The OP's question was not about ordinary English at all. — Srap Tasmaner
And, yes, the equivalence is per the material conditional. — TonesInDeepFreeze
English as a meta-language regarding formal logic. In that meta-language, 'if then' is taken in the sense of the material conditional. — TonesInDeepFreeze
Any argument with inconsistent premises is valid, according to Tones. Weird indeed. It requires a strained reading of the fine print of portions of definitions of validity, taken out of context. Earlier posters usefully leveraged the word "sophistry."
(Note that this is different from the modus ponens reading of the OP and it is different from the explosion reading of the OP. The effect of explosion requires explicit argumentation. The OP, for example, is susceptible to explosion, but it is not wielding explosion. Tones is just doing a weird, tendentious, definitional thing.) — Leontiskos
I think, though, we can allow a somewhat negative connotation because reliance in argumentation on degenerate cases is often inadvertent or deceptive. "There are a number of people voting for me for President on Tuesday [and that number happens to be 0]." — Srap Tasmaner
"Therefore, an argument with contradictory/inconsistent premises cannot have a false conclusion while the premises are true" [Paraphrase of Tones] — Leontiskos
"a major topic in the study of deductive logic is validity. This is a relationship..." — TonesInDeepFreeze
That is the second time you put quotes around words I didn't say. — TonesInDeepFreeze
"A sentence Phi is a consequence of a set of sentences Gamma if and only if threre are no interpretations in which all the sentences in Gamma are true and Phi is false." (Elementary Logic - Mates)
"An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false." (The Logic Book - Bergmann, Moor and Nelson). — TonesInDeepFreeze
Oh. So then any argument that has no true premises is valid. That's weird. — frank
There is no question. He does not presuppose it. — TonesInDeepFreeze
I did not claim that validity requires that there is no interpretation in which the premises are all true. — TonesInDeepFreeze
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
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
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
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
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
analogous predication — Count Timothy von Icarus
I don't know what you mean. — TonesInDeepFreeze
Well, while I think Srap has a good point about our being able to live without A→~A in most situations, I think it is important that statements like "nothing is true," are able to entail their own negation—that logic captures how these claims refute themselves. — Count Timothy von Icarus
It may seem bizarre that a valid argument could have at least one premise that is necessarily false at first glance, but I think it is fairly intuitive if one thinks in terms of truth-preservation. If the premises were true, it would preserve truth. But the "truth" of a false premise cannot be preserved.
And it's a good thing that it is valid because we often can reason from necessarily false conclusions in valid arguments to identifying false premises. — Count Timothy von Icarus
It may seem bizarre that a valid argument could have at least one premise that is necessarily false at first glance, but I think it is fairly intuitive if one thinks in terms of truth-preservation. — Count Timothy von Icarus
...prioritizing truth-functional process over logical telos. — Leontiskos
Yes. I edited that post. It's just weird that any argument that can't have all true premises is going to be valid. — frank
As I said, in this particular regard, I'm merely applying the definitions of ordinary formal logic. — TonesInDeepFreeze
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
Just trying to think of real world examples of a formula like "A → ~A", likely dressed up enough to be hard to spot. Excluding reductio, where the intent is to derive this form. What I want is an example where this conditional is actually false, but is relied upon as a sneaky way of just asserting ~A.
I suppose accusations of hypocrisy are nearby. "Your anti-racism is itself a form of racism." "Your anti-capitalism materially benefits you." "Your piety is actually vanity." — Srap Tasmaner
A→B
B→~A
A
∴ B — Leontiskos
I'm sure there are more convoluted ways to go about it, but does that satisfy your objection? — Hanover
Only arguments are valid, and "A, therefore A," is not an argument. Argument, at the very least, involves rational movement. — Leontiskos
Another argument:
A -> ~A
A
therefore A
valid — TonesInDeepFreeze
The losing party, in one sense, grants that they lost, but continues in the competitive spirit, which means they have to shift ground from whether they "officially" or "technically" lost to whether that was a "real" loss, or whether there had a been a "real" competition in the first place. — Srap Tasmaner
As Banno notes, validity is determined by asking if the conclusion flows from the premises, and so he argues under mp, it does, so it is valid.
The wiki cite adds criteria, namely (1) that the negation of the conclusion cannot also flow from the premises for validity and (2) the premises under any formulation must also reach the same conclusion. — Hanover
But it's not validity we usually disagree over, but soundness, and inconsistent premises make valid inferences unsound. — Srap Tasmaner
I find this particularly unconvincing as respects "afterlife" beliefs because many ancient visions (and the dominant modern vision) of the afterlife seem significantly more unpleasant than just ceasing to exist. — Count Timothy von Icarus
I don't think it's that hard to define at all. — Count Timothy von Icarus
Their argument is roughly that the intuitive/informal notion of logical consequence is multiply-realizable (granted it is more technical in its details). — Count Timothy von Icarus
Were debating whether to call certain formulations "modus ponens." — Hanover
The basic idea is "formally correct but misleading". Akin to sophistry. Or to non-cooperative implicature, like saying "Everyone on the boat is okay" when it's only true because no one is left on the boat and all the dead and injured are in the water. — Srap Tasmaner
Nor do I. What about stimming? — fdrake
The intentionality associated with stimming is not toward the stim source, it's a means of the body coordinating to produce a regulated and focussed state. — fdrake
I suppose where the above gets complicated is that being able to stim like that allows a form of stimming play, which is what Baggs is doing. — fdrake
The structuralist approach is to see the signifiers as forming a system, the whole group of them, and what's important is just that they can be and are distinguished from each other, a "system of differences" . — Srap Tasmaner
On the typical road maps I look at, towns and cities are indicated by circles, filled circles of different sizes and stars (for capitals). — Srap Tasmaner
If you look at formal approaches to language -- Frege, Tarski, Montague, that sort of thing -- language is a system for representing your environment. That could, conceivably, be just for you. A language of thought.
And it is only because you can put the world, or some part of it, into language, that it is useful for communication. When you communicate, you put part of the world into words (or claim to) and pass those words to someone else. Language as descriptor of the world underlies language as means of communication. — Srap Tasmaner
One way of telling the story of Western philosophy over the last few centuries is to present it as the rise and fall of a particular view of language. Gradually, piecemeal, the idea of language as primarily a matter of accurate naming and information-sharing has yielded to a recognition of language as what we could call a matter of orienting ourselves in our world—developing a range of diverse strategies for collaboration in finding our way around. The more complex the world we encounter (in introspection as well as observation), the more diverse and sophisticated will be those strategies, and the less they will have to do with carving up our environment into bite-sized pieces with definitive labels. Whatever a still over-con dent popular scientism claims, coping adequately and sustainably with our environment requires more than a catalog of isolated substances with fixed attributes. — Rowan Williams, Romantic Agenda
Reality is what's interesting here -- what I don't want to do is define reality within my logic, though. And I don't think that logic needs to restrict itself to objects since reality is not composed of objects and objects only -- it also contains sentences. — Moliere
As I see it right now the objection is — Moliere
I've asked you if you'd accept a defense of dialetheism, the belief that there are true contradictions, as a basis for making the inferences that there is more than one logic. — Moliere
Marx and Hegel are philosophers which, like the liar's, utilizes contradiction in their reasoning. — Moliere
Which was a counterpoint to the idea that one cannot hope to recognise whether something is a language unless one already speaks it. — fdrake
Calling it a language with a spoken component (the humming) when it's produced by someone who as a premise of the video cannot communicate in spoken language is hopelessly reductive and easily refutable. And for the purpose of normalising autism no less. — fdrake
Is it not language unless the meaning relation is conventional rather than natural? The traditional answer is obviously "yes" but I'm not so sure. Especially if you wonder how language could get started in the first place. — Srap Tasmaner
If it's not absolutely essential, then what's the relation here? Is it the other way? That is, conventional meanings as a subset of linguistic meaning? That looks to be the story with writing. (Or with the use of natural gestures, like folding your arms, to indicate an attitude.) Are there counterexamples? Any cases of conventional but non-linguistic meaning? — Srap Tasmaner
The obvious example was right in front of me: cartographic symbols. While there is obviously structure in the way these are placed on the map, that structure is not grammatical. — Srap Tasmaner
One way of "problematizing" the concept of language would be to step back and ask, "What am I/we trying to do by offering the Wikipedia page definition of language?" — J
I understand why you might think that, but sign language just is language. Children who are deaf will, if put together in groups, develop sign language just as they would regular language, in the same way, along the same developmental axis, and with the same resulting richness of potential expression. Body language is nothing like sign language or spoken language. It doesn't fulfil the basic criteria I provided earlier, but sign language does (including e.g. distinct linguistic units that can be recombined to produce new meanings, and indicate grammatical categories, such as case, tense, voice, mood etc). — Baden
Is that the kind of answer you were looking for? — Srap Tasmaner
Whether the picture is being used as a picture or a sign. — Srap Tasmaner
Further reply with example.
Sometimes maps for children will have little pictures. At Paris, a little Eiffel Tower; at South Dakota, a little Mount Rushmore. Here the picture is a straightforward representation of a thing, but used by a sort of metonymy to mean the whole place where that thing is. So in such a case, both. — Srap Tasmaner
I mean, it depends, right? — Srap Tasmaner
For instance, semiotics has been brought up here. But on the wider Augustinian/Peircrean view of semiotics, all sorts of things are semiotic, so that isn't all that informative on as to language. — Count Timothy von Icarus