## Poll on the validity of two arguments

What is the basis for reason? And mathematics?

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## Are these two arguments valid?

1st argument - Valid
4
25%
1st argument - Not valid
3
19%
1st argument - I don't know
1
6%
1st argument - The argument doesn't make sense
1
6%
2nd argument - Valid
4
25%
2nd argument - Not valid
3
19%
2nd argument - I don't know
0
2nd argument - The argument doesn't make sense
0

Logik
Posts: 4048
Joined: Tue Dec 04, 2018 12:48 pm

### Re: Poll on the validity of two arguments

Speakpigeon wrote:
Sun Feb 03, 2019 12:59 pm
I tried my best to make them formally valid, so on this account I'm doing better than the three people I quoted.
You can't make them "formally valid" because you can't satisfy the decidability criterion without being upfront about the semantics you are defaulting to. There are dozens of modal logics each with different semantics.

To attempt to make your argument "valid" is to attempt to satisfy the semantics of some particular modal logic.Which one?

I'll point you to reading in the hopes that it doesn't go over your head this time:

https://en.wikipedia.org/wiki/Decidabil ... cal_system
Each logical system comes with both a syntactic component, which among other things determines the notion of provability, and a semantic component, which determines the notion of logical validity.

surreptitious57
Posts: 3082
Joined: Fri Oct 25, 2013 6:09 am

### Re: Poll on the validity of two arguments

The definition of valid I use which is acceptable for all these threads

Where every premise is logically consistent with the previous one
Where the conclusion is logically consistent with the last premise

Atla
Posts: 1889
Joined: Fri Dec 15, 2017 8:27 am

### Re: Poll on the validity of two arguments

Speakpigeon wrote:
Sun Feb 03, 2019 12:59 pm
Atla wrote:
Sat Feb 02, 2019 7:14 pm
Yes, these are much clearer (to me at least), no "for all we know" / "state" / "determined" / "does" / "may be" confusion, much clearer structure.
It's easy to tell that these arguments are totally invalid. Well yeah, the second one is really trying hard to cheat its way through.
I couldn't really follow this one, seems to be invalid as well to me, F is concrete and F2 is a mix of concrete and abstract (the added element has one more abstraction layer, leading to nonsense)? Well, could be valid depending on what we consider a mathematical proof, I guess. Is "I am F" really a mathematical proof? Nah scratch that, I really can't make sense of the argument.
OK, maybe my arguments are hard to process, but they are what they are and I couldn't make them easier to read.
Still, you're welcome to offer an easier formulation.
I tried my best to make them formally valid, so on this account I'm doing better than the three people I quoted.
EB

1st

P1 - It's possible that: B(x) = A
P2 - C depends on B(x)
C - Therefore, it's possible that: C depends on A

2nd

P1 - It's possible that: some part of B(x) = A
P2 - C depends on some part of B(x)
C - Therefore, it's possible that: C depends on A

(Okay I may have changed the "some part" thing in the 2nd argument a little, but I think structurally it's the same.)

Age
Posts: 2324
Joined: Sun Aug 05, 2018 8:17 am

### Re: Poll on the validity of two arguments

Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
Age wrote:
Sun Feb 03, 2019 4:42 am
Speakpigeon wrote:
Sat Feb 02, 2019 3:10 pm
This thread is defined by its first post. That's all there is to it.
EB
If this thread is defined by its first post, then just about any argument that starts with "As far as 'we' know" could be taken as being valid or invalid.
???
Are you sure of that?!
Yes.
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
Look at this argument:
Okay
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
As far as we know, water is H2O;
Ice is frozen water;
Therefore, Trump is H2O and Vladimir Putin is water.
You say that is valid?!
I looked at that argument. Now, why would you, and why did you, ASSUME such a ridiculous thing as this, and then write such a stupid remark as you have here?.

I NEVER said that that is valid. But if I was ever given a chance to reply to your statement, or given a chance to answer your statement that has a question mark on the end of it, then I would say, No. I NEVER would and I NEVER could say that that argument is valid until I had clarified some things up with you first.
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
Whoa.
Did you NOT read the actual words that I wrote, which are in front of you?
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
Age wrote:
Sun Feb 03, 2019 4:42 am
The CORRECT answer is depended SOLELY upon on who/what is the 'we' you are referring to?
Sure.
Yes.
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
If you don't know who we are then I'm not sure who I am and even who you are.
Well I do NOT know who/what the 'we' is that you are referring to in YOUR argument.

And, I am pretty sure that you do NOT even know who/what 'I' am' and who/what 'you' are also but that does not really have much to do with what I was saying, which was the CORRECT answer is SOLELY depended upon who/what the 'we' IS that you are referring to.
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
And then there's no need to post anything here or indeed anywhere.
If that is what you now see or believe, then so be it.
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
Age wrote:
Sun Feb 03, 2019 4:42 am
Until that is made KNOWN how could any one really respond accurately?
Supposed it is "made known", would we really know it, though?
At least I would. Then I could correctly answer your question. That is what you are seeking here, am I right?
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
We're not discussing soundness here but validity.
Yes I know.
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
So, whether there is a "we" and whether it knows anything is completely irrelevant.
What assumptions are you making to get so far off track from what I am talking about?

If you start an argument with "As far as 'we' know ...", and you want to know whether the argument is valid or not, from another's perspective, then I am telling you from MY perspective I need to KNOW who/what is the 'we' that you are referring to before I could correctly answer your question.

NEVER have I even suggested anything about "whether there is a 'we' or not, nor have I ever suggested any thing about whether the 'we' knows any thing or not. So, I agree with you that THIS is completely irrelevant, and still wonder WHY you would even bring such an irrelevant statement into a discussion where NEITHER things have even been alluded to previously?
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
Just assume it does,
Just assume WHAT, does WHAT?

By the way I do NOT like to assume any thing whatsoever. So, I will NOT assume any thing here.

If you are unable to or unwilling to answer some simple open clarifying questions, then that is what it is.
Speakpigeon wrote:
Sun Feb 03, 2019 12:50 pm
using the usual definitions of the words used in the argument as can be found in any English dictionary.
EB
Okay but so what?

What the word 'we' mean, in any dictionary, has absolutely NO bearing on who/what the 'we' refers to in YOUR argument.

(I ask the most simplest, straightforward of questions to people, which usually triggers the most off topic, irrelevant - and some times the most stupid and ridiculous of - ASSUMPTIONS, which then those people then start BELIEVING that their OWN assumption is what I am actually talking about and referring to. When it is clearly OBVIOUS that I was NOT.)

surreptitious57
Posts: 3082
Joined: Fri Oct 25, 2013 6:09 am

### Re: Poll on the validity of two arguments

Age wrote:
I ask the most simplest straightforward of questions to people which usually triggers the most off topic irrelevant - and sometimes the most stupid and ridiculous of ASSUMPTIONS - which then those people then start BELIEVING that their OWN assumption is what I am actually talking about and referring to. When it is clearly OBVIOUS that I was NOT
Welcome to the internet we hope you enjoy your time here

Atla
Posts: 1889
Joined: Fri Dec 15, 2017 8:27 am

### Re: Poll on the validity of two arguments

Age wrote:
Sun Feb 03, 2019 1:42 pm
(I ask the most simplest, straightforward of questions to people, which usually triggers the most off topic, irrelevant - and some times the most stupid and ridiculous of - ASSUMPTIONS, which then those people then start BELIEVING that their OWN assumption is what I am actually talking about and referring to. When it is clearly OBVIOUS that I was NOT.)
Surely your epic inability to understand human language has nothing to do with it.. hehe

Speakpigeon
Posts: 957
Joined: Sat Nov 11, 2017 3:20 pm
Location: Paris, France, EU

### Re: Poll on the validity of two arguments

Atla wrote:
Sun Feb 03, 2019 1:32 pm
Speakpigeon wrote:
Sun Feb 03, 2019 12:59 pm
Atla wrote:
Sat Feb 02, 2019 7:14 pm
Yes, these are much clearer (to me at least), no "for all we know" / "state" / "determined" / "does" / "may be" confusion, much clearer structure.
It's easy to tell that these arguments are totally invalid. Well yeah, the second one is really trying hard to cheat its way through.
I couldn't really follow this one, seems to be invalid as well to me, F is concrete and F2 is a mix of concrete and abstract (the added element has one more abstraction layer, leading to nonsense)? Well, could be valid depending on what we consider a mathematical proof, I guess. Is "I am F" really a mathematical proof? Nah scratch that, I really can't make sense of the argument.
OK, maybe my arguments are hard to process, but they are what they are and I couldn't make them easier to read.
Still, you're welcome to offer an easier formulation.
I tried my best to make them formally valid, so on this account I'm doing better than the three people I quoted.
EB

1st

P1 - It's possible that: B(x) = A
P2 - C depends on B(x)
C - Therefore, it's possible that: C depends on A

2nd

P1 - It's possible that: some part of B(x) = A
P2 - C depends on some part of B(x)
C - Therefore, it's possible that: C depends on A

(Okay I may have changed the "some part" thing in the 2nd argument a little, but I think structurally it's the same.)
I expected something entirely in English.
Your solution is to mix symbolic and lexical. I don't think that's a good idea. I could have posted entirely symbolic arguments, although not quite like the ones you propose here. I didn't want to do that, though, because most people don't understand symbolic notations and I was interested in having as many opinions as possible.
Here is a different example of an argument written entirely symbolically.
∃A
∃B
∃C
∀x, ∀y, ∀z, ((x ⊂ y) ∧ (y ⊂ z) → (x ⊂ z))
∀x, ∀y, ((x ⊂ y) ∧ (y ⊂ x) → (x ≡ y))
◇(A ⊂ C)
◻(B ⊂ C)
∴ ◇(A ≡ B)
It's a simple argument and easy to assess, but I don't think most people would be able to assess it's validity.
Can you?
EB

Speakpigeon
Posts: 957
Joined: Sat Nov 11, 2017 3:20 pm
Location: Paris, France, EU

### Re: Poll on the validity of two arguments

Age wrote:
Sun Feb 03, 2019 1:42 pm
If you start an argument with "As far as 'we' know ...", and you want to know whether the argument is valid or not, from another's perspective, then I am telling you from MY perspective I need to KNOW who/what is the 'we' that you are referring to before I could correctly answer your question
There's only one way to interpret "we" and it is to see it from your own perspective as you're reading the argument.
Still, if you read the argument without being able to make up your mind as to who are "we", then so be it, there's nothing I can do for you.
And don't blame me.
EB

Atla
Posts: 1889
Joined: Fri Dec 15, 2017 8:27 am

### Re: Poll on the validity of two arguments

Speakpigeon wrote:
Sun Feb 03, 2019 9:06 pm
I expected something entirely in English.
Your solution is to mix symbolic and lexical. I don't think that's a good idea. I could have posted entirely symbolic arguments, although not quite like the ones you propose here. I didn't want to do that, though, because most people don't understand symbolic notations and I was interested in having as many opinions as possible.
Here is a different example of an argument written entirely symbolically.
∃A
∃B
∃C
∀x, ∀y, ∀z, ((x ⊂ y) ∧ (y ⊂ z) → (x ⊂ z))
∀x, ∀y, ((x ⊂ y) ∧ (y ⊂ x) → (x ≡ y))
◇(A ⊂ C)
◻(B ⊂ C)
∴ ◇(A ≡ B)
It's a simple argument and easy to assess, but I don't think most people would be able to assess it's validity.
Can you?
EB
Well I only added two symbols and one of them is the equal sign, I think most people will understand this much. Could have written it as "is" I guess.

As for your example, I had to look up the last few symbols, seems valid to me.

Arising_uk
Posts: 11857
Joined: Wed Oct 17, 2007 2:31 am

### Re: Poll on the validity of two arguments

Speakpigeon wrote:
Sat Feb 02, 2019 3:13 pm
Arising_uk wrote:
Fri Feb 01, 2019 10:30 am
so effectively you are saying there are two things hence the relation can be formalised as 'if B then A'
No.
What I said is the following:
1st argument.
P1 - For all we know, A may be the state of B;
P2 - What C does is determined by the state of B;
C - Therefore, for all we know, what C does may be determined by A.
2nd argument
P1 - For all we know, A may be the state of some part of B;
P2 - What C does is determined by the state of some part of B;
C - Therefore, for all we know, what C does may be determined by A.
If you can't read properly, not my problem.
EB
Which bit of the difference between 'may be' and 'may be the state of' don't you understand?

However you are right I should have read more closely and I'm surprised that you didn't point out my formulation of P2 in argument one was incorrect.

P1. if B then A
P2. if B then C
Therefore if A then C

It should have been
P1. if B then A
P2. if A then C
Therefore if A then C.

So the 'therefore' is redundent and we actually have,
P1. if B then A
Therefore if A then C.

Which is also invalid under a truth table analysis.

Now of course this makes the assumption that the state of B we are talking about is A. If that is not what is wanted then the formulation becomes,

P1. if B then A
P2. if X then C - Some other state of B
Therefore if A then C.

Which is also invalid under a truth table analysis.

But of course you could say 'But I'm saying that it may be that X=A' but if it is then it is logically invalid.

As has been pointed-out to you you need to give a logical formulation for your 'may' and the truth-table associated with it for us to truly check if it is logically valid, if you don't accept mine that is. My guess is it'll have to be some form of modal or probabilistic logic so no truth-table but semantic tableaux(depending on the modal logic you come up with) to test their validity.

Arising_uk
Posts: 11857
Joined: Wed Oct 17, 2007 2:31 am

### Re: Poll on the validity of two arguments

Speakpigeon wrote:...
Here is a different example of an argument written entirely symbolically.
∃A
∃B
∃C
∀x, ∀y, ∀z, ((x ⊂ y) ∧ (y ⊂ z) → (x ⊂ z))
∀x, ∀y, ((x ⊂ y) ∧ (y ⊂ x) → (x ≡ y))
◇(A ⊂ C)
◻(B ⊂ C)
∴ ◇(A ≡ B)
It's a simple argument and easy to assess, but I don't think most people would be able to assess it's validity.
Can you?
EB
Are you missing some spaces in the above as I can't see how that is meant to be an argument?

Its also a real mish-mash of conventions about the logical operators, where did you get it from? As these,
∃A
∃B
∃C
Pretty much mean nothing in this form as where're the predicates?

These,
∀x, ∀y, ∀z, ((x ⊂ y) ∧ (y ⊂ z) → (x ⊂ z))
∀x, ∀y, ((x ⊂ y) ∧ (y ⊂ x) → (x ≡ y))
Don't need the quantifiers as the formulas are propositional logic formulas. Why have they mixed up ⊂ and → and why even bother using ⊂ and the lack of clarifying brackets make the formulas ambiguous or are they using a convention that the conjunction binds tightest? Also why use x,y,and z when P,Q,R.. are the norm in most logics. Is it a maths thing?
A much clearer exposition would be,
((P -> Q) ∧ (R -> P)) -> (R -> Q) - which I guess is a proof of the transitivity of the material conditional (can't remember age is a terrible thing )

((P -> Q) ∧ (Q -> P)) -> (P≡ Q) - which is a proof of the biconditional I guess.

This,
◇(A ⊂ C)
◻(B ⊂ C)
∴ ◇(A ≡ B)
is actually an argument in a modal logic although again I can't understand why it isn't written,
◇(P -> Q)
◻(P -> R)
∴ ◇(Q ≡ R)
Can't check the validity right now as it's been an age since I used semantic tableau but it seems plausible given it's about possiblity and necessity.

Logik
Posts: 4048
Joined: Tue Dec 04, 2018 12:48 pm

### Re: Poll on the validity of two arguments

Speakpigeon wrote:
Sun Feb 03, 2019 9:06 pm
∃B
∃C
∀x, ∀y, ∀z, ((x ⊂ y) ∧ (y ⊂ z) → (x ⊂ z))
∀x, ∀y, ((x ⊂ y) ∧ (y ⊂ x) → (x ≡ y))
◇(A ⊂ C)
◻(B ⊂ C)
∴ ◇(A ≡ B)
This is a grammatical error.

I know of no set theory which allows for sets that can be members of each other. I certainly cannot express that proposition in any regular language.

Furthermore. if x ≡ y then, this: ((x ⊂ y) ∧ (y ⊂ z) → (x ⊂ z)) becomes this: ((y ⊂ y) ∧ (y ⊂ z) → (y ⊂ z)).

How do you even parse y ⊂ y ? Y is a subset of itself?

WAT?!?
Speakpigeon wrote:
Sun Feb 03, 2019 9:06 pm
It's a simple argument and easy to assess, but I don't think most people would be able to assess it's validity.
Can you?
EB
I can certainly tell it's grammatically inconsistent.

There is a really simple test for validity: Write it in a programming language!
The computer tells you when you botch the grammar/semantics.

It's MUCH faster feedback loop than starting a poll on a philosophy forum.

Arising_uk
Posts: 11857
Joined: Wed Oct 17, 2007 2:31 am

### Re: Poll on the validity of two arguments

Oh! This is mathematical logic then? X is a subset of Y, etc.. that explain it as in other logics that sign is a material conditional and an inverse one at that.

Logik
Posts: 4048
Joined: Tue Dec 04, 2018 12:48 pm

### Re: Poll on the validity of two arguments

Arising_uk wrote:
Mon Feb 04, 2019 2:34 am
Oh! This is mathematical logic then?
All logic is mathematical. All mathematics is logical.

Logic and Mathematics are the same thing. Different names for deductive systems.

And the irony in my statement above is that it's equivalent to: ∀x, ∀y, ((x ⊂ y) ∧ (y ⊂ x) → (x ≡ y))

And the implication of that equivalence is that in the context of this argument ⊂ means the same thing as ≡

Equivocation.

Arising_uk
Posts: 11857
Joined: Wed Oct 17, 2007 2:31 am

### Re: Poll on the validity of two arguments

Logik wrote:
All logic is mathematical. All mathematics is logical. ...
Well I agree that both have their logic.
Logic and Mathematics are the same thing. ...
Hmm...don't think that is quite true as propositional logic is a logic and its not maths.
And the irony in my statement above is that it's equivalent to: ∀x, ∀y, ((x ⊂ y) ∧ (y ⊂ x) → (x ≡ y))

And the implication of that equivalence is that in the context of this argument ⊂ means the same thing as ≡

Equivocation.
Ah! Understand although still don't understand why the quantifiers are needed as in predicate logic you have to have predicates in the formula?

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