I get that, but a 3 permits explosion, which can force anything anywhere. — Hanover
Deduction should allow you to pass, by valid inference, from what you know to what you did not know. Yes?
In mathematics, these elements are well-defined. What do we know? What has been proven. How do we generate new knowledge? By formal proof.
Neither of these elements are so well-defined outside mathematics (and formal logic, of course). There is no criterion for what counts as knowledge, and probably cannot be. And that defect cannot be made up by cleverness in how we make inferences.
I see no reason to question the traditional view. "Our reasonings concerning matters of fact are merely probable," as the man said. There is deduction in math and logic; everyone else has to make do with induction, abduction, probability. — Srap Tasmaner
Deduction should allow you to pass, by valid inference, from what you know to what you did not know. Yes? — Srap Tasmaner
Can we say the conclusion is valid or do we reserve the term "valid" only to argument forms and not to conclusions? — Hanover
Are you claiming that knowledge does not exist outside mathematics? I don't see why "the elements being less well-defined" results in any serious problem here. — Leontiskos
It's not raining and it's raining therefore it's not raining.. So yeah, it's "incoherent" in that its premises are inconsistent.
— Michael
Accepting that definition of "incoherent," — Hanover
we have (1) valid and coherent arguments and (2) valid and incoherent arguments [and] (3) valid and sound arguments and (4) valid and unsound arguments. — Hanover
Would you agree that:
A. All 3s are 1s, but not all 1s are 3s?
B. All 2s are 4s, but not all 4s are 2s.
C. No 1s or 3s are 4s or 2s.
D. No 4s or 2s are 1 or 3s. — Hanover
Arguments can be:
1. Valid, consistent, and sound
2. Valid, consistent, and unsound
3. Valid, inconsistent, and unsound
4. Invalid — Michael
No 3 is a 4 because no argument can be both valid and invalid.
— Michael
I get that, but a 3 permits explosion, which can force anything anywhere. — Hanover
Can we say the conclusion is valid or do we reserve the term "valid" only to argument forms and not to conclusions? — Hanover
(C) and (D) are WRONG (see below). — TonesInDeepFreeze
"that's a valid conclusion" — Hanover
That's ambiguous. It could mean two things: — TonesInDeepFreeze
Of course. Nice.there's no such thing as an uncountable recursive set. — TonesInDeepFreeze
Cool. So we have {p, q, r} with r designated as the conclusion, and that's an argument, and then in addition if it is a valid argument, r is also the logical consequence of {p, q}. Thanks for clearing this up.No, because that would be defining 'valid argument', not 'argument' in general. — TonesInDeepFreeze
We're actually debating what terms each of us can make up and the best terms that would describe whatever we're trying to say. — Hanover
What I mean by "incoherent" is that which is "expressed in an incomprehensible or confusing way; unclear." — Hanover
"Gloobelfooble" could indeed be a statement, inasmuch as A can be statement and Q can be a statement.
If Gloobelfooble, then Q
Gloobelfooble
Q — Hanover
You have a preference for the model-theoretic account of logical consequence, if I've understood aright. — Banno
The SEP article notes "One of the main challenges set by the model-theoretic definition of logical consequence is to distinguish between the logical and the nonlogical vocabulary" — Banno
"the admissible models for a language"The "Tonk" argument undermines proof-theoretical accounts by showing them to be arbitrary. — Banno
Yeah, I baulked at that too.But I don't know what it means to say "all sets are in the real world". — TonesInDeepFreeze
But these seem ad hoc to me... I may be just misunderstanding them.The specific relationship between introduction and elimination rules as formulated in an inversion principle excludes alleged inferential definitions such as that of the connective tonk, — Proof-Theoretic Semantics
If an epistemological theory leads us to think we don't know anything, isn't that just evidence that the theory has gone astray?While I think it's defensible to say that "knowledge does not exist outside mathematics," I don't think I have to, to show the difficulty. — Srap Tasmaner
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