Validity of a simple logical argument

What's keeping you from voting? Fear of committing yourself?
EB

 

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OK, so we have for now two "valid", and probably two "not valid".

Good point but you can't cherry-pick the premises. You have to assume all of them true.

The Devil is in the details. There are subtle differences between the various definitions that float on the Internet. So, here is what Wikipedia gives as definition of validity:

So, not quite what you posit yourself and I think there's a difference. Tell me if you can spot it.

I saw once a philosopher explain that if the result of an inference was a contradiction, you needed to question your assumptions. There was a contradiction, he could see it, he was able to explain how one could solve it by questioning one's assumption, and yet could do that himself.
As I understand what you say here, there's a contradiction. You can see it. You implicitly admit to it. So, what are you going to do about it? Or are you going to live with it?
EB

 

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Sure - I was merely pointing out how a cursory view might lead one to assume invalidity of the argument.

Yes, yes, it needs to be of a form that makes it impossible, rather than just specific examples that happen to make it impossible. But we both knew what was meant, and thus no harm.

I'll live with it because the argument has no value to me beyond identifying that it is valid, and why it is valid. I have no interest in resolving the contradictions.

 

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But the contradiction I meant was between you're expressed impression that the argument is not valid and your explicit inference from the definition of validity that the argument is valid.
Still, if you can live with that, fine.
EB

 

The expressed impression was simply by way of explaining how it might appear to be invalid, before I went on to explain how it is actually considered valid. The only contradiction that arises is of that between any correct answer and incorrect answer. Since I know which is which in this case, it is of no concern to me.

 

terms
you failed to define the meaning of the word "logically valid" as it pertains to reasoned debate logic
the abstract 1st year philosophy deals with a reasoned argument.
however "logic" as pure logic is math.
using the term "valid" with "logic" removes the example from "reasoned debate forms of "philosophy"
into applied mathematical reasoning of Logic as a deductive tool.

logical validity has been lost by the last sentence

Is this argument logically valid?

no it has defied logic in its applied validity.
because it is invalid for

you become illogical by stating joe is an elephant. this makes the next statement illogical and invalid.

i think you may be missing the cut n thrust of the long form of the explanation of the supposition of premise for reasoning of an argument by applying logic. logic having validity is like mathematics having equations.

had you just asked "is it valid" then as Baldee points out it would be a different question and the rules would be different

 

Yes, but Joe cannot be tall and short at the same time.
Or be an elephant and a squid at the same time.
I guess that was too obscure for you.

 

But I have a giraffe named Joe.

 

Do you keep him in an aquarium?
Does he have a trunk?

 

How did you know?

 

I am very "perceptive".........(oops..., that belongs in another thread)............

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OK, OK, I am an empath, I confess.............

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But,
I saw a squid (cuttlefish) once who disguised himself as an elephant, trunk and all. Come to think of it, he had a very long neck as well. Overall very small though.
Must have been watching too much small screen tv. Crocodile Dundee...

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I know "down under" they don't have elephants or giraffes, but they do have cuttlefish.
And TV.......

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The set of premises in the OP appear to be mutually contradictory.

Sarkus says (and Baldeee agrees, as do I):

The Wikipedia article on the paradoxes of material implication agrees with Sarkus' wording, putting it this way:

"Validity is defined in classical logic as follows: An argument (consisting of premises and a conclusion) is valid if and only if there is no possible situation in which all the premises are true and the conclusion is false."

This definition has some very counter-intuitive consequences, such as the 'Principle of Explosion'.

https://en.wikipedia.org/wiki/Principle_of_explosion

For those who don't know, this is the principle in classical logic that one can derive anything from a contradiction. It can be easily shown why that is, see the Wikipedia article in the link above for a very simple proof.

This is one of several Paradoxes of Material Implication, where classical logic produces very counter-intuitive results. This happens because implication in natural language and in classical logic are understood differently.

https://en.wikipedia.org/wiki/Paradoxes_of_material_implication

Wikipedia says,

"The root of the paradoxes lies in a mismatch between the interpretation of the validity of logical implication in natural language, and its formal interpretation in classical logic...

The paradoxes of material implication arise because of the truth-functional definition of material implication, which is said to be true merely because the antecedent is false or the consequent is true. By this criterion, "If the moon is made of green cheese, then the world is coming to an end," is true merely because the moon isn't made of green cheese. By extension, any contradiction implies anything whatsoever, since a contradiction is never true."

So that if a set of premises contains any contradiction, then every statement that one can possibly formulate according to the syntactic rules of one's logical system becomes a theorem. The whole thing explodes in a shower of wffs.

Addressing this has motivated some of the more interesting developments in 20th century formal logic and a number of the newer non-classical logics such as Relevance Logic.

Wikipedia:

"Relevance logic aims to capture aspects of implication that are ignored by the "material implication" operator in classical truth-functional logic, namely the notion of relevance between antecedent and conditional of a true implication."

https://en.wikipedia.org/wiki/Relevance_logic

Relevance Logic is an example of a Paraconsistent Logic.

https://en.wikipedia.org/wiki/Paraconsistent_logic

Wikipedia:

"A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent (or "inconsistency-tolerant") systems of logic...

The characteristic or defining feature of a paraconsistent logic is that it rejects the principle of explosion. As a result, paraconsistent logics, unlike classical and other logics, can be used to formalize inconsistent but non-trivial theories."

Logical systems that can prevent contradictions from exploding have lots of possible real life applications, ranging from computer science to quantum logic.

 

Well, seems I was not that confused about the OP after all, .....

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There seems to be a concensus forming among "learned fellows".
Yippeeee....

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p.s. EB, I need not know the formal descriptions of "logic". All I need is to understand the concept, ok?
In a mathematical universe logical values and logical functions create all there is.

 

p.s. did you know cuttlefish are cross-dressers?

https://www.mnn.com/earth-matters/animals/blogs/5-amazing-facts-about-strange-beautiful-cuttlefish

I think this is cool....

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You haven't explained at all "how it might appear to be invalid". You've explicitly said it appears invalid.
You said "It certainly doesn't seem to be (valid) on the surface". And you also said the validity of the argument is "a rather counter-intuitive result of such a definition of validity".
So, it seems clear to me that for you the argument is intuitively invalid. You voted valid explicitly to comply with your interpretation of the definition.

Not exactly. You explained how the argument "is to be considered valid" given the definition of validity.

I don't think so. There's no correct answer as such because the question in this thread is whether the argument is valid, not whether it is valid according to the particular definition of validity you're using. So, all you can claim is that the argument is to be considered valid given the definition of validity. For this answer to be correct, you would at least need to know that the definition you used is itself correct. But who says it is correct. People. Aren't you "people" yourself?
So, as I see it, and it seems undeniable, there is a contradiction between you intuition, which says "invalid", and the definition of validity, which seems to you to say "valid". And it can only be a contradiction between two different parts of your own brain. Nobody else is involved here. So, should you trust you intuition which says "invalid", or should you trust your interpretation of a definition, which says "valid"?

You don't know which is which because nobody knows. You claim you know merely to be consistent with your choice to go with the definition despite your intuition telling you otherwise.
EB

 

So, the logical validity of an argument is whether the logic of the argument can be trusted or believed.
I'm sure this notion of logical validity applies to any argument, although I would agree that this may not really be a concern in mathematical logic.

I'm quite sure Aristotle's syllogisms are logically valid, not just valid.

De Morgan explained it all:

Does the conclusion follow if the premises be true.
Not so different from Aristotle:

So true...

I agree there are two different views of validity, mainly that of most philosophers and that of most mathematicians, at least those who have a view at all.
But the cut isn't between "validity" and "logical validity", the cut is between what philosophers and what mathematicians want to achieve with logic.
Thanks, I find your contribution helps to clarify the question of validity.
EB

 

No, it is clear to me that it is obscure to you how logic works. You cannot reason about the validity of an argument if you assume anything more than what the premises say.
You should learn to discipline yourself. You need to be able to read an argument without adding anything to the premises.
EB

 

Given your post, I take it you didn't vote because, again, you don't know what to vote...
Does the argument, on the face of it, seems valid to you?
If you can answer this question you can vote.
EB

 

FFS. You just look for disagreement, don't you, even when there is none to be had. You seem to have conveniently ignored: "and indeed if you only consider the syllogism made up of premises 3, 5, and the conclusion, then that syllogism would be invalid" as an example of how it might appear invalid.
I have also not explicitly state that it appears invalid. I stated that it doesn't seem to be on the surface - i.e. cursory glance, e.g. just picking a few of the premises upon which to make one's judgement etc. Once you do look beneath that cursory glance it appears logically valid, according to the definition of logical validity.

I voted that it is logically valid because it is logically valid. That is the question you asked in the OP. That is the question I answered.

And given the definition it is valid. Thus it is to be considered valid. I'm not in the habit of saying things are to be considered one thing if they're not.

In the OP you specifically asked about logical validity. In logic, validity has the particular definition I gave - or words to that effect, as far as I am aware. If you wish to ask about other notions/definitions of validity, however, feel free to offer them up.

I am but a user of the definition, not an arbiter. If you want to change what it means to be logically valid, because it leads to counterintuitive results, by all means go for it. I'll stick with the contextual definition that has been used from before I was born, and still used, and just go from there. If you want to offer up an alternative definition for logical validity...?

There may well be a contradiction for those that aren't aware of the meaning of validity in logic, and that it differs to the one we may otherwise intuitively have based on more colloquial usage. Once you realise that there is a difference there is no contradiction, merely a matter of applying the right notion in the right context. Do that and you avoid contradiction.

There may have been such a contradiction when first I was taught about this, many years ago, when I couldn't resolve the difference in notions. But the contradiction was resolved some time ago, thanks, and duly compartmentalised.

I do know which is which, thanks. You asked about logical validity. Validity has the definition to the effect as previously stated. You have an alternative definition of what it means to be logically valid?
Of course, if you had just asked "is it valid?" in the OP then you'd be right to raise question about which notion of validity. Your question was with regard logical validity. But if there is an alternative definition of logical validity, by all means present it, and I will have learnt something new today.

 

It initially looked invalid to me, because I was thinking of a subtly different definition of validity. My (incorrect) version was something like: 'An argument (premises and conclusion) is valid iff, when all the premises are interpreted as being true, the conclusion must also be true.' Using that definition, if the premises are contradictory, then the premises can't possibly all be true. Hence the argument couldn't be valid.

I was about to triumphantly write that it was invalid when I read your post. That backed me up a bit and I went to Wikipedia to see which definition of validity was correct (in terms of classical logic).

(Hey, it's been many years since I studied logic at a university. I'm pretty vague on this stuff these days...)

Wikipedia agreed with your and Baldeee's version. Namely: 'An argument is valid if and only if there is no possible situation in which all the premises are true and the conclusion is false'. Which sounds like my version, but isn't. The correct version is volatile and explodes when contradictions appear in the premises.

So I decided to go with your and Baldeee's judgement that it is valid (if exceedingly counterintuitive, one of the 'paradoxes of material implication'). If the premises are mutually contradictory, then anything can be derived from them.