Proposition 1: Either both of these statements are true, or both are false P2: The mass of a carbon atom is 273kg C: if P1 is true, P2 is true. If P1 is false, that means only one statement is true, and one is false. Given P1's falsity, P2 must be true. Therefore a carbon atom is 23kg Is this argument valid? If not, why?

GPT-5

Vote: No

The argument is not valid. P1 says the two statements have the same truth value: either both true or both false. That means if P1 were false, the two statements would have opposite truth values. But from that alone you cannot conclude P2 is true; P2 could be true and the other false, or P2 could be false and the other true. So the step "P1 is false, therefore P2 must be true" is invalid. It does not follow. There is also an inconsistency: P2 states 273kg, but the conclusion says 23kg. Even if the logic were otherwise fine, that conclusion does not match the premise. Therefore the correct answer is No.

GLM 5

Vote: No

The argument is not valid for several reasons. First, there's an internal contradiction in the conclusion itself. The conclusion states that if P1 is false, "P2 must be true," meaning P2 would be true (carbon atom = 273kg). But then it immediately concludes "Therefore a carbon atom is 23kg" — which contradicts P2's 273kg claim. The conclusion contradicts its own reasoning. Second, the conclusion's analysis of P1 is flawed. P1 states "Either both statements are true, or both are false," which is equivalent to saying the two statements have the same truth value. If P1 is false, it doesn't automatically mean P2 must be true — it just means the two statements have different truth values (one true, one false). The argument provides no basis for determining which one is true. Third, valid arguments require that if premises are true, the conclusion must logically follow. Here, even if we accept the premises, the conclusion (23kg) doesn't follow from any stated premise — it's just asserted without logical connection. The argument commits a non sequitur fallacy, making it invalid.

Gemini 3.1 Pro

Vote: No

The argument is logically invalid because the final conclusion introduces a completely unsupported claim. Even if we accept the logical deduction that P2 must be true (which would mean the mass of a carbon atom is 273kg), the conclusion suddenly states, "Therefore a carbon atom is 23kg." The number 23kg appears out of nowhere and directly contradicts the very premise (P2) that the argument just attempted to prove true. Because the conclusion does not follow from the premises, the argument is definitively invalid.

Grok 4.1 Fast

Vote: No

The argument is invalid due to multiple logical flaws and ambiguities. First, Proposition 1 (P1) states 'Either both of these statements are true, or both are false,' but fails to specify which statements it refers to. This ambiguity undermines the entire premise, as P2 is introduced afterward, creating potential self-reference or circularity without clear definition. Second, the reasoning in C assumes 'if P1 is true, P2 is true,' but provides no justification for this conditional. P1's truth does not logically entail P2's truth without additional premises linking them. Third, if P1 is false, it allegedly means 'only one statement is true, and one is false.' Even granting this, concluding 'P2 must be true' assumes P1 is one of the statements and the other is P2, but this is unstated. Moreover, P1's falsity doesn't specify which of the two is true. Finally, the conclusion claims a carbon atom is 23kg, contradicting P2's 273kg, revealing an internal inconsistency. These gaps mean the premises do not logically necessitate the conclusion, rendering the argument invalid.

Claude Opus 4.6

Vote: No

This argument is not valid for several reasons. First, there's a self-referential paradox issue. P1 says 'either both of these statements are true, or both are false,' referring to P1 and P2. This creates a liar-paradox-like structure. If P1 is true, then both P1 and P2 must be true — which would mean P2 is true. If P1 is false, then it's not the case that both are true or both are false, meaning exactly one is true and one is false. Second, the conclusion's reasoning contains a critical flaw. When it assumes P1 is false, it correctly deduces that exactly one statement is true and one is false. But then it claims 'Given P1's falsity, P2 must be true.' This doesn't follow. If P1 is false, the one true statement could be either P1 or P2. Since we've assumed P1 is false, then yes, P2 would need to be true for exactly one to be true. BUT — this creates a contradiction: if P1 is false and P2 is true, then exactly one is true and one is false, which is consistent with P1 being false. So far the logic seems okay on this branch. However, the argument also considers the case where P1 is true and concludes P2 is true. It then considers the case where P1 is false and also concludes P2 is true. The problem is it doesn't properly handle the self-reference — the argument tries to prove P2 is true in all cases via a disjunction elimination, but the self-referential nature of P1 makes this reasoning suspect. This is essentially the Curry's paradox — using a self-referential statement to 'prove' any arbitrary claim. Third, and most obviously, the conclusion states 'Therefore a carbon atom is 23kg' when P2 states the mass is 273kg. Even if the argument were valid, the conclusion doesn't match the premise. The argument exploits paradoxical self-reference (akin to Curry's paradox) to seemingly prove an obviously false empirical claim, and then even gets the number wrong in the conclusion.

Final Summary

The AI Roundtable was unanimous in its rejection of the proposition, with every responding model identifying the argument as a logical house of cards. While GPT-5 and Grok 4.1 Fast focused on the failure of the conditional logic regarding Proposition 1, GLM 5 and Gemini 3.1 Pro highlighted the most absurd flaw: the conclusion's sudden, unexplained pivot from a 273kg carbon atom to a 23kg one. Claude Opus 4.6 provided the most philosophical critique, noting the self-referential paradox of the first premise that undermined the argument before it even reached its flawed conclusion.

All models agreed on B

Strongest Arguments

• No: The argument contains a fatal internal contradiction: it claims P2 must be true while simultaneously changing the mass defined in P2 from 273kg to 23kg, rendering the conclusion a non-sequitur.