4 very easy arguments. Are they valid?

[fast]

You think sentences are true or false even when nobody thinks what they mean?!

Well, sorry , but you'll to prove that.

I don’t think there’s much question as to whether statements are true or false. As to the question of whether sentences are true or false, I say they can be. We use sentences to make statements, and we have no problem saying statements and propositions are true or false. I’d say that a sentence can be called true by virtue of their usage when a statement is ultimately made. I would only say that a sentence is neither nor false when no statement (and ultimately no proposition) is expressed.

The sentence “gum gum although quack” is neither true nor false; in other words, the sentence is not true, and the sentence is not false. To say it’s true is incorrect, and to say it’s false is incorrect. Incidentally, this is an example that highlights the difference between “not true” and “false.”

Case 3: Joe is not an elephant, and Joe is an elephant.

That’s two sentences, and each is an independent statement with its own proposition.

Actually, there are three truth values here. That of each of the conjuncts and that of the conjunction.

So, we think we know the truth value of the conjunction, i.e. false.

Now, your turn, you tell me the truth value of each of the conjunct.

Hint

Show

It's either true or false.

EB

I’m not sure, to be honest.

A contradiction isn’t exactly incoherent, so if there’s a truth value, I’d side with false, but I still havn’t ruled out the absence of a truth vaue, in which case it’s neither true nor false.

These contradictions, self referential sentences, and seemingly paradoxical semantic peculiarities seems better regarded as having no truth value. The resolution is in unmasking the absurdities for what they are; we just don’t have a convention everyone’s willing to adhere to.

 

[steve_bank]

https://plato.stanford.edu/entries/logic-inductive/
https://www.iep.utm.edu/ded-ind/

There are deductive arguments and arguments that are not deductive. Inductive arguments are not deductive arguments.



Inductive. You are making probabilistic assessments about the causes (not necessarily with numbers) on the basis of observations.

You arrive on the scene, like the CSI TV show, and see blood, a knife on the ground and other evidence. From the observed evidence you conclude an event occurred. Is that deductive or inductive?

Inductive.

But if you prove that on the basis of ZF, the Axiom of Choice is equivalent to Zorn's Lemma and to the Well Ordering Principle, that is deductive. And the arguments A1, A2, A3 and A4 are all deductive ones too.

Real world reasoning is never perfectly deductive or inductive, it is a mix of the two.

That is false. It might be that inductive arguments involve deductive implicity supporting arguments in many cases, though I doubt this is universal. But deductive arguments certainly do not always involve inductive ones (even if one might intuitively make probabilistic assessments about your chances of having erred in the deduction).

An argument can be tested for validity, meaning the conclusion proceeds from the hypothesis and premise.

By that definition, A1, A2, A3 and A4 are all valid, because the conclusion is entailed by the premises.

A logically valid argument does not have to be tied to reality.

True.

I spent 30years problem solving day in and day out. Things do not in practice fit neatly into an academic categories. I had 4 or 5 classes in philosophy. You can not really commend until you go out and apply and are confronted with situations, at least IMO. I usually refrain from any lengthy philosophical debate because it generally leads no where. People cite net references or authors.

 

[Speakpigeon]

And I'm still waiting for you to provide the justification by professional specialists for the definition of validity you use.

You are still being irrational, as I have told you many times I will not do that, and it is not proper of you to make such demand, for the reasons repeatedly stated.

What reasons?

Either there is such a justification and I don't see why you would not provide it unless you were ignorant of it, or there is no justification.

Either way, not providing the justification is admitting you don't know of such.

You will deny that, of course.
EB

 

[Speakpigeon]

I don’t think there’s much question as to whether statements are true or false.

You might have noticed that people routinely disagree about which statements are true and which are false. So, I think it is definitely more accurate to say that there is no question that each human has his own set of statements he believes to be true, taking all the others to be false. The thing is, we don't have the same sets of statements we think are true. So, it seems obvious to me that truth is relative to our beliefs. And when we get to agree on the truth of a statement, we take it as confirmation that statements are true or false. But there's no absolute authority in the matter. If we both believe we are looking at a tree, we will agree that the statement "there is a tree there" is true. We will interpret our agreement as the confirmation that our beliefs form a coherent whole, including the belief that a statement is true or false. And when I have the impression that I'm looking at a tree, who is going to convince me that the statement "there is a tree here" is false? So, we agree with ourselves that a statement is true or false. And if not, how could we possibly have any kind of rational debate? So, sure, it's rather crucial that we trust that statements are really true or false.

Yet, not one human being could possibly be aware of any true statement if he was not there to be able to consider it and its truth. So, truth is dependent on the human mind. And that's true.

Actually, there are three truth values here. That of each of the conjuncts and that of the conjunction.

So, we think we know the truth value of the conjunction, i.e. false.

Now, your turn, you tell me the truth value of each of the conjunct.

Hint

Show

It's either true or false.

EB

I’m not sure, to be honest.

A contradiction isn’t exactly incoherent, so if there’s a truth value, I’d side with false, but I still havn’t ruled out the absence of a truth vaue, in which case it’s neither true nor false.

These contradictions, self referential sentences, and seemingly paradoxical semantic peculiarities seems better regarded as having no truth value. The resolution is in unmasking the absurdities for what they are; we just don’t have a convention everyone’s willing to adhere to.

So, we have two statements, "Joe is not an elephant", and "Joe is an elephant", each of which is either true or false, but two statements that cannot be true at the same time so that their conjunction is necessarily false by the definition of the conjunction. But we do have the conjunction, and so it is a statement, and we know it's false because it is necessarily false.

What we don't know is which statement is true and which is false. I guess we agree so far.

Now, do you think there has ever been any human being who would have known which of these two statements is true and which is false?

How do you solve that? Anybody knows?
EB

 

[Speakpigeon]

When two dogmatics meet..

Given P2 all of P1 is irrelevant. I'd say it is non sequeter, C does not follow from P1,P2.

That is false. C follows from P1 and P2. Why do you think otherwise?

There are deductive arguments and arguments that are not deductive. Inductive arguments are not deductive arguments.

I spent 30years problem solving day in and day out. Things do not in practice fit neatly into an academic categories. I had 4 or 5 classes in philosophy. You can not really commend until you go out and apply and are confronted with situations, at least IMO. I usually refrain from any lengthy philosophical debate because it generally leads no where. People cite net references or authors.

Nice.

Nothing to do with empiricism, though.
EB

 

[fast]

That’s not what I meant.

Contingently, sentences are true or false.
Necessarily, statements are true or false.
Necessarily, propositions are true or false.

It is not the case that all sentences are true or false; in fact, in some cases, sentences are neither true nor false

However, just like statements and propositions, sentences are always true or not true.

My reasoning for thinking a sentence is even the kind of thing that can be true could definitely use an argument, and I may not have a great one, but if a statement is true, I see no good reason to reject the notion that the sentence, “the cat is on the mat” is true. For instance, if we stipulate that the statement, “the cat is on the mat,” why in the world would we be so insistent that a sentence cannot have a truth value when there’s no good reason in opposition given.

 

[fast]

You might have noticed that people routinely disagree about which statements are true and which are false. So, I think it is definitely more accurate to say that there is no question that each human has his own set of statements he believes to be true, taking all the others to be false. The thing is, we don't have the same sets of statements we think are true. So, it seems obvious to me that truth is relative to our beliefs. And when we get to agree on the truth of a statement, we take it as confirmation that statements are true or false. But there's no absolute authority in the matter. If we both believe we are looking at a tree, we will agree that the statement "there is a tree there" is true. We will interpret our agreement as the confirmation that our beliefs form a coherent whole, including the belief that a statement is true or false. And when I have the impression that I'm looking at a tree, who is going to convince me that the statement "there is a tree here" is false? So, we agree with ourselves that a statement is true or false. And if not, how could we possibly have any kind of rational debate? So, sure, it's rather crucial that we trust that statements are really true or false.

Yet, not one human being could possibly be aware of any true statement if he was not there to be able to consider it and its truth. So, truth is dependent on the human mind. And that's true.

I’m not sure, to be honest.

A contradiction isn’t exactly incoherent, so if there’s a truth value, I’d side with false, but I still havn’t ruled out the absence of a truth vaue, in which case it’s neither true nor false.

These contradictions, self referential sentences, and seemingly paradoxical semantic peculiarities seems better regarded as having no truth value. The resolution is in unmasking the absurdities for what they are; we just don’t have a convention everyone’s willing to adhere to.

So, we have two statements, "Joe is not an elephant", and "Joe is an elephant", each of which is either true or false, but two statements that cannot be true at the same time so that their conjunction is necessarily false by the definition of the conjunction. But we do have the conjunction, and so it is a statement, and we know it's false because it is necessarily false.

What we don't know is which statement is true and which is false. I guess we agree so far.

Now, do you think there has ever been any human being who would have known which of these two statements is true and which is false?

How do you solve that? Anybody knows?
EB

I’m not convinced that the new sentence created with the conjunction has a truth value. The sheer fact the inclusion creates a contradiction lends credence to the idea that no true proposition has been expressed.

 

[Speakpigeon]

So, we have two statements, "Joe is not an elephant", and "Joe is an elephant", each of which is either true or false, but two statements that cannot be true at the same time so that their conjunction is necessarily false by the definition of the conjunction. But we do have the conjunction, and so it is a statement, and we know it's false because it is necessarily false.

What we don't know is which statement is true and which is false. I guess we agree so far.

Now, do you think there has ever been any human being who would have known which of these two statements is true and which is false?

How do you solve that? Anybody knows?
EB

I’m not convinced that the new sentence created with the conjunction has a truth value. The sheer fact the inclusion creates a contradiction lends credence to the idea that no true proposition has been expressed.

OK, I'm good with that.

And you're good with Aristotle against the Dogmatics. Good job!

But you do realise this means the conjunction is not a statement, right?

Me, I would say it is, which means, against fast, that a statement needs not have a truth value.

Ah, conundrums.
EB

 

[Speakpigeon]

"Tout leur effort consiste à élaborer une théorie de la pensée qui soit étrangère à toute pensée". Benedetto Croce.

All their efforts consist in elaborating a theory of thought that is foreign to all thought.

Benedetto Croce (25 February 1866 – 20 November 1952) was an Italian idealist philosopher, historian and politician, who wrote on numerous topics, including philosophy, history, historiography and aesthetics. In most regards, Croce was a liberal, although he opposed laissez-faire free trade and had considerable influence on other Italian intellectuals, including both Marxist Antonio Gramsci and fascist Giovanni Gentile. Croce was President of PEN International, the worldwide writers' association, from 1949 until 1952. He was nominated for the Nobel Prize in Literature sixteen times.

I could have said that.
EB

 

[Angra Mainyu]

And I'm still waiting for you to provide the justification by professional specialists for the definition of validity you use.

You are still being irrational, as I have told you many times I will not do that, and it is not proper of you to make such demand, for the reasons repeatedly stated.

And I'm still waiting for you to provide the justification by professional specialists for the definition of validity you use.

You are still being irrational, as I have told you many times I will not do that, and it is not proper of you to make such demand, for the reasons repeatedly stated.

What reasons?

Either there is such a justification and I don't see why you would not provide it unless you were ignorant of it, or there is no justification.

Either way, not providing the justification is admitting you don't know of such.

You will deny that, of course.
EB

No, what I deny is the rationality of your question.

First, given that the empirical evidence supports the hypothesis that the use of the term "valid" in the sense applicable to deductive arguments relevant in this context is a technical term and there is ample evidence that mathematicians, logicians, and most philosophers use the term in the sense I said, at least in most cases - which you concede -, then that is a justification for the meaning of "valid" being what I said it is, when used by lay people as well.

That is my justification, not that of philosophers, mathematicians, logicians, etc., but instead you keep asking for such a justification. Well, philosophers, mathematicians, logicians, etc., are generally not even interested in arguing that ordinary people are using the technical term in the very few times they say "valid" in the context in question. So, if some of them attempted to address that, I do not know. Nor is this relevant.

Second, even you provided a definition of "valid" that you considered to be a good one, and it turned out to be a technical definition as well - which you denied.
Now, I agreed to assess whether the arguments (these ones or the ones in the other thread) were valid under the definition that you provided, but then, you went on to repeatedly ignore my points about the arguments and - worse - told me
"If you're interested in logical arguments, please start your own thread.", when I was, as a matter of fact, using the definition of logical validity provided by you to debunk (once again) your false claim that "
And a conclusion and its negation cannot both follow." - a claim you have repeatedly failed to retract, despite the fact that it has been shown repeatedly that it is false, even by your own chosen definition of validity.

So, you keep ignoring points that debunk some of your claims, ignoring the justification for the meaning that I provide, ignoring even the definition of validity chosen by yourself when you realize that it is no longer convenient, and keep making an improper demand.

Third, it gets even worse: when I do start my own thread, instead of addressing the matters at hand, you derail it by repeating your irrational question, and by repeatingly failing to address the questions in the OP. Not only do you refuse to participate in a debate addressing the OP despite your posting here, but you will not let go on a question that is irrational in either thread, and also derailing in this one.

Fourth, on top of all of that, after you failed to address my arguments in the other thread about the validity of the argument whose validity you asked in the OP and even on the basis of the definition that you provided, and after you told me to start my own thread, you changed the subject again, by coming up with more definitions of validity, making them broad by appealing to a definition of "Argument" which was obviously not relevant to the matter at hand. In fact, you said

Argument
An argument is a statement or set of statements that you use in order to try to convince people that your opinion about something is correct.

Obviously, it would be absurd of you to say "Mathematical logic, as it is recognised by most mathematicians today as the standard method of logical calculus, says the argument is valid.", since mathematical logic is not in the business of talking about the "validity" of any "argument" defined as above - and neither has the concept of validity intuitively used by mathematicians, which does not require the formalism of mathematical logic anything to do with that definition.

Your behavior is not highly irrational, even if you fail to realize that - but you ought to realize that.

 

[fast]

So, we have two statements, "Joe is not an elephant", and "Joe is an elephant", each of which is either true or false, but two statements that cannot be true at the same time so that their conjunction is necessarily false by the definition of the conjunction. But we do have the conjunction, and so it is a statement, and we know it's false because it is necessarily false.

What we don't know is which statement is true and which is false. I guess we agree so far.

Now, do you think there has ever been any human being who would have known which of these two statements is true and which is false?

How do you solve that? Anybody knows?
EB

I’m not convinced that the new sentence created with the conjunction has a truth value. The sheer fact the inclusion creates a contradiction lends credence to the idea that no true proposition has been expressed.

OK, I'm good with that.

And you're good with Aristotle against the Dogmatics. Good job!

But you do realise this means the conjunction is not a statement, right?

Me, I would say it is, which means, against fast, that a statement needs not have a truth value.

Ah, conundrums.
EB

Where there is no proposition, there is no statement. The utterance of a sentence where there is no proposition is not the utterance of a statement, so yes, if a contradiction has no expressed proposition, the sentence uttered is not a statement. All statements necessarily express propositions—as opposed to sentences.

 

[Treedbear]

In that case I just don't understand the value of syllogisms when they allow you to create a paradox by simply inserting a contradictory premise into an argument for no other purpose. That seems to be the sole purpose of P2". I can see the value of creating sorites ("a form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms the subject of the next until the subject of the first is joined with the predicate of the last in the conclusion.") But I don't see that happening here. They're simply unconnected arguments.

They do not allow you to "create paradoxes". It is not a paradox that from some premises, a contradiction follows. The reason I'm doing this is to try to help reduce some of the confusion caused by Speakpigeon in the other thread. It seems to me there might be room for some progress here, but I would like to know where you are, so I would like to ask you two questions:

1. Do you realize why A1, A2, and A3 are valid?
2. Do you realize why A4 is valid?

I realize that A1, A2, and A3 are valid. The reason is that none of them, taken by itself, contains a contradiction.

I would say that A4 is not valid because it appears to me that two or more premises contradict each other. In particular P1 and P2".

A4:

P1: Joe is either a squid or a giraffe.
P1’: A giraffe is not an elephant.
P1’’: An elephant is not a squid.
P2’’: Joe is an elephant.
C’’’: Joe is not an elephant, and Joe is an elephant.

The fact that these premises are valid when they appear in A1, A2, and A3 has no bearing on whether A4 is valid.

Sorry, but I haven't read any of Speakpigeon's other post, so I guess that means I've missed the point you're making. Also, sorry for taking so long to respond. I don't usually have internet access on weekends. I visit the forum during work hours to provide some sanity to my days, and I rely on an hour or so after work to address the more thought-provoking posts.

 

[Angra Mainyu]

I realize that A1, A2, and A3 are valid. The reason is that none of them, taken by itself, contains a contradiction.

That is not why they are valid. In fact, whether they contain a contradiction is not related to validity. The reason that they are valid is that the premises entail the conclusion.


Another (perhaps more direct) example:

Q1: A is either an X or a Y.
Q2: A is not an X.
C(Q1,Q2): A is a Y.

That is clearly valid, because C(Q1,Q2) follows from Q1 and Q2.

Q1: A is either an X or a Y.
Q2: A is not an X.
Q3: A is not a Y.
C(Q1,Q2): A is a Y.
C(Q1,Q2,Q3): A is a Y, and A is not a Y.

That is clearly valid, because C(Q1,Q2, Q3) follows from Q3 and C(Q1,Q2), and in turn C(Q1,Q2) follows from Q1 and Q2.

The fact that the conclusion is a contradiction is not relevant as to whether it is valid. But perhaps, you have other concept of validity in mind. If so, what do you understand as "valid"?

I would say that A4 is not valid because it appears to me that two or more premises contradict each other. In particular P1 and P2".

A4:

P1: Joe is either a squid or a giraffe.
P1’: A giraffe is not an elephant.
P1’’: An elephant is not a squid.
P2’’: Joe is an elephant.
C’’’: Joe is not an elephant, and Joe is an elephant.

The fact that these premises are valid when they appear in A1, A2, and A3 has no bearing on whether A4 is valid.

Premises are not the sort of thing that can be valid or invalid. Premises can be true or false. But arguments can be valid or invalid. Assuming that A1, A2, and A3 are valid, it follows at once that A4 is also valid, since the premises of A4 entail the conclusion (I already explained why in my previous reply to you, and in the hidden part of the OP).

Sorry, but I haven't read any of Speakpigeon's other post, so I guess that means I've missed the point you're making. Also, sorry for taking so long to respond. I don't usually have internet access on weekends. I visit the forum during work hours to provide some sanity to my days, and I rely on an hour or so after work to address the more thought-provoking posts.

No problem.

 

[GenesisNemesis]

:l

Is this thread some kind of satirical send-up of transgenderism?

Must be. After all, that's the only thing those damned atheists care about.

 

[fast]

I have a question.

If a valid deductive argument entails a contradiction, does that guarentee that a premise is false?

 

[Angra Mainyu]

I have a question.
If a valid deductive argument entails a contradiction, does that guarentee that a premise is false?

It guarantees that at least one premise is false, though it might be undetermined which one is so if we are talking about the formal argument and we have not determined the premises. For example, if you go by the argument:

P1: A.
P2: ¬A.
C: A and ¬A,

the argument is valid by its form, but we have not yet chosen what A is. Whatever A is, given that A is a statement, either A is false or ¬A is false. But as long as we have not chosen A, it is undetermined which one is false. Also, saying A="Joe is an elephant" is not enough to determine the premises, since "Joe" is just a name, and without further information, it is not determined whether Joe is an elephant, so determination will depend on context.

 

[fast]

And to follow up,

No valid deductive argument with a contradictory conclusion can be sound.

 

[Speakpigeon]

And to follow up,

No valid deductive argument with a contradictory conclusion can be sound.

Good point!
EB

 

[fast]

And to follow up,

No valid deductive argument with a contradictory conclusion can be sound.

Good point!
EB

Well, it helps to keep my intuition in check. I am comforted in knowing I can disregard unsoundness when assessing the validity of an argumemt. We can’t do that with just any ole use of “valid.”

Contradiction in conclusion? No problem. It’s not like it’s leading anyone astray. When the big bad wolf tells little red riding hood that

P1 the house is just over the next hill and
P2 the house is not just over the next hill
So
C the house is both just over and not just over the next hill

She’ll see the truth and know not to trust. If an argument is valid, we should trust that flow is such that the premises in fact lead just where it’s said they do, to the conclusion. Having an unsound argument doesn’t imply that the arguments form is faulty. In this case, it’s unsoundness isn’t a function of a lack of validity; the only thing else (the only thing, thanks to a particular definitional use) is that at least one premise is false.

Edited to add:

Bad wolfy

 

[untermensche]

I have a question.

If a valid deductive argument entails a contradiction, does that guarentee that a premise is false?

Of course not.

But the only way an argument is set up rationally is with true premises.