I don't know what you mean by "minimal inconsistency guard". — TonesInDeepFreeze
specialized sense of consistency ― that P and ~P are inconsistent, for any P — Srap Tasmaner
you can say A and B are inconsistent if A → C and B → ~C. — Srap Tasmaner
unless you want to start with the Sheffer stroke — Srap Tasmaner
we need both consistency and consequence as core ideas — Srap Tasmaner
any given idea (claim, thought, etc.) has a twin that is the one thing guaranteed under no circumstances to follow from it — Srap Tasmaner
We have that. — TonesInDeepFreeze
We already have: — TonesInDeepFreeze
We define consistency from provability. — TonesInDeepFreeze
Why is that lacking? — TonesInDeepFreeze
How do you know there is only one thing? — TonesInDeepFreeze
Set theory is needed for the rest of math and so is logic — Srap Tasmaner
let the negation of C(P) be N(P) — TonesInDeepFreeze
Much of classical math existed before the introduction of set theory. — jgill
Might be interesting to adduce a formal sentence and demonstrate somehow that it can't be said in English alone (not just that all known attempts failed). — TonesInDeepFreeze
The support relation is also notoriously tricky to formalize (given a world full of non-black non-ravens), so there's a lot to say about that. For us, there is logic woven into it though:
"Billy's not at work today."
"How do you know?"
"I saw him at the pharmacy, waiting for a prescription."
It goes without saying that Billy can't be in two places at once. Is that a question of logic or physics (or even biology)? What's more, the story of why Billy isn't at work should cross paths with the story of how I know he isn't. ("What were you doing at the pharmacy?")
As attached as I've become, in a dilettante-ish way, to the centrality of probability, I'm beginning to suspect a good story (or "narrative" as Isaac would have said) is what we are really looking for. — Srap Tasmaner
Well, the thing is, deducibility is for math and not much else. — Srap Tasmaner
Candidly, there can't be any sensible doubt that the argument in the OP is valid for formal propositional logic. So in order for those who claim it is invalid to be correct, there must be more than one form of validity, and hence logical pluralism follows. — Banno
If P then not P
P
Not P
This is valid and not sound, but also not coherent. — Hanover
If I went to the store, I did not go to the store, and I went to the store, so I did not go to the store." That is valid, but meaningless. I have no idea what you did, whether you went to the store, didn't go to the store, and I can't understand how your going to the store made you not go to the store." — Hanover
The incoherently true statement is also distinct from the vacuously true statement. As in, "if Tokyo is in Spain, then the Eiffel Tower is in Bolivia." There the antecedent cannot ever be satisfied — Hanover
if I've misunderstood this — Hanover
It isn't meaningless. We have an idea of what it would be to go to the store, and not to go to the store. Yep, you can't do both.As in, "If I went to the store, I did not go to the store, and I went to the store, so I did not go to the store." That is valid, but meaningless. — Hanover
there can't be any sensible doubt that the argument in the OP is valid for formal propositional logic. So in order for those who claim it is invalid to be correct, there must be more than one form of validity, and hence logical pluralism follows. — Banno
what is the logical structure of an argument, in contrast to its syntax, grammar, and semantics. — Banno
Your challenge could be taken as: Provide a definition such that any language is exactly one of: formal and informal. — TonesInDeepFreeze
Perhaps one might ask, is that designation arbitrary? Why this sentence rather that that one? Is there more, such that the designated sentence is in addition a Logical Consequence (whatever that is) of the others?An argument is a non-empty set of sentences with exactly one of the members designated as the conclusion. — TonesInDeepFreeze
my hunch is that we cannot provide any such clear cut distinction — Banno
uncountable number of formation rules — Banno
Perhaps one might ask, is that designation arbitrary? — Banno
supose we have the sentences {p, q, r} and designate r as the conclusion. Is that an argument, or is there something more, such that in addition, r is the "logical consequence" of {p.q}? — Banno
relevant logic — Banno
Given the explanation, can we deduce that Billy is not at work? — Leontiskos
There is deduction in math and logic; everyone else has to make do with induction, abduction, probability. — Srap Tasmaner
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
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