Improved Squid Argument

[Angra Mainyu]

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.

Yes, you got it right.

 

[fast]

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.

I changed the argument. I’m just using letters. I’m trying to put a pause on the obstacle that distracts. You are hung up on truth. The elements or parts of the equation for an argument to be sound needs to be compartmentalized. Look at sheer validity alone.

An animal cannot be both an elephant and a squid, but to speak of that is to speak about what cannot be true. We are looking to see if what is given leads to the conclusion, but don’t let knowledge of what’s true or false interfere.

So,

If I tell you that Joe is a Squam (C), you might not know what that is and ask how I know. I say to you because he’s an elequam (P3). Next, you’re like, okay, I don’t know what that is either but feel you need more to go on. After all, given that Joe is an elequam (whateve that is) hardly seems to be enough information to lead you to think therefore he’s a squam. See, I’m stripping the baggage away. If I tell you Squam is code for Squid and elequam is code for elephant, you’ll mix truth into your assessment of the arguments validity. Keep them separate.

 

[Cheerful Charlie]

"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.

I changed the argument. I’m just using letters. I’m trying to put a pause on the obstacle that distracts. You are hung up on truth. The elements or parts of the equation for an argument to be sound needs to be compartmentalized. Look at sheer validity alone.

An animal cannot be both an elephant and a squid, but to speak of that is to speak about what cannot be true. We are looking to see if what is given leads to the conclusion, but don’t let knowledge of what’s true or false interfere.

So,

If I tell you that Joe is a Squam (C), you might not know what that is and ask how I know. I say to you because he’s an elequam (P3). Next, you’re like, okay, I don’t know what that is either but feel you need more to go on. After all, given that Joe is an elequam (whateve that is) hardly seems to be enough information to lead you to think therefore he’s a squam. See, I’m stripping the baggage away. If I tell you Squam is code for Squid and elequam is code for elephant, you’ll mix truth into your assessment of the arguments validity. Keep them separate.

Since we know Joe cannot be a squid and an elephant, we know that is a malformed series of propositions.

Substituting mere letters or symbols in a set of propositions does not change the issue. Without a sanity check on what propositions are accepted as definitions, nonsense can result even if the form is seemingly logical and correct. Since we cannot evaluate mere symbols, that does not solve the problem casting it into that form. It does not supply a true sanity check on propositions we are reasoning about. That then is meaningless as it does not solve the basic problem of how we should treat propositions such as Joe is an elephant and Joe is a squid, though it is clear that by definition Joe cannot be both.

Garbage in, garbage out.

 

[fast]

"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.

I changed the argument. I’m just using letters. I’m trying to put a pause on the obstacle that distracts. You are hung up on truth. The elements or parts of the equation for an argument to be sound needs to be compartmentalized. Look at sheer validity alone.

An animal cannot be both an elephant and a squid, but to speak of that is to speak about what cannot be true. We are looking to see if what is given leads to the conclusion, but don’t let knowledge of what’s true or false interfere.

So,

If I tell you that Joe is a Squam (C), you might not know what that is and ask how I know. I say to you because he’s an elequam (P3). Next, you’re like, okay, I don’t know what that is either but feel you need more to go on. After all, given that Joe is an elequam (whateve that is) hardly seems to be enough information to lead you to think therefore he’s a squam. See, I’m stripping the baggage away. If I tell you Squam is code for Squid and elequam is code for elephant, you’ll mix truth into your assessment of the arguments validity. Keep them separate.

Since we know Joe cannot be a squid and an elephant, we know that is a malformed series of propositions.

Substituting mere letters or symbols in a set of propositions does not change the issue. Without a sanity check on what propositions are accepted as definitions, nonsense can result even if the form is seemingly logical and correct. Since we cannot evaluate mere symbols, that does not solve the problem casting it into that form. It does not supply a true sanity check on propositions we are reasoning about. That then is meaningless as it does not solve the basic problem of how we should treat propositions such as Joe is an elephant and Joe is a squid, though it is clear that by definition Joe cannot be both.

Garbage in, garbage out.

Of course nonsense can result. That’s why we deny that the argument is sound.

It’s going to take more than me speeding to get a speeding ticket. There’s also going to have to be an officer out there doing his job. A sound argument requires both true premises and valid form. If you don’t have one without the other, you don’t have a sound argument.

We’re trying to look at the constituent parts independently. Why? Because not only can we have a deductive argument with true premises but bad form, we can also have a deductive argument with good form but false premises.

Moreover, obviously, there’s four possibilities:

1 all true premises (and valid form)
2 all true premises (and invalid form)
3 not all true premises (and valid form)
4 not all true premises (and invalid form)

Notice that number one is the only sound possibility. If (if, I say) all premises are true, and if the form is engineered such that what follows must, then the conclusion is guarenteed to be true. The argument we’ve been dealing with is valid. But, that’s not the biggest deal on the block. Accepting an argument as valid isn’t to embrace it as trustworthy. It’s not the great award winning prize that we can place high stakes in.

Too often, people want to deny validity when the argument is clearly loony or flawed. The flaw (oh yes, it’s there), but it has to do with the obvious falsehoods of the premises —which makes it unsound, not invalid.

By the way, and this may serve to confuse more than help, but in the sense we’re using valid and invalid, it doesn’t apply to nondeductive arguments. While it’s true that you’ll see dictionaries define “invalid” as “not valid,” it’s explanatorily inadequate. It’s subtle but I think worthy of attention.

Nondeductive arguments are neither valid nor invalid. They are not the kind of arguments that can guarentee a conclusion. With sound deductive arguments, the conclusion is guarenteed. While it’s true nondedictive arguments are not valid, it’s false to say of them that they are invalid, since validity applies only (in the sense we’re speaking) to deductive arguments.

With deductive arguments, there’s no meaningful difference between “invalid” and “not valid”, but I point out that there is still a difference because the guarentee through form and true premises is at the heart of the divide between deductive and nondeductive arguments.

In fact, one of the sad criticisms of inductive arguments (a kind of nondeductive argument) is that it doesn’t provide a guarentee like is possible with deductivity. I call it sad because it’s unfounded. The nondeductive argument is a tool with its own purpose and limitations. I wouldn’t criticize a hammer for not doing what a skill saw can, nor vice versa.

Keep the notion of form separate from the distractions of the other necessary ingredient for the makings of SOUND arguments.

 

[Cheerful Charlie]

Inductive and abductive arguments are the unavoidable ways of thinking about the real world. And that is why we have developed the scientific method. We do the best we can in an imperfect wold

 

[Valjean]

Joe's either a squid or giraffe.
Joe is an elephant.

The premises contradict each other

 

[A Toy Windmill]

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

Angra Mainyu has given a justification that I would cosign. Have you responded to it, yet?

 

[Speakpigeon]

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.

Good. You're on your way!

Still, formally, it's true elephants are not squid only because it is a deductive consequence of our definitions of the words "elephants" and "squid".

When we discuss the logic of an argument, we are only interested in the question of validity. For assessing validity, you don't consider or assume any definition of the lexical terms like "elephant" or "squid". You only look at form: all words spelt the same are assumed to have the same referent, and the truth value of both the premises and the conclusion are all assumed to depend on their form only. Thus, the actual truth of the propositions involved is entirely irrelevant to discussing the logic of an argument. If you want to have an argument about elephants that are not squid, then your premises will have to spell it out, like I did in my squid argument.

Actual truth only becomes an issue what you apply the argument to the real world. However, at this stage, you need to have sorted out whether the argument is valid or not. Applying an invalid argument is only as good as trying your luck, with fifty percent probability that the conclusion be true, whereas applying a valid argument, the truth of the conclusion is guarantied 100% by the truth of the premises. You won't ever find any better than that.

Thus, there are two distinct phases, with validity independent of soundness but soundness dependent on validity. An invalid argument is unsound by definition whereas an unsound argument can be valid and no problem.

All discussion about the logic of arguments are therefore about the validity of the arguments. Validity really just means logicality. And applying an argument is irrelevant to the logicality of it. It's no use applying an argument to find out whether it is valid or not. Finding that the conclusion is false of the real world will never make an argument not valid. What it does is that it makes at least one of the premises false: If A implies B and not B, then not A. The conclusion B is false makes the premises A false, it doesn't make the argument A implies B not valid.

However, a valid argument will be useless whenever the premises are known to be false. So, essentially, you only apply logic to premises you believe true. And, very possibly, application will reveal that the conclusion is false, which will show you that the premises are in fact false. The theory of Newtonian gravitation, in itself a logical argument, is falsified by the orbit of Mercury. Yet, the theory is logically valid.
EB

 

[fast]

Joe's either a squid or giraffe.
Joe is an elephant.

The premises contradict each other

Actually, they don’t. They are contrary but not contradictory.

I’m in Florida
I’m not in Florida
That’s contradictory

I’m in Florida
I’m in South Carolina
That’s contrary

In the case where it’s contradictory
One must be false
One must be true

In the case where it’s contrary
Only one may be true
Both could be false

Joe is an elephant
Joe is not an elephant
One is true, for sure. For instance, if Joe is the zoo keeper, P2 is true. No matter what Joe is, if he’s not an elephant, P2 is true. Of course, If P1 is true, then P2 is not. One or the other is gonna be true. There’s no falling through the cracks with this one, since together, it’s classification is collectively exhaustive.

Joe’s either a squid or a giraffe
Joe is neither a squid or a giraffe
Again, contradictory. If the top one is true, the bottom is false and vice versa. If Joe is an elephant, then p2 is true; otherwise, p1 would be true.

Now to your argument

Joe’s either a squid or a giraffe
Joe is an elephant
One or the other could be true, but then again both could be false. If it were contradictory, one must be true and one must be false, but like I said, Joe could be a zoo keeper. Both premises could be false.

 

[Speakpigeon]

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.

LOL. This shows you are just ignoring two of the premises. Sorry, you can't do that. You have to get to the conclusion of the five premises of the argument, not that of some arbitrary subset of them. You are effectively validating a different argument. The premise asserting that Joe is an elephant cannot be ignored.

Yeah, I know, it is nonetheless precisely what mathematicians do but this shows they don't have a clue as to what deductive logic is. Please note that they also pretend that their mathematical logic is logical in the sense of Aristotle's logic. They will insist there's no contradiction. Yet, here we are, mathematical logic says Joe is a Squid while Aristotelian logic says we can't infer that.

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.

Yeah, and this is a real shame. Mathematicians don't understand logic because of their training and then they go about the world lording it over teaching other people their inane beliefs. They've learnt a dogma at school and live the rest of their lives under the false notions they've learnt, insisting ordinary folks are wrong when it is they who are wrong. They are a mathematical sect.

And one funny thing is, you can't reason them because they no longer reason logically. Even funnier, their brain still works the Aristotelian way. It is only their formal logic, their arguments, their reasoning, that's wrong. And they keep arguing logically about a wrong logic. That has to be darkly ironic.

What I haven't been able to establish yet, since AM doesn't understand shit, is whether mathematicians still rely on their intuitive Aristotelian logical sense to produce proofs of theorems, or whether they make any use of mathematical logic. I'm sure some of it has been used, but I still have no example of that. I asked repeatedly, but AM somehow doesn't understand or doesn't want to understand.

Still, we're moving forward.
EB

 

[Speakpigeon]

This is not a new problem. In the middle ages, logicians accepted that contradictions could lead to logical explosion.

Some of them only. Most didn't accept the idea. The guilty one is William of Soissons. All other renown logicians of the period didn't accept his proposal.

And Aristotle himself said something that clearly shows it thought the idea barmy.

Unfortunately, although our logic is essentially as good as any of our natural capacities, say, like our visual sense, our formal logic is subject to our performance. An idiot can invent a wrong formal logic.

The real problem today is that of the enormous scale of the problem: millions of mathematicians throughout the world taught the wrong formal logic! Whoa. It's the Catholic Church all over again and just as dogmatic.
EB

 

[A Toy Windmill]

LOL. This shows you are just ignoring two of the premises. Sorry, you can't do that. You have to get to the conclusion of the five premises of the argument, not that of some arbitrary subset of them.

You said in the other thread that you accept weakening. So you accept that a valid argument stays valid even if you add extra premises. Consequently, you only need to consider a subset of the premises, get to the conclusion, and then weaken the argument by adding back the remaining premises.

 

[Speakpigeon]

Joe's either a squid or giraffe.
Joe is an elephant.

The premises contradict each other

Which is the point: Do you believe you can infer validly anything from contradictory premises?

Formally speaking, the premises you quoted don't contradict themselves since for validity we don't assume any definition of the lexical terms such as "elephant" and "squid".

It's only the five premises together that are formally contradictory.

But you have to take into account all premises. So, the premises are indeed irredeemably contradictory.
EB

 

[Speakpigeon]

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

Angra Mainyu has given a justification that I would cosign. Have you responded to it, yet?

Spell it out in your own words, please.

And please vote before any comment.
EB

 

[A Toy Windmill]

Spell it out in your own words, please.

I've no faith that will advance the conversation.

And please vote before any comment.

I will comment as I choose.

 

[Speakpigeon]

Joe's either a squid or giraffe.
Joe is an elephant.

The premises contradict each other

Actually, they don’t. They are contrary but not contradictory.

(...)

Now to your argument

Joe’s either a squid or a giraffe
Joe is an elephant
One or the other could be true, but then again both could be false. If it were contradictory, one must be true and one must be false, but like I said, Joe could be a zoo keeper. Both premises could be false.

Yes, contradiction comes from the five premises taken together. You can't assume that an elephant is not squid. This has to follow from the premises, as in my formulation of the squid argument.
EB

 

[Speakpigeon]

Spell it out in your own words, please.

I've no faith that will advance the conversation.

And please vote before any comment.

I will comment as I choose.

Sure. Says it all.
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.

Yes, you got it right.

Thank you!

I’m at the top of a modular water slide and need to find a way to the pool (C) below.

P1, P4, and P5 are the three modular pieces which when fit together will allow me free-flowing passage to the refreshing conclusion below.

There are two unused barriers sitting on the ground below that do not impede my ability to slide to the water below, but then again, if they were placed on the slide (one between the first and second slide) (and one between the second and third slide), I’d have two barriers that would not let me traverse my way along the entirety of the slide.

I’ve been told that we cannot add new premises to valid argument and make it invalid. That means they may be ignored and not factored into our thinking. There seems to be some that think not factoring all the pieces distorts validity.

If there are only two people in the building, we’ll only need one fire truck
There are only two people in the building.
Eight more people enter the building
Therefore, we’ll only need one fire truck.

You and I, well, we see clearly the argument is unsound, but it’s valid. There’s this sense that it shouldn’t be valid because it should (yet doesn’t) incorporate all the premises and repercussions in totality. Is there a calling to change the rules of logic so it wouldn’t be called valid?

Me, well, I’m just rolling with the punches. It’s valid in one sense (I see that), but why in the world do we have these nutty rules? There should be exceptions for crazy situations. For instance, any argument with a contradiction should be invalidated. That should be a no-brainer. This choosing to completely disregard premises also raises some eyebrows.

I need you to have your people look into having this logic thing revamped. Have them give it an overhaul. It’s the new millineum already and the speakpigeons of the world doesn’t want to lose what sembalance or normalcy that used to come with the traditional notion of validity. Heck, I can throw something on the grill, he’ll bring the music, you make a few text book alterations; everyone’ll be happy.

 

[Angra Mainyu]

Joe's either a squid or giraffe.
Joe is an elephant.

The premises contradict each other

If they did contradict each other, they would imply anything.

 

[Angra Mainyu]

Just a reminder to readers:

A Toy Windmill pointed out that Speakpigeon accepts weakening. What is weakening?

But what is weakening? It was explained by A Toy Windmill in the other thread:

https://talkfreethought.org/showthr...gical-validity&p=691752&viewfull=1#post691752

Yes. The observation here is that adding additional premises to a valid argument cannot make it invalid. It's something that most logics accept, and goes by the name "weakening", since the more assumptions your argument has, the fewer scenarios it applies to, and so the weaker it is.

Speakpigeon said:

https://talkfreethought.org/showthr...gical-validity&p=692280&viewfull=1#post692280

I accept Modus Tollens and weakening.

Now, suppose that you have a valid argument:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Conclusion: Tom is a mollusc.

Now, you add the following premise:

Premise 3: It is not the case that Tome is a squid.


And you get:

Premise 1: All squids are molluscs.
Premise 2: Tom is a squid.
Premise 3: It is not the case that Tome is a squid.

Conclusion: Tom is a mollusc.

So, that is a valid argument with contradictory premises. It follows that some valid arguments have contradictory premises. But moreover, you can ignore Premise 3, and derive the conclusion from Premise 1 and Premise 2, contrary to Speakpigeon's other claim that

LOL. This shows you are just ignoring two of the premises. Sorry, you can't do that. You have to get to the conclusion of the five premises of the argument, not that of some arbitrary subset of them.

Well, that is false, and as A Toy Windmill pointed out, Speakpigeon's own claims commit Speakpigeon to that position, even if Speakpigeon denies it.