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Are all true synthetic judgments satisfied?

I'm guessing not. But, equally, I wondered if it touches on any discussion. I am not sure what word to use instead of 'satisfied', so I'll illustrate instead.

  • First off, it doesn't seem to the the case for a priori analytic judgments. All bachelors are unmarried men, but perhaps there are no bachelors.

  • But what about synthetic a priori judgments? Every triangle consists of three angles adding up to 180 degrees. Does that mean that triangles do exist?

  • What about synthetic a posteriori judgments? If ophthalmologists are rich, does that mean there are rich people or that there are ophthalmologists?

I am especially concerned with the following judgments, which I think are both synthetic a priori:

  1. Everything that dies is born. Can we infer that there are some born things that die?
  2. At any future time, every self occurs after now. Can we infer that at any future time I occur after now?
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    See Existential import and Existential fallacy. The question is settled by convention, under the modern convention, existential statements cannot be inferred from universal ones. But the real issue in your examples is not whether ∃ can be inferred from ∀ (one can set up a system with existential import, after all, if one so pleases), but with whether either of them is true or a priori, which is very doubtful. – Conifold Dec 31 '21 at 09:50
  • hm I'm not sure about your last claim at all @Conifold why does it matter? –  Dec 31 '21 at 09:51
  • Because if you are concerned with the truth of boldfaced judgments the rest is irrelevant, and if not, only with the inferences, then the answer is pick your preference. – Conifold Dec 31 '21 at 09:56
  • I can't imagine new first one being a posteriori or the second being analytic. but both seem fairly certain: without having to rely on experience. idk. @Conifold I'm interested in finding stuff out anyway. thanks for the links anyway. the first is interesting / relevant, though perhaps not specific enough –  Dec 31 '21 at 10:00
  • I'm not saying that either bolded assertion is certain or apodicitic, but that they are likely and not due to my familiarity with the births of dying people, etc. I suppose perhaps implicitly, but that's confusing. besides which, the second assertion is very close to canonical synthetic a priori judgments, and I have no idea of how to prove it in the real world –  Dec 31 '21 at 10:10
  • On the other hand, it is easy to imagine both being false, and it is hard to see how the first is not a posteriori. An imaginary being can surely live for eternity of the past, and then die, just as it can be born and then never die. If there is any basis for "likely" here it is imported exactly from empirical familiarities. – Conifold Dec 31 '21 at 10:15
  • I definitely disagree with you if you think the second claim is a posteriori. empirical conceptions about shape etc. are a priori. the claim may be less robust, but hardly. anyway, it's a distraction from the question @Conifold i think I can imagine a man that does not act, so I'm unsure what difference it makes that we can imagine the prime mover dying –  Dec 31 '21 at 10:17
  • If you classify math theories as synthetic a priori (similar to Kant), then there're well-known consistent theories which are unsound, such as the theory of T=PA+¬Con(PA), the sentence ∃x(x+1=0) cannot be satisfied in the standard model of PA but it's clearly a theorem of T... – Double Knot Dec 31 '21 at 20:48

1 Answers1

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Kant is traditionally said to claim the "existential import" (which is the required quality here) of some judgments

This article reconstructs Kant’s view on the existential import of categorical sentences. Kant is widely taken to have held that affirmative sentences (the A and I sentences of the traditional square of opposition) have existential import, whereas negative sentences (E and O) lack existential import. The article challenges this standard interpretation. It is argued that Kant ascribes existential import only to some affirmative synthetic sentences.

https://philarchive.org/archive/VANKOE-3.

Reading this may help.

Both bolded claims look a bit like universal affirmative categorical assertoric judgments, as they do not include a negation, disjunction, conditional, possibility, necessity, particular or singular definition.

But it may not work out that way, because they are not expressed as F's are G's

Consistently with Kant’s “privileging of predication,” it is arguable that his logical forms are all either modifications or else truth-functional compounds of simple monadic (i.e.,1-place) categorical (i.e., subject-predicate) propositions of the general form “Fs are Gs.”

https://plato.stanford.edu/entries/kant-judgment/