. Alex claims to know (i) by observation; it's less obvious how we know (ii), but one who claims to know it seems on pretty firm ground. From (i) and (ii), then, it follows that "snow is white" is true and so, by a simple logical inference, that there is at least one true statement (viz, "snow is white"). To challenge this argument, one must either challenge (i) or (ii) or one must find fault with the reasoning used.

'All statements are false' is necessarily false, so there is at least one true statement.

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