a notion of "follows from," — Leontiskos
Well, what do we say here ― leaving aside whether color exclusion is a tenable example? What you're after is a more robust relationship between premises and conclusions, something more like grasping why it being the case that P, in the real world, brings about Q being the case, in the real world, and then just representing that as 'P ⇒ Q' or whatever. Not just a matter of truth-values, but of an intimate connection between the conditions that 'P' and 'Q' are used to represent. Yes? — Srap Tasmaner
Validity is a relationship between premises and conclusion. This is what I say is the common interpretation of your sources on validity:
1. Assume all the premises are true
2. See if it is inferentially possible to make the conclusion false, given the true premises
3. If it is not possible, then the argument is valid
...
...validity is an inferential relationship between premises and conclusion. — Leontiskos
I encourage respectful discussion of these topics by all parties. — NotAristotle
I have learned — NotAristotle
Now the question arises: is it invalid? I don't claim that. — Leontiskos
What you're after is a more robust relationship between premises and conclusions, something more like grasping why it being the case that P, in the real world, brings about Q being the case, in the real world, and then just representing that as 'P ⇒ Q' or whatever. Not just a matter of truth-values, but of an intimate connection between the conditions that 'P' and 'Q' are used to represent. Yes? — Srap Tasmaner
validity is about deducibility — Leontiskos
I don't even need to advert to real-world cases — Leontiskos
an argument is supposed to answer the "why" of a conclusion — Leontiskos
I don't claim to have academic definitions of 'univocal' and 'equivocal', but at a naive level, as I'm merely winging it here, it seems to me that:
'totally univocal' is redundant. An expression is univocal if and only if it has one meaning. That's total.
'totally equivocal' is hard to conceive. An expression is equivocal if and only if it has more than one meaning. What would it mean to say it is totally equivocal?
Not sure what you mean by this.
Tones' argument:
An argument is valid when it is not possible for the conclusion to be false while the premises are true
An argument with contradictory/inconsistent premises cannot have (all) true premises
Therefore, an argument with contradictory/inconsistent premises cannot have a false conclusion while the premises are true
Therefore, an argument with contradictory/inconsistent premises is valid. — Leontiskos
Tones is talking about assignment or inconsistency, not necessary falseness. — Leontiskos
This is what I say is the common interpretation of your sources on validity:
1. Assume all the premises are true
2. See if it is inferentially possible to make the conclusion false, given the true premises
3. If it is not possible, then the argument is valid — Leontiskos
Your interpretation — Leontiskos
Your interpretation changes the ordering of the conjunction and condition — Leontiskos
You want to say that if we cannot assume that all the premises are true (on pain of contradiction), then the argument is valid by default. — Leontiskos
we don't need an additional implication operator ― that is, one that might appear in a premise, say, and another for when we make an inference. — Srap Tasmaner
Propositional logic deals in propositions. Your piece has the form of a modus ponens, but doesn't deal in propositions. That makes it interesting in several ways. But "not-a" is pretty well defined in propositional logic, in various equivalent ways. And by that I mean that the things we can do with negation in propositional logic are set. There are not different senses of "not-A" in propositional calculus.I think it shows that 'not-A' has at least two different senses. — Janus
is not an example of 'not-A', nor of propositional logic, although it is a striking example of the creativity of language.1.Life therefore death
2.Life
Therefore
3.Death. — Janus
I don't know what you mean. Example? — TonesInDeepFreeze
1. A → ¬A
2. A ⊢ ¬A
3. A ⊨ ¬A
4. A ∴ ¬A — Michael
I affirm that it is valid by any of these considerations:
(1) Apply the definition of 'valid argument'.
— TonesInDeepFreeze
And that is the option we are talking about, nitpicker.
— Leontiskos
Three options have been given: modus ponens, explosion, and the definition of validity. TonesInDeepFreeze's is the latter, — Leontiskos
From the post you sidestepped:
Your interpretation is mistaken because validity is an inferential relationship between premises and conclusion. You would establish an inferential relationship without examining the inferential structure and relations. To say, "The premises are contradictory, therefore an inferential relationship between premises and conclusion holds," is to establish an inferential relationship without recourse to inferential relations.
— Leontiskos — Leontiskos
The sources I cited include a notion of "follows from," which obviously excludes Tones' approach of relying on the degenerative case of the material conditional. When A is false (A→B) is true, but B does not follow from A. — Leontiskos
As Enderton notes, validity is about deducibility. — Leontiskos
It is not merely about truth values. — Leontiskos
As Enderton notes, validity is about deducibility. It is not merely about truth values. It is about the inferential relationship between premises and conclusion. In order to show that Q follows from P, we have to show how Q is correctly inferred from P, and we need to have evidence that ~Q cannot also be inferred from P. — Leontiskos
A key contention of mine is that I am representing the notion of validity in formal logic better than Tones is. — Leontiskos
It is not valid since there are interpretations in which the premises are true but the conclusion is false. — TonesInDeepFreeze
A sad thread, this one. A low point in the history of the forums. — Banno
I guess you mean there are interpretations where the sentences are uttered in a context where they could be true. — frank
I don't know what you mean. Example? — TonesInDeepFreeze
https://en.wikipedia.org/wiki/Proof_by_contradiction — Hanover
This is what I say is the common interpretation of your sources on validity:
1. Assume all the premises are true
2. See if it is inferentially possible to make the conclusion false, given the true premises
3. If it is not possible, then the argument is valid — Leontiskos
But how is that "checking the validity of one argument using another"? — TonesInDeepFreeze
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