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All truths are relative, and this is the only absolute principle.

wrote August Comte.

Anyway a radical relativism poses a serious problem: if every truth is always relative, is the latter an absolute truth?

(R) Self-refutation of Relativity:

(1) All truths are relative.

(2) If (1) is true, the truth of (1) is not relative, then (1) is false.

(3) If (1) is false, the truth is not always relative.

From the truth of (R), it follows that (1) "every truth is relative" is always false.

But:

Refutation of (R):

(4) It is possible to adopt an axiomatic system where the truth value of (R) changes,

(5) Therefore (R) is not always true, and consequently (1) "every truth is relative" is not always false.

Is it correct?

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A more correct rendering of Comte's "absolute principle" would be

All truths are relative, except if they are statements about truths, and this is the only absolute principle.

Since this "reformed absolute principle" is a statement about truths, it explicitely exceptuates itself from its own domain.

I suspect that Comte knew that, but liked the paradox for rhetorical reasons.

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  • "All truths are relative, except if they are statements about truths". But thiis is a truth about statements: thus it must be relative. Aug 30 '18 at 6:13
  • No, Mauro: all truths are relative, except if they are statements about truths. So, statements about truths may not be relative. And since "All truths are relative, except if they are statements about truths" is a statement about truths, it may be not relative. Aug 30 '18 at 12:36
  • @Luís Henrique The answer does a great job in explaining the context (as the quote was by August Comte and if what he meant was different then the quote is no more useful) but I am afraid I feel that your answer still doesn't answer OP's question. What he seems to ask is : whether it is right to infer that there exists atleast one absolute truth from the given statement and that question still remains unanswered. May 10 '20 at 18:37
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How can adopt a different axiomatic system? That's trying to replace the logic we all know with a different, made-up logic? If not then this still falls into the problem of "is (4) and (5) true?". If you did then that still means (1) isn't always true since its truth value could change according to (4)(if (R)'s truth value changes then (1)'s truth value does too) so the problem is still there. Regardless, choosing an "axiomatic system that makes that false statement a true one" doesn't prove anything since you need a common ground to prove something and logical statements work because logic is a common ground so picking an axiomatic system you only agree on just means that (4) is relative meaning (1) is relative(since for others who apply logic without this axiomatic system have that (R) is true therefore (1) is false) which again just proves it's false.

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