the law of (v or ~v)

[chrislav]

is the rule of inference: v or ~v) a valid argument ?

 

[topsquark]

is the rule of inference: v or ~v) a valid argument ?

If by "argument" you are saying "it is always true", then yes, this is a tautology.

The statements like "Am I awake or am I not awake?" are always true.

-Dan

 

[Dr.Peterson]

is the rule of inference: v or ~v) a valid argument ?

In what sense are you considering this a rule of inference, and an argument? I think of a rule of inference as a tautological implication (if you know this is true, then you know that is true); what are you inferring from what?

But since [imath]p\vee \neg p[/imath] is equivalent to [imath]\neg p\to \neg p[/imath] or [imath]p\to p[/imath], you could call this an argument -- what you might call a trivial or circular argument.

 

[chrislav]

I said a valid argument and not just an argument,there is agreat difference between them
A valid argument is the argument in which whenever the conclusion of the argument is true then the pemisses of the argument must be true
A rule of inference is a valid argument.
Suppose now that the premisses of the above argument are :v, ~v and the conclusion of the above argument is : v or ~v which is true
Hence according to the defininition of a valid argument the premisses of the above argument must both be true.
But this cannot happen in our case because when one of them is true the other is false and vice versa ??
please correct me if iam wrong some where

 

[Dr.Peterson]

I said a valid argument and not just an argument,there is agreat difference between them

Of course! But it can't be a valid argument without first being an argument. How are you defining "argument"?

A valid argument is the argument in which whenever the conclusion of the argument is true then the pemisses of the argument must be true

What are the premises of this "argument"? I don't see any explicitly stated! In order to talk about an argument, the premises and conclusion have to be stated.

But your statement here is wrong. In a valid argument, whenever the premises are true, the conclusion must be true!

Suppose now that the premisses of the above argument are :v, ~v and the conclusion of the above argument is : v or ~v which is true

On what grounds do you call those premises? The premises of an argument are assumed to be both true, and here they can't be!

In an argument, the premises are independent; we don't state arguments with one premise already dependent on the other. So it doesn't really make sense to call these premises. What you would be doing is applying to a pair of premises p = v and q = ~v the argument that if p and q, then [imath]p\vee q[/imath]. That is a valid argument, but unsound because the premises are not both true.

One way you might think of your statement as an argument is to say that it has no premises, and the statement itself is the conclusion; so the argument says that, regardless of the truth value of p, [imath]p\vee \neg p[/imath] is true. That is valid.

Hence according to the defininition of a valid argument the premisses of the above argument must both be true.
But this cannot happen in our case because when one of them is true the other is false and vice versa ??
please correct me if iam wrong some where

Yes, this more or less agrees with what I said above. (I've been writing without reading ahead.)

So you are perhaps thinking correctly, and just failed to clearly say what you are taking to be the premises. Again, an argument must be clearly stated in order to be able to discuss it, and you did not express it as a complete argument.

(By the way, I've been changing your v to p in part because I recently corresponded with someone who used "v" to mean "true" (he's from Brazil), so I want to be sure we are talking about an arbitrary statement p.)

 

[chrislav]

Of course! But it can't be a valid argument without first being an argument. How are you defining "argument"?

What are the premises of this "argument"? I don't see any explicitly stated! In order to talk about an argument, the premises and conclusion have to be stated.

But your statement here is wrong. In a valid argument, whenever the premises are true, the conclusion must be true!

On what grounds do you call those premises? The premises of an argument are assumed to be both true, and here they can't be!

In an argument, the premises are independent; we don't state arguments with one premise already dependent on the other. So it doesn't really make sense to call these premises. What you would be doing is applying to a pair of premises p = v and q = ~v the argument that if p and q, then [imath]p\vee q[/imath]. That is a valid argument, but unsound because the premises are not both true.

One way you might think of your statement as an argument is to say that it has no premises, and the statement itself is the conclusion; so the argument says that, regardless of the truth value of p, [imath]p\vee \neg p[/imath] is true. That is valid.

Yes, this more or less agrees with what I said above. (I've been writing without reading ahead.)

So you are perhaps thinking correctly, and just failed to clearly say what you are taking to be the premises. Again, an argument must be clearly stated in order to be able to discuss it, and you did not express it as a complete argument.

(By the way, I've been changing your v to p in part because I recently corresponded with someone who used "v" to mean "true" (he's from Brazil), so I want to be sure we are talking about an arbitrary statement p.)

Argument is sequense of statments of which one is itended as a conclusion and the others,the premisses, are intended to prove or at least provide some evidence for the conclusion
Quote me on a book of logic that says
1)the premisses have to be independed of each other
2)There are valid arguments with no premisses

 

[Dr.Peterson]

Argument is sequense of statments of which one is itended as a conclusion and the others,the premisses, are intended to prove or at least provide some evidence for the conclusion

So where in your one statement are there any premises? Why do you think what you wrote fits the definition you are quoting?

And where did you get your question? Did someone tell you that was a "rule of inference" and an "argument", or is it your own invention?

 

[chrislav]

let us clear out something important
You mean that is my own invention that a valid argument is arule of inference

 

[Dr.Peterson]

let us clear out something important
You mean that is my own invention that a valid argument is arule of inference

No, I was referring to your question itself:

is the rule of inference: v or ~v) a valid argument ?

Did someone tell you, or ask you, about "v or ~v", and whether it is, or is not, a valid argument? Or did you yourself think of that statement and wonder if it is a valid argument? I want to know why you are asking this, and in particular why you are thinking of that as an argument in the first place.

 

[chrislav]

the above (v or~v) is mention as a rule of inference in Angelo Margaris book ,1st order mathematical logic ,and because all rules of inference are simple valid arguments whose validity can be checked by using truth tables ,i tried to do that .
And although the procces did work with most of the rules of inference that are mention in page 71 in that particular i got stuck

 

[pka]

I said a valid argument and not just an argument,there is agreat difference between them
A valid argument is the argument in which whenever the conclusion of the argument is true then the pemisses of the argument must be true
A rule of inference is a valid argument.
Suppose now that the premisses of the above argument are :v, ~v and the conclusion of the above argument is : v or ~v which is true
Hence according to the defininition of a valid argument the premisses of the above argument must both be true.
But this cannot happen in our case because when one of them is true the other is false and vice versa ??
please correct me if iam wrong some where

To chrislav: you are asking about an topic that varies from author to author.
Copi & Quine are among the most important logicians of the last century.
If I were you I cheek out their textbooks from your school's mathematics library.
The following is from Copi's Symbolic Logic.
[imath]\text{All trout are mammals.}\\\text{All mammals have wings}.\\\text{Therefore all trout have wings.}[/imath]
This is a valid argument form even though neither premise nor conclusion is true.
To go a little deeper into the logical weeds: If [imath]\rm P[/imath] is declarative sentence about objects in the domain of discourse then
[imath]\bf{\rm P\;\vee\;\neg\rm P}[/imath] must be a true statement.
Frankly you lost me in much that you posted.

 

[chrislav]

So where in your one statement are there any premises? Why do you think what you wrote fits the definition you are quoting?

well i did mention the premisses and what makes you think that are not
And i did i ask you to refere me to book of logic that claims that there exist valid arguments with no premisses

 

[chrislav]

To chrislav: you are asking about an topic that varies from author to author.
Copi & Quine are among the most important logicians of the last century.
If I were you I cheek out their textbooks from your school's mathematics library.
The following is from Copi's Symbolic Logic.
[imath]\text{All trout are mammals.}\\\text{All mammals have wings}.\\\text{Therefore all trout have wings.}[/imath]
This is a valid argument form even though neither premise nor conclusion is true.
To go a little deeper into the logical weeds: If [imath]\rm P[/imath] is declarative sentence about objects in the domain of discourse then
[imath]\bf{\rm P\;\vee\;\neg\rm P}[/imath] must be a true statement.
Frankly you lost me in much that you posted.

Here we are talking for argument forms actually and not substitusions of argument forms
A substitusion of valid argument form can sometimes result into nonsenses
What makes you think i am student, you should ask 1st if you want to be polite
I have all copis books

 

[pka]

What makes you think i am student, you should ask 1st if you want to be polite
I have all copis books

From the level of your remarks, I just assumed that you were a beginner in logic.
If indeed you have all of Irving Copi's books why have you not used them?

 

[chrislav]

From the level of your remarks, I just assumed that you were a beginner in logic.
If indeed you have all of Irving Copi's books why have you not used them?

and from your remarks i think you have no idea about basic logic
or perhaps you are an author of a book of logic that escapes my attention

 

[Dr.Peterson]

the above (v or~v) is mention as a rule of inference in Angelo Margaris book ,1st order mathematical logic ,and because all rules of inference are simple valid arguments whose validity can be checked by using truth tables ,i tried to do that .
And although the procces did work with most of the rules of inference that are mention in page 71 in that particular i got stuck

@pka's comment is one that I was about to make: authors differ considerably in their notation and terminology, so I always feel awkward talking about things like this, not being sure how your author may express things (and not being at all expert on the subject). Not having taught a full course on the subject, I have a mixed knowledge of various schemes, rather than a consistent presentation of one version, and I am never sure what terms or notations I should use.

well i did mention the premisses and what makes you think that are not

As I understand it, an argument explicitly lists some statements as premises, and a conclusion. You seem to be saying this is your argument (in one form I am accustomed to):

p​

~p​

-------​

p v ~p​

But here the conclusion doesn't depend on the supposed premises at all; and, as you pointed out, the premises can't both be true. I know of no standard argument in which the premises are dependent on one another, either in the sense that one implies another, or that one denies another. That just isn't how arguments work. The best I can do to make it an argument is what I said here:

What you would be doing is applying to a pair of premises p = v and q = ~v the argument that if p and q, then [imath]p\vee q[/imath]. That is a valid argument, but unsound because the premises are not both true.

That deals with your concern about the "premises" not being possible: The argument is unsound (the premises not being true) rather than invalid (which it is not, because the conclusion is definitely true). Perhaps you could say that the "argument" is vacuously valid?

On the other hand, it does make sense to say what I said here:

One way you might think of your statement as an argument is to say that it has no premises, and the statement itself is the conclusion; so the argument says that, regardless of the truth value of p, \(p\vee \neg p\) is true. That is valid.

Since the conclusion is known to be true, we don't need any premises! True, it is not normal to talk about an argument without premises; but my point it that I don't think this is really an argument in the traditional sense at all, so I don't expect it to be typical if you do try to call it an argument.

And i did i ask you to refere me to book of logic that claims that there exist valid arguments with no premisses

I will do so momentarily.

I was going to ask you to show how your book represents arguments and rules of inference, but first tried searching and found page 71 of your book in Google Books. It doesn't call the list there either "rules of inference" or " arguments"; it calls them "tautologous schemes". But then I found how the author writes "rules of inference" on page 2:

​

Note that this specifies the premises on top.

When there are more than one premise, they are separated by commas:

​

This notation is also reasonable for "arguments"; I suppose somewhere the author uses that term? I couldn't find it.

But on the next page I find vindication of what I said:

​

These (including your own example, the law of the excluded middle, #13) are arguments, or rules of inference, that have no premises! So your own book answers your question.

 

[topsquark]

and from your remarks i think you have no idea about basic logic
or perhaps you are an author of a book of logic that escapes my attention

You have a history here of taking comments that you either disagree with or that question you in some (usually innocent) way and taking offense to them. No one here has issued any insults at you: they have only questioned your definitions so they could better understand what you are talking about. If you are going to ask questions you need to be prepared to define your terms, especially in a field of study such as logic, where the definitions vary greatly from one source to another.

And most members that come here asking questions are students, so that was a natural assumption.

Please be more polite: we are trying to help you, not offend you.

-Dan

 

[stapel]

What makes you think i am student, you should ask 1st if you want to be polite

Or, since you value politeness so greatly, perhaps you could re-read the "Read Before Posting" message, and provide the requested information before attacking people for not being able to read your mind when they volunteer their time to provide you with free help.

Thank you.

 

[chrislav]

No argument has no premisses and particularly a valid argument
That is agaist the definition of an argument (valid argument)
The book states and i quote : Some rules of inference state outright conclusion
And not your claim:
That there arguments (to be exact valid arguments) or rules of inference ,that have no premisses??
Can you not see the huge
difference between those two claims
The author no where in his book states or gives a definition of an argument, that justifies his stupid definition and i quote :The rules of logic are called rules of inference
The main scope of the book is to write formal proofs for some well known theorems , in algebra,groups ,rings ,numbers e.t.c ,e.t.c. in 1st order theories using 1st order ligic

 

[stapel]

No argument has no premisses and particularly a valid argument
That is agaist the definition of an argument (valid argument)
The book states and i quote : Some rules of inference state outright conclusion
And not your claim:
That there arguments (to be exact valid arguments) or rules of inference ,that have no premisses??
Can you not see the huge
difference between those two claims

You have one block of bolded typed. Which parts are the "two claims"? Kindly please make your meaning clear. Thank you.

The author no where in his book states or gives a definition of an argument, that justifies his stupid definition....

Then perhaps you have an argument with the book's author. However, this does not justify rudeness toward the volunteers who are trying to help you. Thank you.