When Carl Linnaeus classifed animals into mammals, bird, reptiles, amphibians, etc. it wasn't the case that he knew, beforehand, what these various classes of animals were - he began by collecting specimens, studying them, looking at anatomical characteristics that were similar or dissimilar and these classes of animals emerged from that study. Carl Linnaeus didn't possess a criterion for the various classes of animals before he classified them - the criterion emerged from his studies of animals. — TheMadFool

The criterion didn't emerge, the definition of each animal was expanded to include the species. How is this example different in principle from saying, for example, if X is red then X is coloured? If X is a bear, then X is a mammal? At best, I think you've injected the problem of the ontological status of universals (abstract categories) into what you've presented as an epistemological dilemma.

I stand by the transcendental argument that, since knowledge is self-evidently a reality, it cannot be impossible to achieve knowledge. Knowledge means you believe something and what you believe is true. If a belief is false, then it is refutable. If it is not false, then it is not refutable.

Nothing irreparably wrong with most of that, but the point is being overlooked, in that the original PC claims knowledge is impossible. Knowledge herein pertaining not of things, but knowledge itself. In order to refute the PC, the negation of it must be demonstrated. We don’t need to prove we know about things, we only need to prove we have the capacity for knowledge, the things being whatever they may. It follows that rudimentary mathematical concepts are sufficient to justify the possibility of knowledge, because it is we ourselves who create the predicates mathematics employs. The added bonus being, that experience serves as the apodeictic proof that these definitive inventions are sound, and thus it is that we can prove our capacity for knowledge beyond its mere possibility.

Still, the vagueness you mentioned arises, in that the conditions under which mathematical concepts themselves are possible, being given from the very same notion of categories already mentioned, yours of the empirical kind, mine of the rational, remains valid, but for all that, nonetheless theoretically plausible. And when facts are absent, as is always the case with epistemological speculation, all that’s left to work with, is theory.

The criterion didn't emerge, the definition of each animal was expanded to include the species. How is this example different in principle from saying, for example, if X is red then X is coloured? If X is a bear, then X is a mammal? At best, I think you've injected the problem of the ontological status of universals (abstract categories) into what you've presented as an epistemological dilemma.

I stand by the transcendental argument that, since knowledge is self-evidently a reality, it cannot be impossible to achieve knowledge. Knowledge means you believe something and what you believe is true. If a belief is false, then it is refutable. If it is not false, then it is not refutable. — Pantagruel

You mean to say that Carl Linnaeus knew, beforehand, what mammals/birds/reptiles/amphibians are? But the characteristic defining qualities (the criterion) of what these various classes of animals are were developed after he took note of how these classes of animals were alike and unlike.

You get these kinds of false conundrums if you dont factors in Innate knowledge. Innate ideas.
If knowledge is Description then it makes no sense to suggest we start off with "zero Description" or a blank slate.

You mean to say that Carl Linnaeus knew, beforehand, what mammals/birds/reptiles/amphibians are? But the characteristic defining qualities (the criterion) of what these various classes of animals are were developed after he took note of how these classes of animals were alike and unlike. — TheMadFool

Linnaeus did not create the taxonomic structure, he only described it. And he could be wrong. Alternate taxonomies may also apply.

In one word: Essentialism.

@Shawn Essentialism is essential!
I would say essentialism is like a minimal or necessary description. Necessary qualities. I say this because the platonic or aristotelian
essentialism is nonsense. Just positing unobservsble abstract entities.

. To know The Problem Of The Criterion is to know the truth of the propositions that constitute it or are entailed by it. — TheMadFool

You might be well acquainted with the problem without knowing the truth of it. A logical argument can be deemed valid and yet not validated.

You might be well acquainted with the problem without knowing the truth of it. A logical argument can be deemed valid and yet not validated. — apokrisis

Well, that's true about particular individuals but surely you won't deny that knowing The Problem Of The Criterion involves, in terms of justified true belief theory of knowledge, the justification, the truth, and belief in re the propositions in The Problem Of The Criterion and the propositions that can be inferred from it.

Linnaeus did not create the taxonomic structure, he only described it. — Pantagruel

Of course he didn't create the taxonomic structure but the point is there were no compelling prior reasons, i.e. there was no pre-existing criterion, that guided Linnaeus in the classifcation scheme he developed. As far as I know, the terms mammals/reptiles/aves/amphibians didn't exist, as a criterion of categorization, before Linnaeus did his thing.

Well, that's true about particular individuals but surely you won't deny that knowing The Problem Of The Criterion involves, in terms of justified true belief theory of knowledge, the justification, the truth, and belief in re the propositions in The Problem Of The Criterion and the propositions that can be inferred from it. — TheMadFool

Again, if I don’t accept that criterion, the problem as stated doesn’t exist for me. Just because a paradox can be proposed and accepted as such doesn’t mean one is trapped. It means one is demonstrably better off considering the alternatives.

@apokrisis@Pantagruel

What about the contradiction if one opts for skepticism?

1. If I know The Problem Of The Criterion then I know I can know nothing (premise 1)

2. If I know I can know nothing then I know I can't know The Problem Of The Criterion (premise 2)

3. If I know The Problem Of The Criterion then I know I can't know The Problem Of The Criterion (1, 2 HS)

4. If I know I can't know The Problem Of The Criterion then I don't know The Problem Of The Criterion

5. I know The Problem Of The Criterion (assume)

6. I know I can't know the Problem Of The Criterion (3, 5 MP)

7. I don't know The Problem Of The Criterion (4, 6 MP)

8. I know The Problem Of The Criterion AND I don't know The Problem Of The Criterion (contradiction)

9. I don't know The Problem Of The Criterion (5 to 8 reductio ad absurdum)

Basically, The Problem Of The Criterion is unknowable :chin:

There seems to be an embedded contradiction in The Problem Of The Criterion viz. that it claims, at one moment that

1. Propositions can't be true prior to the existence of a criterion (hence the need for a criterion)

and the next moment it claims that

2. Propositions have to be true prior to the existence of a criterion (hence the Problem Of The Criterion) — TheMadFool

@apokrisis@Pantagruel

Again, if I don’t accept that criterion, the problem as stated doesn’t exist for me. Just because a paradox can be proposed and accepted as such doesn’t mean one is trapped. It means one is demonstrably better off considering the alternatives. — apokrisis

Precisely. This problem isn't for any kind of a pragmatic epistemology. :up: