POLL 3 on the validity of a simple argument on Joe the Squid

[Speakpigeon]

By the way I think you have completely misunderstood what I was getting at because you have NOT corrected your post in regards to what I was referring to.

Then explain again.
If you can't be bothered, it's fine.
EB

It is NO bother.

If we are to ASSUME that the premises are true, and not on whether the premises are actually true or false, then EVERY time we looked at an argument to access if the argument is a valid argument or not, then we would ALWAYS arrive at the same conclusion.

What conclusion? That the argument is valid?! That it is invalid?!
Can't you try to be specific. I can't possibly guess what it is you're trying to say, for God sake!

So, let's assume you mean that if we assume all the premises true, we inevitably conclude that the argument is valid. Let's try that on our Squid argument:

A squid is not a giraffe
A giraffe is not an elephant
An elephant is not a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Let's assume all the premises are true. So?
Can you explain why we would inevitably conclude the argument is valid?
Me, I'm definite that's not true.
EB

[Age]

Then explain again.
If you can't be bothered, it's fine.
EB

It is NO bother.

If we are to ASSUME that the premises are true, and not on whether the premises are actually true or false, then EVERY time we looked at an argument to access if the argument is a valid argument or not, then we would ALWAYS arrive at the same conclusion.

What conclusion? That the argument is valid?! That it is invalid?!
Can't you try to be specific. I can't possibly guess what it is you're trying to say, for God sake!

Obviously, if we are to ASSUME that the premises are true, then we would ALWAYS arrive at the same conclusion that the argument is valid.

So, let's assume you mean that if we assume all the premises true, we inevitably conclude that the argument is valid. Let's try that on our Squid argument:

Let's assume all the premises are true. So?
Can you explain why we would inevitably conclude the argument is valid?
Me, I'm definite that's not true.
EB

Of course, an argument is valid only if the truth of the premises logically guarantees the truth of the conclusion.

Could your squid argument, in its current form, ever logically guarantee the truth of the conclusion?

If i understand you correctly here you also agree that your squid argument is not logically valid. Is this right?

[Speakpigeon]

It is NO bother.

If we are to ASSUME that the premises are true, and not on whether the premises are actually true or false, then EVERY time we looked at an argument to access if the argument is a valid argument or not, then we would ALWAYS arrive at the same conclusion.

What conclusion? That the argument is valid?! That it is invalid?!
Can't you try to be specific. I can't possibly guess what it is you're trying to say, for God sake!

Obviously, if we are to ASSUME that the premises are true, then we would ALWAYS arrive at the same conclusion that the argument is valid.

But that doesn't make sense.
It should read: if we assume that the premises are true, then if the argument is valid, then we will conclude that the conclusion of the argument is true.

So, let's assume you mean that if we assume all the premises true, we inevitably conclude that the argument is valid. Let's try that on our Squid argument:

Let's assume all the premises are true. So?
Can you explain why we would inevitably conclude the argument is valid?
Me, I'm definite that's not true.
EB

Of course, an argument is valid only if the truth of the premises logically guarantees the truth of the conclusion.
Could your squid argument, in its current form, ever logically guarantee the truth of the conclusion?
If i understand you correctly here you also agree that your squid argument is not logically valid. Is this right?[/quote]
Yes, at least according to the interpretation of validity in line with Aristotle, something I favour over modern logic.
It doesn't seem to make any sense to claim this argument valid, as you do if you abide to the definition of validity proposed in modern mathematical so-badly-called "classical logic".
OK, so we agree and also on the second argument in the other thread.
EB

[Age]

What conclusion? That the argument is valid?! That it is invalid?!
Can't you try to be specific. I can't possibly guess what it is you're trying to say, for God sake!

Obviously, if we are to ASSUME that the premises are true, then we would ALWAYS arrive at the same conclusion that the argument is valid.

But that doesn't make sense.

That does not make sense to you because of how far you have drifted off track.

To get you back on track.

You wrote:
you have to assess the validity of an logical argument on the basis of what the premises and the conclusion mean and assuming they are true, not on whether they are actually true or false.

I responded:
If we are to ASSUME that the premises are true, and not on whether the premises are actually true or false, then EVERY time we looked at an argument to access if the argument is a valid argument or not, then we would ALWAYS arrive at the same conclusion.


It should read: if we assume that the premises are true, then if the argument is valid, then we will conclude that the conclusion of the argument is true.

It should NOT read that at all: because we were discussing ASSESSING THE VALIDITY OF A LOGICAL ARGUMENT. We were NOT discussing if AN argument is valid or not. Instead, we were talking about assessing procedure to see if an argument is valid or not. That is WHY I responded with what I did.

So, let's assume you mean that if we assume all the premises true, we inevitably conclude that the argument is valid. Let's try that on our Squid argument:

Let's assume all the premises are true. So?
Can you explain why we would inevitably conclude the argument is valid?
Me, I'm definite that's not true.
EB

Of course, an argument is valid only if the truth of the premises logically guarantees the truth of the conclusion.
Could your squid argument, in its current form, ever logically guarantee the truth of the conclusion?
If i understand you correctly here you also agree that your squid argument is not logically valid. Is this right?

Yes, at least according to the interpretation of validity in line with Aristotle, something I favour over modern logic.
It doesn't seem to make any sense to claim this argument valid, as you do if you abide to the definition of validity proposed in modern mathematical so-badly-called "classical logic".

What do you mean by: to claim this argument valid, as I do.

Just to make it clear, I do NOT claim this squid argument to be valid.

By the way I do NOT abide by the definition of the word 'validity' proposed in any thing if that definition is NOT uniform across all things. I do NOT see that there is one set of logic over another set of logic. To me that just appears blatantly illogical. Of course different systems with different sets of rules may use different "logic" but I would NEVER use one over another nor would I ever abide by the definition of the word 'valid' for just one sort of "logic" for all those different systems and rules, which are made up by human beings.

OK, so we agree and also on the second argument in the other thread.
EB

I am not sure, because I do not know what you are saying we agree on here.

[Logik]

Your entire argument can be interpreted as propositions. The truth-value of each proposition can be determined independently from the rest of the argument.

https://repl.it/repls/SuperiorTimelyBug

A squid is not a giraffe: True
A Giraffe is not an Elephant: True
An Elephant is not a Squid: True
Joe is either a squid or a giraffe (50/50 odds)
Joe is an Elephant: False
Therefore Joe is a Squid: True

You are no closer to explaining your semantics to us. So we are no closer to asserting validity for you.

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

In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation (model) that makes the formula true.[1] A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and invalidity, that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false. These four concepts are related to each other in a manner exactly analogous to Aristotle's square of opposition.

The four concepts can be raised to apply to whole theories: a theory is satisfiable (valid) if one (all) of the interpretations make(s) each of the axioms of the theory true, and a theory is unsatisfiable (invalid) if all (one) of the interpretations make(s) each of the axioms of the theory false.

[Speakpigeon]

Your entire argument can be interpreted as propositions. The truth-value of each proposition can be determined independently from the rest of the argument.

Sure. Good boy.

You are no closer to explaining your semantics to us.

I didn't set out to do that. I'm using an implicit semantics that all normal people, even children, understand straight away.
We have a brain. We don't need to justify that we have one.

So we are no closer to asserting validity for you.

I asked a simple question. If you are incapable of answering it, it's fine. No answer is an empirical fact unto itself. Absence of evidence is evidence of absence.
Plus, all the empirical evidence I now have says I won't ever get any substantial reply from you.
That, too, is marvellous.
EB

[Logik]

I didn't set out to do that. I'm using an implicit semantics that all normal people, even children, understand straight away.
We have a brain. We don't need to justify that we have one.

"Normal" people (even children) use very ambiguous semantics. As is evident by the multiple definitions of all of the adverbs you have used.

So whatever answer you get from "normal" people - it will not be consistent with your intended meaning.

Of course, I may be giving you far too much credit by assuming any intentionality.

Plus, all the empirical evidence I now have says I won't ever get any substantial reply from you.
That, too, is marvellous.
EB

Like most philosophers, you can no more tell substance from sophistry than you can tell your head from your ass.

[Speakpigeon]

Here is the OP again, if you're interested to answer it...

This is a poll on the logical validity of the following argument:

A squid is not a giraffe
A giraffe is not an elephant
An elephant is not a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Is this argument logically valid?
Either way, please articulate why.
EB

[Arising_uk]

Here is the OP again, if you're interested to answer it...

This is a poll on the logical validity of the following argument:

A squid is not a giraffe
A giraffe is not an elephant
An elephant is not a squid
Joe is either a squid or a giraffe
Joe is an elephant
Therefore, Joe is a squid

Is this argument logically valid?
Either way, please articulate why.
EB

Well if you accept this formalisation of the argument;
1.
∀x (S(x) -> ¬G(x))
∀x (G(x) -> ¬E(x))
∀x (E(x) -> ¬S(x))
∃y (J(y) -> (S(y) v G(y)))
∃y (J(y) -> E(y))
∴ ∃y (J(y) -> (S(y))


Then by negating the conclusion and using the semantic tableaux proof procedure along with the premises the argument is invalid as there is an open branch which means the original argument is invalid. But phew! That was a nightmare to analyse due to all the universal material conditionals but luckily the first branch was open.

Still, I could have made a mistake due to the complexity so I'm happy for you to recheck using the same proof procedure.
p.s.
Still plodding along with the proof of your other argument but again mixing modal logic with quantifiers makes it a pain.
p.s.
Bollocks! Just saw that ∃y (J(y) -> E(y)) could probably be ∃y (J(y) ^ E(y)) and also ∃y (J(y) -> (S(y)) could be ∃y (J(y) ^ (S(y)). Be back later.
p.p.s
Oh! In fact I could probably do this with them all so;
2.
∀x (S(x) ^ ¬G(x))
∀x (G(x) ^ ¬E(x))
∀x (E(x) ^ ¬S(x))
∃y (J(y) ^ (S(y) v G(y)))
∃y (J(y) ^ E(y))
∴ ∃y (J(y) ^ (S(y))

Which formalisation would you accept or would you prefer a mix of the two? In fact could you please produce your own preferred formalisation from the above as then I can just analyse that.

[Arising_uk]

...

A squid is not a giraffe: True
A Giraffe is not an Elephant: True
An Elephant is not a Squid: True
1. Joe is either a squid or a giraffe (50/50 odds)
2. Joe is an Elephant: False
Therefore Joe is a Squid: True

...

Wouldn't this depend on what kind of 'Or' you are using, inclusive or exclusive?
So the answer to 2. being true or false would depend upon this.

I'm also slightly puzzled as to how you get 2. as False as presumably you are using 1. as some form of contradiction to prove this but I thought you didn't use LEM? Just asking as definitely may have the wrong end of the stick, in fact it could just be Reductio ad Absurdum and I'm not sure if this is based upon LEM.

[Logik]

Wouldn't this depend on what kind of 'Or' you are using, inclusive or exclusive?
So the answer to 2. being true or false would depend upon this.

*shrug* I have merely translated the argument into another language and to the best of my understanding.

Whether I have understood the original meaning correctly is for the OP to confirm or disconfirm.

I'm also slightly puzzled as to how you get 2. as False as presumably you are using 1. as some form of contradiction to prove this but I thought you didn't use LEM? Just asking as definitely may have the wrong end of the stick, in fact it could just be Reductio ad Absurdum and I'm not sure if this is based upon LEM.

There are no contradictions in computer languages. Everything is deduced from the propositions put forth.

I am merely choosing how to interpret his argument. What the author meant is anybody's guess. I can re-write this in 100 different ways all syntactically valid in Python, without knowing whether they were semantically identical to the OP's intended meaning..

I could say "Joe is an Elephant." as a statement of fact. Which translates to 'Joe = Elephant()' in Python.
I could also say "Joe is an Elephant.' as a propositional statement. Which translates to 'Joe.__class__ == Elephant' and evaluates to False.

I don't know which one he meant, so I made a choice. I did the same every time I faced ambiguity.

[Arising_uk]

Well thanks for the answer but I was asking about the disjunction?


A bit puzzled how you get Joe being of the class 'Elephant' equates to false?

[Logik]

Well thanks for the answer but I was asking about the disjunction?


A bit puzzled how you get Joe being of the class 'Elephant' equates to false?

Look at the code. I am not getting to anything. All the text is the output of the program provided.

Joe is probabilistically either a squid or an elephant. 50/50. Every time you run the program the computer flips a coin.

And then it tells you if Joe is an elephant. If Joe isn't an Elephant (e.g if the coin toss above elected him a squid) - the proposition evaluates to False.

There's a 50% chance it evaluates to 'true'.

[Speakpigeon]

Well if you accept this formalisation of the argument;
1.
∀x (S(x) -> ¬G(x))
∀x (G(x) -> ¬E(x))
∀x (E(x) -> ¬S(x))
∃y (J(y) -> (S(y) v G(y)))
∃y (J(y) -> E(y))
∴ ∃y (J(y) -> (S(y))

Then by negating the conclusion and using the semantic tableaux proof procedure along with the premises the argument is invalid as there is an open branch which means the original argument is invalid. But phew! That was a nightmare to analyse due to all the universal material conditionals but luckily the first branch was open.

Still, I could have made a mistake due to the complexity so I'm happy for you to recheck using the same proof procedure.

Post your proof once you're sure of it.

p.s.
Still plodding along with the proof of your other argument but again mixing modal logic with quantifiers makes it a pain.
p.s.
Bollocks! Just saw that ∃y (J(y) -> E(y)) could probably be ∃y (J(y) ^ E(y)) and also ∃y (J(y) -> (S(y)) could be ∃y (J(y) ^ (S(y)). Be back later.
p.p.s
Oh! In fact I could probably do this with them all so;
2.
∀x (S(x) ^ ¬G(x))
∀x (G(x) ^ ¬E(x))
∀x (E(x) ^ ¬S(x))
∃y (J(y) ^ (S(y) v G(y)))
∃y (J(y) ^ E(y))
∴ ∃y (J(y) ^ (S(y))

Which formalisation would you accept or would you prefer a mix of the two? In fact could you please produce your own preferred formalisation from the above as then I can just analyse that.

That's how I would formalise the argument:

P1 S → ¬G
P2 G → ¬E
P3 E → ¬S
P4 J → (S ⊻ G)
P5 J → E
C J → S

That's the simple way to do it but you can also use predicate logic as you did in your first formalisation here.
EB

[Logik]

P4 J → (S ⊻ G)
P5 J → E

Your system is inconsistent.

The above implies E ⇔ (S ⊻ G)

WAT?