Improved Squid Argument

[ruby sparks]

You might be wondering what kind of logic allows that, as it might not always accord with what a dictionary has to say. But, it’s in the tool belt of the logician and well respected the world over. It just takes a little getting used to.

I have to admit that I don't know what practical applications might be possible from an argument/process which is unsound and/or untrue, but still valid. But if I had to guess, I'd guess that there are many. There usually are when it comes to stuff that really brainy humans bother to do. Not always, I guess. But as I said, what those practical applications, if there care any, might be, I don't know. It's an interesting question. Perhaps some here who are more familiar with logic could suggest answers. Gotta have something to do with computers, I'm thinking. But presumably no computer function based on a valid line of 'computer logic' would execute unless the initial 'premise' (if that's the right term in computing) is true?

Off the top of my head I'm wondering, if, say, you really want a conclusion to be true, is it sometimes a matter of working backwards through the premises to see if there is any possible way to make them true? In other words, perhaps 'mere' validity is a stepping stone, or the first rung on a ladder?

 

[Angra Mainyu]

You might be wondering what kind of logic allows that, as it might not always accord with what a dictionary has to say. But, it’s in the tool belt of the logician and well respected the world over. It just takes a little getting used to.

I have to admit that I don't know what practical applications might be possible from an argument/process which is unsound and/or untrue, but still valid. But if I had to guess, I'd guess that there are many. There usually are when it comes to stuff that really brainy humans bother to do. Not always, I guess. But as I said, what those practical applications, if there care any, might be, I don't know. It's an interesting question. Perhaps some here who are more familiar with logic could suggest answers. Gotta have something to do with computers, I'm thinking. But presumably no computer function based on a valid line of 'computer logic' would execute unless the initial 'premise' (if that's the right term in computing) is true?

Off the top of my head I'm wondering, if, say, you really want a conclusion to be true, is it sometimes a matter of working backwards through the premises to see if there is any possible way to make them true? In other words, perhaps 'mere' validity is a stepping stone, or the first rung on a ladder?

For example, it is sometimes useful to find the consequences of some premises, in order to tell whether they are all true. If the consequences contradict something you know it's true, then that way you figure that one of the premises (at least) is false. This is also useful when you know that all of the premises are true except perhaps for one, and you're trying to figure out whether that one is true.

It's also a way of making arguments by reduction ad absurdum.

 

[A Toy Windmill]

I have to admit that I don't know what practical applications might be possible from an argument/process which is unsound and/or untrue, but still valid. But if I had to guess, I'd guess that there are many. There usually are when it comes to stuff that really brainy humans bother to do. Not always, I guess. But as I said, what those practical applications, if there care any, might be, I don't know. It's an interesting question. Perhaps some here who are more familiar with logic could suggest answers. Gotta have something to do with computers, I'm thinking. But presumably no computer function based on a valid line of 'computer logic' would execute unless the initial 'premise' (if that's the right term in computing) is true?

This is all exactly right and makes me happy.

The arguments being described in these threads are artificial. No-one, not even a mathematician, writes such arguments. A computer scientist does not write these arguments. And as you say, when we build computers that execute logical arguments, we design them so that they cannot execute the ones with false premises.

But...it happens that when we formalized logic into universal rules, those rules allowed an infinity of silly and artificial arguments. Many of these arguments are valid, but degenerately so, since no-one would ever make them. Many of us accept the formalized rules of validity, and so, by consistency, we are forced to accept an infinity of silly but valid arguments. It's not a ideal situation, and I'd rather we had a few elegant rules that kept in all the arguments we want and kept out all the silly ones, but that might not be achievable.

Angra Mainyu makes an excellent point about indirect proof. Every valid but unsound argument can be flipped to make a valid and sound argument, thereby showing that one of the original premises is false because the conclusion is false. In many logics, this is exactly how one proves a falsehood, by supplying a valid argument where the falsehood is used as a premise. Reductio ad absurdum.

In computing, such arguments are still never executed, but you will see them in some programming language code. The code is called "dead-code", precisely because it cannot execute. In most cases, dead-code is a bad thing, and the compiler will ask you to eliminate it. Sometimes though, dead-code is just part of a reductio proof, that is there to convince the compiler that the program is doing the right thing, because the wrong thing cannot be executed and is dead.

 

[fast]

You might be wondering what kind of logic allows that, as it might not always accord with what a dictionary has to say. But, it’s in the tool belt of the logician and well respected the world over. It just takes a little getting used to.

I have to admit that I don't know what practical applications might be possible from an argument/process which is unsound and/or untrue, but still valid. But if I had to guess, I'd guess that there are many. There usually are when it comes to stuff that really brainy humans bother to do. Not always, I guess. But as I said, what those practical applications, if there care any, might be, I don't know. It's an interesting question. Perhaps some here who are more familiar with logic could suggest answers. Gotta have something to do with computers, I'm thinking. But presumably no computer function based on a valid line of 'computer logic' would execute unless the initial 'premise' (if that's the right term in computing) is true?

Off the top of my head I'm wondering, if, say, you really want a conclusion to be true, is it sometimes a matter of working backwards through the premises to see if there is any possible way to make them true? In other words, perhaps 'mere' validity is a stepping stone, or the first rung on a ladder?

In everyday life, people are constantly saying or writing something. They communicate with us. Many times, they’re not merely purporting a truth or factual claim but also make either a very clear and obvious argument or one that is subtle and just beneath the surface. Either way, it’s not always the truth of what’s being said that is important but the flow of their logic. We might not even know what a particular widget is or can do (or we might not know the truth of something particular), but our ignorance of truth doesn’t stop us from seeing a fault in whether an argument flows properly.

I think being able to spot and properly analyze arguments gives us a real world advantage over those that cannot. Buy this car and you’ll be able to drive where you want. Didn’t you say you always wanted to visit Hawaii?

 

[Cheerful Charlie]

No elephant is a squid.
Joe is an elephant.

Joe then cannot be a squid.

Therefore, Joe is a squid
Any sort of "logic" that can conclude Joe is a squid is obviouslt flawed.

Let me try to persuade you otherwise.

Argument 3:

P1: No giraffe is an elephant.
P2: Joe is either a squid or a giraffe.
P3: Joe is an elephant.
C: Therefore, Joe is a squid.​

Is that valid?

Consider, for example, the following argument:

Argument 4:

P1: No giraffe is a mollusc.
P2: Joe is either a squid or a giraffe.
P3: Joe is an mollusc.
C: Therefore, Joe is a squid.​

If you take a look, you will see that Argument 4 and Argument 3 have exactly the same form. Before I go on, I would like to ask you whether you think Argument 3 and Argument 4 are both valid, or neither, or only one (depending on the answer, I might or might not try to convince you that the original OP argument is valid).

Joe is an elephant.
No elephant can be a squid.

Therefore Joe is either a giraffe or a squid is invalid.

Joe is defined as an elephant.

 

[fast]

No elephant is a squid.
Joe is an elephant.

Joe then cannot be a squid.

Therefore, Joe is a squid
Any sort of "logic" that can conclude Joe is a squid is obviouslt flawed.

Let me try to persuade you otherwise.

Argument 3:

P1: No giraffe is an elephant.
P2: Joe is either a squid or a giraffe.
P3: Joe is an elephant.
C: Therefore, Joe is a squid.​

Is that valid?

Consider, for example, the following argument:

Argument 4:

P1: No giraffe is a mollusc.
P2: Joe is either a squid or a giraffe.
P3: Joe is an mollusc.
C: Therefore, Joe is a squid.​

If you take a look, you will see that Argument 4 and Argument 3 have exactly the same form. Before I go on, I would like to ask you whether you think Argument 3 and Argument 4 are both valid, or neither, or only one (depending on the answer, I might or might not try to convince you that the original OP argument is valid).

Joe is an elephant.
No elephant can be a squid.

Therefore Joe is either a giraffe or a squid is invalid.

Joe is defined as an elephant.

You’re making a new argument that gives us reason to question the truth value of a premise in the old argument. You’re using information you know about elephants and squids to formulate:

No elephant can be a squid.

How about this:

P1: No G is an E.
P2: Joe is either an S or a G.
P3: Joe is an E.
C: Therefore, Joe is an S.

It’s not about truth. It’s about flow.

 

[Speakpigeon]

Just a thought. I may not be raising a valid point......

Is it confusing that argument 3 (above) and indeed the OP argument, are using categories (hope that's the right word) that are, in the real world, mutually exclusive (Joe can't in the real world be a squid and an elephant, given the definitions of what those are)?

Does it help if we use categories that aren't mutually exclusive?

P1: No tall person is a fat person.
P2: Joe is either a black person or a tall person.
P3: Joe is a fat person.
C: Therefore, Joe is a black person.​

Or am I talking shite?

All I can say is that it is easier for me to see how that's valid, I guess.

That's a good point but my argument, by having, broadly, categories that nearly all of us will see as true of the real categories of giraffes, elephants and squids, might skew the result in favour of "valid".

Much more likely, I think your suggestion would very likely skew the results in favour of "not valid", simply because inevitably some people will focus on the wrong claim that no tall person is a fat person (while ignoring that this is irrelevant to validity).

So, I'm being fair with the opposition ("shoot first, you bastard British", that sorts of thing).

Of course, your argument here is indeed valid, and obviously so (even if you have to look carefully at it), so the situation cannot be compared with my squid argument.

So, perhaps you may consider this one, which is the equivalent of my squid argument but with the first three premises rather obviously false, as per your requirement.

P1: No tall person is a fat person;
P2: No fat person is a black person;
P3: No black person is a tall person;
P4: Joe is either a black person or a tall person;
P5: Joe is a fat person;
C: Therefore, Joe is a black person.

I'm not sure why it would help since P1 to P2 make P4 and P5 hopelessly contradictory, which also makes the premises necessarily false. Having P1 to P3 false of themselves sort of introduces the confusion that the argument would be invalid because of the false first three premises. This is not my point. I specifically want people to consider an example of an argument with contradictory premises.

And we already have a clear majority who think the argument is not valid.
EB

 

[Speakpigeon]

Here is the Squid argument again, with improved wording following the suggestion from a specialist in mathematical logic (A Toy Windmill).

No squid is a giraffe
No giraffe is an elephant
No elephant is a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Thank you to vote to say whether you think the argument is valid or not.

Thanks for your answers.

Please no comment without vote.
EB

No elephant is a squid.
Joe is an elephant.

Joe then cannot be a squid.

Therefore, Joe is a squid
Any sort of "logic" that can conclude Joe is a squid is obviouslt flawed.

Thanks for explaining.
EB

 

[fast]

P1: No tall person is a fat person;
P2: No fat person is a black person;
P3: No black person is a tall person;
P4: Joe is either a black person or a tall person;
P5: Joe is a fat person;

C: Therefore, Joe is a black person.

Everything you gave us in bold is sufficient to get us to the underlined.
You gave me a lug wrench, a jack, and a spare tire. That’s all I needed to change the flat.

Granted, you also gave us a skill saw and a push lawn mower, and though appreciated, it was in the way, so I just sat it to the side. Don’t get me wrong; you still gave me everything to change the flat—everything I needed to change the tire was there.

 

[Speakpigeon]

You might be wondering what kind of logic allows that, as it might not always accord with what a dictionary has to say. But, it’s in the tool belt of the logician and well respected the world over. It just takes a little getting used to.

I have to admit that I don't know what practical applications might be possible from an argument/process which is unsound and/or untrue, but still valid.

The usefulness of using arguments with false premises to discuss validity is that it allows you consider validity in itself, without soundness to skew your reasoning soundness. Admitting that an argument with obviously false premises is valid has much more value than believing perhaps for the wrong reason that an argument with true premises is valid. Thus, the study of logic is best done with false premises, or indeed with mute variable names (such as A implies B). Aristotle didn't see that. He insisted on true premises. It's only later that the Stoics understood the usefulness of false premises. The Scholastics also understood this point that logic is best considered in the abstract. True premises may sometimes be a distraction.
EB

 

[Speakpigeon]

when we build computers that execute logical arguments, we design them so that they cannot execute the ones with false premises.

That would be one way to correct mathematical logic but no.

And computers work perfectly good with false premises.
EB

 

[fast]

No elephant is a squid.
Joe is an elephant.

Joe then cannot be a squid.

Therefore, Joe is a squid
Any sort of "logic" that can conclude Joe is a squid is obviouslt flawed.

Thanks for explaining.
EB

If most people have two legs, then elephants are squids
Most people have two legs
Therefore elephants are squids

I find that valid even though I know it’s false that elephants are squids.

 

[Speakpigeon]

But...it happens that when we formalized logic into universal rules, those rules allowed an infinity of silly and artificial arguments. Many of these arguments are valid, but degenerately so, since no-one would ever make them. Many of us accept the formalized rules of validity, and so, by consistency, we are forced to accept an infinity of silly but valid arguments. It's not a ideal situation, and I'd rather we had a few elegant rules that kept in all the arguments we want and kept out all the silly ones, but that might not be achievable.

God gracious, this shows conclusively you prefer to no understand logical validity at all to begin with. A logic with only "sensible" arguments would be less convincing. Basically, you're saying that the truth of the premises should be a condition for assessing the validity of arguments.

You're a mathematician?

Can you produce an example of a justification by professional logicians, i.e. mathematicians, philosophers, computer scientists etc., that ANY definition of validity used in mathematical logic is correct?
EB

 

[Speakpigeon]

P1: No tall person is a fat person;
P2: No fat person is a black person;
P3: No black person is a tall person;
P4: Joe is either a black person or a tall person;
P5: Joe is a fat person;

C: Therefore, Joe is a black person.

Everything you gave us in bold is sufficient to get us to the underlined.
You gave me a lug wrench, a jack, and a spare tire. That’s all I needed to change the flat.

Granted, you also gave us a skill saw and a push lawn mower, and though appreciated, it was in the way, so I just sat it to the side. Don’t get me wrong; you still gave me everything to change the flat—everything I needed to change the tire was there.

Yeah, except it's not deductive logic anymore.

What it is, I don't know. It may be always called "logic", sure, but like you would say "illogical logic". Is illogical logic logic? According to your logic here it is since it says "logic" in "illogical logic". So, a dead man is man. A married bachelor is a bachelor. Sure, it's fun. But, logical? No. It's dead beat idiotic. It's profoundly irrational. It makes God squirm. What did I do that it should go wrong now?! Millions of mathematicians alive today throughout the world have presumably been trained on this illogical logic. It's the lobotomy of mathematics. It makes mathematicians look like fools who can't make out where their mouth and their arse are. Although, at least now we know that as a fact. I almost got into mathematics. I liked it. Topology especially. But I couldn't make it so I'm the perfect drop out. Yet, here I am and I understand logic while professional mathematicians the world over, millions of them, don't. Ain't that ironic?! And 2,500 years after Aristotle pointed us to it. But mathematicians look at Aristotle's finger, not at logic. The fools. Intellectual workers, repeating what they have learnt at the kindergarten of logic, unable to think. Reason, yeah, sure. Give them axioms and they will work wonders. But thinking is above their pay grade. They wouldn't know how it's done, except, perhaps, for a very small number of them.
EB

 

[fast]

Its still deductive. Most people might put together a 200 piece puzzle. This is a three piece puzzle. If all my pieces are there to make the picture, bam, I can do it. You can put it together too. What’s weird about this is you’ve opened up your very own three piece puzzle set and threw two of your pieces onto my table.

So, here I am sitting with five pieces trying to make the picture on the box (the conclusion), so not only do I have to work out which pieces don’t belong, I have to put together the ones needed to make the picture. Thanks a lot!

Valid just means I can get to where I want with what I got. If that can happen, then there is a flow or path from premise world to conclusion world. The bridge can be built. That don’t make it sound, but it does make it valid.

Although, I haven’t counted you out yet, for if I’m reallly and truly supposed to utilize each and every premise and consider the impact in totality, then no, we can’t do as they teach us and have any sense of validity used by the untrained ones.

 

[Jimmy Higgins]

Here is the Squid argument again, with improved wording following the suggestion from a specialist in mathematical logic (A Toy Windmill).

No squid is a giraffe
No giraffe is an elephant
No elephant is a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Thank you to vote to say whether you think the argument is valid or not.

Thanks for your answers.

Please no comment without vote.
EB

It seems you don't understand what the word "valid" means.

 

[Cheerful Charlie]

No elephant is a squid.
Joe is an elephant.

Joe then cannot be a squid.

Therefore, Joe is a squid
Any sort of "logic" that can conclude Joe is a squid is obviouslt flawed.

Thanks for explaining.
EB

If most people have two legs, then elephants are squids
Most people have two legs
Therefore elephants are squids

I find that valid even though I know it’s false that elephants are squids.

It is not valid because it involves a non sequitur. Any "logic" that mindlessly accepts non sequitus like this is not an adequate logic for real world situations. It has no sanity checks for real world problems. It lends itself to "logical explosion". You can generate any amount of nonsense from a non sequitur.

 

[fast]

If most people have two legs, then elephants are squids
Most people have two legs
Therefore elephants are squids

I find that valid even though I know it’s false that elephants are squids.

It is not valid because it involves a non sequitur. Any "logic" that mindlessly accepts non sequitus like this is not an adequate logic for real world situations. It has no sanity checks for real world problems. It lends itself to "logical explosion". You can generate any amount of nonsense from a non sequitur.

If A, then B
A
Therefore, B

Seems to work out okay

 

[Cheerful Charlie]

Joe is an elephant.
No elephant can be a squid.

Therefore Joe is either a giraffe or a squid is invalid.

Joe is defined as an elephant.

You’re making a new argument that gives us reason to question the truth value of a premise in the old argument. You’re using information you know about elephants and squids to formulate:

No elephant can be a squid.

How about this:

P1: No G is an E.
P2: Joe is either an S or a G.
P3: Joe is an E.
C: Therefore, Joe is an S.

It’s not about truth. It’s about flow.

"Flow" is inadequate. It allows statements to contradict each other. Joe is an elephant. Or Joe is a giraffe or a squid. Two different and self contradictory propositions accepted as true. Obviously that can't be true.

This is not a new problem. In the middle ages, logicians accepted that contradictions could lead to logical explosion. That is nonsense creates more nonsense. We cannot divorce form from content.

It is like dividing by zero. If in an algebraic formula, an expression is essentially equal to dividing by zero, that is an unallowable error.

 

[Angra Mainyu]

Joe is an elephant.
No elephant can be a squid.

Therefore Joe is either a giraffe or a squid is invalid.

Joe is defined as an elephant.

There is no premise that no elephant can be a squid, and the meaning of the word "elephant" does not contain such claim, either, but this is not relevant. The issue is whether the conclusion follows from the premises. Suppose you have the following premises:

Premise 1: Joe is an elephant.
Premise 2: Every elephant is a squid.
Conclusion: Joe is a squid.
​

The conclusion here clearly follows from the premises. Of course, in this case, at least the second premise is false. But that is not the point. Rather, the point is that the conclusion follows from the premises on account of the form of the argument. We do not need to assess whether the premises are true in order to realize that, in this case, the conclusion follows from the premises. Similarly, my examples above are examples of arguments in which the conclusion follows from the premises.