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Induction allows us to use the existential quantifier, deductions allows us to add the universal quantifier. If we want to say something about the world, we are
by scoofy 11y ago
Induction allows us to use the existential quantifier, deductions allows us to add the universal quantifier. If we want to say something about the world, we are bound to empiricism, thus our deductive claims rest upon our inductive evidence. This is a framework. Any use of the universal quantifier (necessary for a negative claim), is unsupported by our empirical data. This is essentially Popper/Hume.
- Retra 11y agoThat's one model of the process. Another is that the distinction between negative and positive claims is entirely artificial, and that there are really only "claims" and the truth of them is determined by their effectiveness at constructing reliable models of reality. And thus any demonstration of self-contradiction is a disprove of a claim, whether negative or not.
- scoofy 11y agoNegative and positive claims are not artificial or equivalent, one is making a claim about positive existence, the other is making claims about lack of existence. Of course we can manufacture the universal quantifier insofar as it's a mapping of the existential quantifier. That is to say, proving something is "not nonexistent" is not a statement that requires the universal quantifier, it's a claim that has simply mapped the equivalency of the existential quantifier, using the universal one. This is still only a statement about positive knowledge.
- deleted 11y ago[deleted]