Hence, we have a counterexample to PAP.
This appears to be a counterexample to P2.
It is obviously a counterexample to any such argument.
This claim, as Parfit allows, is vulnerable to counterexample.
A single counterexample refutes a conjecture as effectively as ten.
This latter kind of case would be a counterexample to (Individuative).
But each improvement seems to simply bring a clever new apparent counterexample.
Would it continue until a rigorous deductive proof of the counterexample is constructed?
Ackermann's paper was the starting point of Kreisel's 1951 “no-counterexample” interpretation of arithmetic.
The model-centered approach to logical consequence takes the validity of an argument to be absence of counterexample.
As the footnote on p. 527 shows, he believed that the set of all propositions is a counterexample to Cantor’s theorem.
So the sentence is odd because it is a counterexample to the generalization that anyone who contradicts himself utters a contradiction.
A further counterexample to RCT, related to the immediately previous one, is that randomness is indifferent to history, while chance is not.
A weak counterexample shows that we cannot at present prove some proposition, but it does not actually refute it; in that sense, it is not a counterexample proper.
Philosophers dissatisfied with this conclusion have continued to search for a propensity definition of fitness that is counterexample-free and not schematic or generic in Brandon’s sense.
They require us to improve the proof, to unearth the “hidden lemma” which the counterexample also refutes, so that it becomes a “local as well as global” counterexample—see (3), below.
The possible existence of such non-qualitative properties as explanations of numerical distinction between substances can be made plausible by considering a famous counterexample to the identity of indiscernibles suggested by Max Black.
There is an asymmetry that was pointed out by Martin, namely, that a definable counterexample to CH is a real counterexample, while no matter how far one proceeds in verifying definable versions of CH at no stage will one have touched CH itself.
For if KML-randomness of a sequence entails its unpredictable generation, then every counterexample to RCT which involves KML-randomness without chance will also involve unpredictability without chance, and also constitute a counterexample to CTU.
Finally, to defeat the objection that merely apparent objects do not produce functional causal results, Vasubandhu provides the memorable counterexample of a wet dream, in which an evident, physical result is produced by an imagined sexual encounter with a nonexistent lover.
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