In natural language, predication is often not totally univocal, but is also not totally equivocal. — Count Timothy von Icarus
For example, we might say that "lentils are healthy," or "running is healthy." These are true statements. And we might also say "Tones is healthy." Yet you would not be "healthy" in the same way that lentils are. — Count Timothy von Icarus
However, neither is the usage totally equivocal. We call lentils "healthy" precisely because (normally) they promote the health of human beings, i.e. the same "health" we refer to in "Tones is healthy." — Count Timothy von Icarus
It's sort of like how, as far as I am aware, there is no popular formalization of the distinction between quia vs. propter quid demonstrations (i.e. demonstrating "that something is the case," vs. demonstration "why it is the case.") I don't think most people would deny that they're different (although some would), but rather it seems that the difference should be entirely reliant on the arguments' content, not their form (i.e. an issue of material logic). — Count Timothy von Icarus
analogous predication — Count Timothy von Icarus
I don't know what you mean. — TonesInDeepFreeze
I can give you a story that comes to mind in which I'd assert something like that -- say I'm commiserating with a coworkers frustration about George not being as reliable as we'd like, even though he's a good enough fellow. — Moliere
The substitution is there only because the OP starts with A -> ~A and asks for validity, so substitution seems to work as a model for the sarcastic talking. I agree that the person speaking sarcastically does not in any way mean these logical implications, though -- it's only an interpretation of everyday speech to try and give some sense to the original question that's not purely formal. — Moliere
I would think
'that it is the case' is a matter of giving an argument
but
'why it is the case' is a matter of exposition, not argument
Knowledge of the fact (quia demonstration) differs from knowledge of the reasoned fact (propter quid demonstrations). [...] You might prove as follows that the planets are near because they do not twinkle: let C be the planets, B not twinkling, A proximity. Then B is predicable of C; for the planets do not twinkle. But A is also predicable of B, since that which does not twinkle is near--we must take this truth as having been reached by induction or sense-perception. Therefore A is a necessary predicate of C; so that we have demonstrated that the planets are near. This syllogism, then, proves not the reasoned fact (propter quid) but only the fact (quia); since they are not near because they do not twinkle, but, because they are near, do not twinkle.
The major and middle of the proof, however, may be reversed, and then the demonstration will be of the reasoned fact (propter quid). Thus: let C be the planets, B proximity, A not twinkling. Then B is an attribute of C, and A-not twinkling-of B. Consequently A is predicable of C, and the syllogism proves the reasoned fact (propter quid), since its middle term is the proximate cause.
From Aristotle's Posterior Analytics I.13:
I answer that it must be said that demonstration is twofold: One which is through the cause, and is called demonstration "propter quid" [lit., 'on account of which'] and this is [to argue] from what is prior simply speaking (simpliciter). The other is through the effect, and is called a demonstration "quia" [lit., 'that']; this is [to argue] from what is prior relatively only to us (quoad nos). When an effect is better known to us than its cause, from the effect we proceed to the knowledge of the cause. And from every effect the existence of its proper cause can be demonstrated, so long as its effects are better known to us (quoad nos); because since every effect depends upon its cause, if the effect exists, the cause must pre-exist.
From St. Thomas' Summa theologiae I.2.2c:
In this case, there is no interpretation in which all the premises are true. — TonesInDeepFreeze
A premise is defined as an analytic truth. It cannot be false, regardless of its synthetic falsity. If C means "Cows bark," it is irrelevant if they don't for the purposes of formal logic.
Put differently, the notion of validity assumes a truth-functional context where truth and form are entirely separable. Yet when we think deeply about inferences themselves, such as modus ponens, truth and form turn out to be less separable than we initially thought. When we stop merely stipulating our inferences and ask whether they actually hold in truth, things become more complicated.
A premise is defined as an analytic truth. — Hanover
An argument without premises is not a syllogism. — Hanover
the OP is not a valid argument because it's not an argument at all. — Hanover
tautology or contradiction — Count Timothy von Icarus
An argument is valid if and only if there are no interpretations in which all the premises are true and the conclusion is false.
In this case there are no interpretations in which all the premises are true. Perforce, there are no interpretations in which all the premises are true and the conclusion is false. So the argument is valid. — TonesInDeepFreeze
What you've done is imported the artificial truth-functionality of the material conditional into the consequence relation itself. You have contradicted ↪Hanover's "flows from." You are effectively saying, <Any "argument" with nonsense premises is "valid."> — Leontiskos
As I said, in this particular regard, I'm merely applying the definitions of ordinary formal logic. — TonesInDeepFreeze
Ordinary formal logic does not define the consequence relation as identical to the material conditional. — Leontiskos
An argument is valid if it would be contradictory (impossible) to have the premises all true and conclusion false. In calling an argument valid, we aren’t saying whether the premises are true. We’re just saying that the conclusion follows from the premises – that if the premises were all true, then the conclusion also would have to be true. — Gensler, Introduction to Logic, Second Edition, p. 3
What is surprising is that the concept of validity turns out to be equivalent to another concept (deducibility)... — Enderton, A Mathematical Introduction to Logic, p. 89
A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises.
...
...the argument is valid [when] the conclusion follows deductively from the premises... — Logical Consequence | SEP
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. — Validity | Wikipedia
TonesInDeepFreeze wants to say that an argument is definitionally/trivially valid if it its premises cannot all be true (i.e. if it is inconsistent). — Leontiskos
An argument is valid if and only if there are no interpretations in which all the premises are true and the conclusion is false.
In this case there are no interpretations in which all the premises are true. Perforce, there are no interpretations in which all the premises are true and the conclusion is false. So the argument is valid. — TonesInDeepFreeze
Here is Gensler speaking about validity in his introductory chapter:
An argument is valid if it would be contradictory (impossible) to have the premises all true and conclusion false. In calling an argument valid, we aren’t saying whether the premises are true. We’re just saying that the conclusion follows from the premises – that if the premises were all true, then the conclusion also would have to be true.
— Gensler, Introduction to Logic, Second Edition, p. 3 — Leontiskos
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.[1] It is not required for a valid argument to have premises that are actually true,[2] but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. — Validity | Wikipedia
Here is Enderton:
What is surprising is that the concept of validity turns out to be equivalent to another concept (deducibility)
— Enderton, A Mathematical Introduction to Logic, p. 89 — Leontiskos
↪TonesInDeepFreeze - Wrong again:
An argument is valid if and only if there are no interpretations in which all the premises are true and the conclusion is false.
In this case there are no interpretations in which all the premises are true. Perforce, there are no interpretations in which all the premises are true and the conclusion is false. So the argument is valid.
— TonesInDeepFreeze — Leontiskos
And with the argument mentioned in the original post, it is the case that there is no interpretation in which all the premises are true. — TonesInDeepFreeze
the argument is valid [if] the conclusion follows deductively from the premises... — Logical Consequence | SEP
And the argument is valid by Gensler, Enderton, SEP and Wikipedia. — TonesInDeepFreeze
Gensler:
"An argument is valid if it would be contradictory (impossible) to have the premises all true and conclusion false."
It is impossible to have both A -> ~A and A true. Perforce, it is impossible to have the premises all true and the conclusion false. — TonesInDeepFreeze
An argument is valid if it would be contradictory (impossible) to have the premises all true and conclusion false. In calling an argument valid, we aren’t saying whether the premises are true. We’re just saying that the conclusion follows from the premises – that if the premises were all true, then the conclusion also would have to be true. — Gensler, Introduction to Logic, Second Edition, p. 3
The question is whether we should read Gensler as presupposing that the premises are consistent. — Leontiskos
A consequence relation is not established by your, "The premises are inconsistent..." — Leontiskos
If there is no interpretation in which all the premises are true, then there is no interpretation in which the premises are all true and the conclusion is false. — TonesInDeepFreeze
you are turning the consequence relation into a material conditional, and claiming that inconsistent premises trivially show an argument to be valid in the same way that the false antecedent of a material conditional trivially shows the conditional to be true. — Leontiskos
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