# logical constants fix the truth value of logical expressions.

1. Philosophy Forum
2. » Logic
3. » logical constants fix the truth value of logical expressions.

Wed 8 Jul, 2009 12:47 am
Logic is said to be a normative science. This means, logic is in the same category as ethics, and aesthetics. The logical language has two component to it. They are the logical constants( e.g: or, for all, and, not etc), and the non-logical constants( p, q , r ..). Philosophers say:

1. -(p&-p) is true in all possible world.

By this, they mean that -(p&-p) is true under all interpretations of p. We say that -( p&-p) is logically necessary. While some propositions are contingent. Say the proposition q := "bill clinton is the president of the America". q is true at 1998, but not true at 2007. We say the truth value of q depends temporally. It is very easy to think of a proposition k, such that the truth value of k changes from interpretation to interpretation.

Here is the problem: What exactly is the relationship between the nonlogical constants, and the logical constants. As we see, the truth value of a proposition can vary from interpretation to interpretation. One possible hint is 1. Note that 1 is true under all interpretations of p. Some how, the logical constants ( &, not) "fixed" the truth value of 1 . The problem is to explicate how exactly does the logical constants fixed the value of 1.

jgweed

Wed 8 Jul, 2009 07:25 am
@vectorcube,
"Logic is said to be a normative science."

I am completely unsure about what a "normative science" is and why logic should be included by some people under that rubric, as well as unclear about the distinction between logical and unlogical constants.

For example, the TRUTH of the assertion that "Clinton is President" by be dependent on when the assertion was made, but it does't seem that "Either Clinton is President or he is not President" depends whatsoever on whether Clinton is in fact President, or even whether "Clinton" or "President" actually exist.

Logic is not about Truth but about rules for drawing valid conclusion from premises. The grounds for the Truth of these premises lies outside of Logic itself.

kennethamy

Wed 8 Jul, 2009 09:23 am
@vectorcube,
vectorcube;75849 wrote:
Logic is said to be a normative science. This means, logic is in the same category as ethics, and aesthetics. The logical language has two component to it. They are the logical constants( e.g: or, for all, and, not etc), and the non-logical constants( p, q , r ..). Philosophers say:

1. -(p&-p) is true in all possible world.

By this, they mean that -(p&-p) is true under all interpretations of p. We say that -( p&-p) is logically necessary. While some propositions are contingent. Say the proposition q := "bill clinton is the president of the America". q is true at 1998, but not true at 2007. We say the truth value of q depends temporally. It is very easy to think of a proposition k, such that the truth value of k changes from interpretation to interpretation.

Here is the problem: What exactly is the relationship between the nonlogical constants, and the logical constants. As we see, the truth value of a proposition can vary from interpretation to interpretation. One possible hint is 1. Note that 1 is true under all interpretations of p. Some how, the logical constants ( &, not) "fixed" the truth value of 1 . The problem is to explicate how exactly does the logical constants fixed the value of 1.

But, that Bill Clinton is president in 1998 is just as true in 2007 as it was true in 1998, and that Bill Clinton is president in 2007 is both not true in 1998, and it is not true in 2007. You have to state the non-logical constants properly, and your problem vanishes. There is no problem, there is a confusion.

---------- Post added 07-08-2009 at 11:41 AM ----------

jgweed;75899 wrote:
"Logic is said to be a normative science."

I am completely unsure about what a "normative science" is and why logic should be included by some people under that rubric, as well as unclear about the distinction between logical and unlogical constants.

For example, the TRUTH of the assertion that "Clinton is President" by be dependent on when the assertion was made, but it does't seem that "Either Clinton is President or he is not President" depends whatsoever on whether Clinton is in fact President, or even whether "Clinton" or "President" actually exist.

Logic is not about Truth but about rules for drawing valid conclusion from premises. The grounds for the Truth of these premises lies outside of Logic itself.

It was C.S. Peirce, the great American philosopher, and the originator of the only indigenous American philosophy, Pragmatism, who said that logic is a normative science. What he meant is that logic sets the rules for how we ought to think, and it is not the descriptive science of psychology (or what is now called, "Cognitive Science") which presents no rules, but simply describes how we do, in fact, think. Rules are always normative, for they tell us how we ought to behave rather than describe how we do behave.

Logic is not about truth, and is about validity. But, what is validity? A valid argument is one in which it is impossible for the premises to be true, and for the conclusion to be false. So the idea of validity is defined in terms of truth and falsity. The OP was talking about truth-functional logic, by which the truth or falsity of statements is entirely a function of the true and the falsity of its components. For instance, a compound statement like, Jack and Jill went up the hill, is defined as true, if, and only if, both Jack and Jill went up the hill, and false otherwise. But the truth functional statement, Jack or Jill went up the hill, is true as long as Jack went up the hill, Jill went up the hill, of both went up the hill, but it is false if neither went up the hill. Therefore, the argument:

1. Jack and Jill went up the hill.

Therefore, 2. Jack went up the hill

is valid, since it would be impossible for 1 to be true, and 2 to be false.

But the argument:

1. Jack or Jill went up the hill.

Therefore, 2. Jack went up the hill.

Is invalid, since it would be possible for 1. to be true, and for 2. to be false.

So the truth values of the constants are central to determining whether the arguments in truth-functional logic are valid or invalid.

vectorcube

Wed 8 Jul, 2009 01:32 pm
@jgweed,
jgweed;75899 wrote:
"Logic is said to be a normative science."

I am completely unsure about what a "normative science" is and why logic should be included by some people under that rubric, as well as unclear about the distinction between logical and unlogical constants..

I don` t know about you but i see it as a gift for me to go study. There are textbooks, and books on it. I don ` t want to give the impression that i am making things up out of nowhere. It is generally agreed by philosophers that logic is normative, and if you read papers in philosophy, all attempt is to explicate what it means for logic to be normative.

Quote:
For example, the TRUTH of the assertion that "Clinton is President" by be dependent on when the assertion was made, but it does't seem that "Either Clinton is President or he is not President" depends whatsoever on whether Clinton is in fact President, or even whether "Clinton" or "President" actually exist.

In my post, i gave only one example, but there are many more examples of proposition that depend no only on time, but on worlds. We can imagine a possible world in which the value of "clinton is president" depends on the matters of fact in each possible world.

Quote:
Logic is not about Truth but about rules for drawing valid conclusion from premises. The grounds for the Truth of these premises lies outside of Logic itself

That is not what i am saying tho. It is true that the propositions depend on interpretations. A fancy name is non-logical constants. Their value do depend on intepretations, but when we mix logical, and nonlogical constants into a expression like the form we see in 1, we seem to be able to fixed the truth value of 1 in all possible interpretation of p. The question is the explication of the relationship between logical and nonlogical constants.

---------- Post added 07-08-2009 at 02:41 PM ----------

Kennethy wrote:

But, that Bill Clinton is president in 1998 is just as true in 2007 as it was true in 1998, and that Bill Clinton is president in 2007 is both not true in 1998, and it is not true in 2007. You have to state the non-logical constants properly, and your problem vanishes. There is no problem, there is a confusion.

This means you are lost in the main point. My drive is never to make sense of "Bill Clinton is president". If you you wish, a slight modification to "Bill Clinton is the president in 1998". In such modification, the proposition is true in 1997, but false in 2008, and thus, work as my example. It does depend on time. No big deal.

The real problem is to explicate the relationship between logical/ nonlogical constants to make 1 true in all possible interpretation of p in 1. How is it possible. How the can logical constant fixed the value of 1.

---------- Post added 07-08-2009 at 02:59 PM ----------

Quote:

Logic is not about truth, and is about validity. But, what is validity? A valid argument is one in which it is impossible for the premises to be true, and for the conclusion to be false. So the idea of validity is defined in terms of truth and falsity.

Validity depends only on the form. It is syntactical. You can explain why the form is such that it is fixed by the fact that true premises lead to true conclusion, but i can still doubt how the congregation of propositions fixed the form. Logic is based on form, and form alone. It is a purely syntactical notion, while true is a semantical notion. You should not mix together like you did here.

kennethamy

Wed 8 Jul, 2009 09:26 pm
@vectorcube,
vectorcube;75959 wrote:
I don` t know about you but i see it as a gift for me to go study. There are textbooks, and books on it. I don ` t want to give the impression that i am making things up out of nowhere. It is generally agreed by philosophers that logic is normative, and if you read papers in philosophy, all attempt is to explicate what it means for logic to be normative.

In my post, i gave only one example, but there are many more examples of proposition that depend no only on time, but on worlds. We can imagine a possible world in which the value of "clinton is president" depends on the matters of fact in each possible world.

That is not what i am saying tho. It is true that the propositions depend on interpretations. A fancy name is non-logical constants. Their value do depend on intepretations, but when we mix logical, and nonlogical constants into a expression like the form we see in 1, we seem to be able to fixed the truth value of 1 in all possible interpretation of p. The question is the explication of the relationship between logical and nonlogical constants.

---------- Post added 07-08-2009 at 02:41 PM ----------

This means you are lost in the main point. My drive is never to make sense of "Bill Clinton is president". If you you wish, a slight modification to "Bill Clinton is the president in 1998". In such modification, the proposition is true in 1997, but false in 2008, and thus, work as my example. It does depend on time. No big deal.

The real problem is to explicate the relationship between logical/ nonlogical constants to make 1 true in all possible interpretation of p in 1. How is it possible. How the can logical constant fixed the value of 1.

---------- Post added 07-08-2009 at 02:59 PM ----------

Validity depends only on the form. It is syntactical. You can explain why the form is such that it is fixed by the fact that true premises lead to true conclusion, but i can still doubt how the congregation of propositions fixed the form. Logic is based on form, and form alone. It is a purely syntactical notion, while true is a semantical notion. You should not mix together like you did here.

Why is the statement that Bill Clinton is the president in 1997/8 false in 2008? Isn't it true that Clinton was the president in 1997/8 (or am I mistaken?) If my facts are not wrong, then what is your objection? The statement is certainly both true in 1998, and also true in 2009. In fact, it was true in the year 1728, and will will true in the year 2,900. It has always been true, and it will always be true.

How exactly did I mix up syntax and semantics? Could you explain why you think so, since I don't think so. Is it not true that a valid argument is one that is defined as an argument for which it is impossible that the premises should be true, and the conclusion be false? And that an example of that would be that: 1. Jack and Jill went up the hill. Therefore, 2. Jack went up the hill. That is a valid argument since if the premise is true, then the conclusion must be true. What have I said that mixes up syntax and semantics? Are you able to say. If you like, I will delete the constants, and put it"

1. P & Q

Therefore,

P

is a valid argument form, and any argument of that form is, therefore a valid argument.

That is the same thing as I said before, only in different language.

If it makes you feel more comfortable, I am glad for you.

vectorcube

Thu 9 Jul, 2009 02:56 am
@kennethamy,
Quote:

Why is the statement that Bill Clinton is the president in 1997/8 false in 2008? Isn't it true that Clinton was the president in 1997/8 (or am I mistaken?) If my facts are not wrong, then what is your objection? The statement is certainly both true in 1998, and also true in 2009. In fact, it was true in the year 1728, and will will true in the year 2,900. It has always been true, and it will always be true.

This is because i did not think much of the modified example. I was in a hurry to go to the mall with girlfriend. Anyways, all i wanted to do was to find an example that is logically contingent. Let ` s use the proposition:

p= "pigs can fly"

Now, p is false in our world, but true in a possible world.

Quote:
How exactly did I mix up syntax and semantics? Could you explain why you think so, since I don't think so. Is it not true that a valid argument is one that is defined as an argument for which it is impossible that the premises should be true, and the conclusion be false? And that an example of that would be that: 1. Jack and Jill went up the hill. Therefore, 2. Jack went up the hill. That is a valid argument since if the premise is true, then the conclusion must be true. What have I said that mixes up syntax and semantics? Are you able to say. If you like, I will delete the constants, and put it"

1. P & Q

Therefore,

P

What i see is that you are using truth to define validity. You said that something is a valid argument if "it is impossible that the premises should be true, and the conclusion be false". This explanation is "reductive" in the sense that you are explaining or define validity in terms of truth, while validity and truth are separate notions all together. Validity is based on form alone. Eg:

1. P & Q |- P is valid

while

1* P&Q|- R is not valid.

Truth is a property of a proposition in relation to reality Eg:

"pigs cannot fly" is true. "Pigs can fly" is false.

validity is about form. Truth is a property of a proposition.
Both are distinct semantic primitives( postuates, or undefined terms).
You can ` t explain one in terms of another( because they are semantic primitives).

Another way to think about it is to think of logic as a formal language. There is a purely formal component to which is basically symbol manipulation, and a interpretive component to it which it basically tell us what the symbol means. The latter is the study of model theory.

goapy

Thu 9 Jul, 2009 05:31 am
@vectorcube,
vectorcube;76035 wrote:

validity is about form. Truth is a property of a proposition.
Both are distinct semantic primitives( postuates, or undefined terms).
You can ` t explain one in terms of another( because they are semantic primitives).

Validity is a semantic notion: an inference (argument) is valid if and only if it is not possible for the premises to be true and the conclusion false; whereas derivability is a syntactic notion. A logic is said to be complete if those inferences that are valid are derivable; it is said to be sound if those inferences that are derivable are valid.

We needn't talk about reality when we are talking the possibility (or impossibility) of "truth" in a bivalent system. These are hypothetical notions of indefeasibility, containment, or preservation. Any relation to reality is another matter.

kennethamy

Thu 9 Jul, 2009 06:42 am
@vectorcube,
vectorcube;76035 wrote:
This is because i did not think much of the modified example. I was in a hurry to go to the mall with girlfriend. Anyways, all i wanted to do was to find an example that is logically contingent. Let ` s use the proposition:

p= "pigs can fly"

Now, p is false in our world, but true in a possible world.

What i see is that you are using truth to define validity. You said that something is a valid argument if "it is impossible that the premises should be true, and the conclusion be false". This explanation is "reductive" in the sense that you are explaining or define validity in terms of truth, while validity and truth are separate notions all together. Validity is based on form alone. Eg:

1. P & Q |- P is valid

while

1* P&Q|- R is not valid.

Truth is a property of a proposition in relation to reality Eg:

"pigs cannot fly" is true. "Pigs can fly" is false.

validity is about form. Truth is a property of a proposition.
Both are distinct semantic primitives( postuates, or undefined terms).
You can ` t explain one in terms of another( because they are semantic primitives).

Another way to think about it is to think of logic as a formal language. There is a purely formal component to which is basically symbol manipulation, and a interpretive component to it which it basically tell us what the symbol means. The latter is the study of model theory.

But how do you define validity without the notion of truth? A valid argument is, by definition, an argument which cannot have true premises, and a false conclusion. Have you any other definition? Let me hear about it? It will be news to me.

To say that p is not true in every possible world, is to say that p is a contingent proposition. To say that p is true in this world, but not in every possible world, is simply to say that p is true, and is a contingent proposition

vectorcube

Thu 9 Jul, 2009 12:26 pm
@kennethamy,
kennethamy;76075 wrote:
But how do you define validity without the notion of truth? A valid argument is, by definition, an argument which cannot have true premises, and a false conclusion. Have you any other definition? Let me hear about it? It will be news to me.

Right. I said validity is based on form. It is true that it is not an explication, for you can question why the forms of logic hold, and not some other from that holds. I am the kind of guy that if i don` t know something, I don `t really waste my time on it. All i know is that your definition is wrong, because validity, and truth are distinctive semantic primitives. You cannot explained one in terms of another. Saying that your definition in incorrect does not follow that i need to give you an explication/definition.

Tho, distinquishing form from semantic is not at all uncommon in formal language in computer science.

[URL="file://\\Take"]Take[/URL] the case of physics. A set of equations would not be a model( or description ) of anything if not for the fact that each variables has a corresponding meaning. In this case, the meaning is the referent.

goapy

Thu 9 Jul, 2009 01:43 pm
@vectorcube,
vectorcube;76114 wrote:
All i know is that your definition is wrong, because validity, and truth are distinctive semantic primitives. You cannot explained one in terms of another. Saying that your definition in incorrect does not follow that i need to give you an explication/definition.

Perhaps. Although you would be obligated to provide an argument for validity and truth being semantic primes. And for the concept of semantic primitives in general.

And also how it is that you're able to provide instances of valid forms without having an "explication/definition". How do you make this assessment? How are you able to pick them out? You've picked them out, so there must be some way in which you've picked them out. So, you should be able to tell us how you picked them out?

vectorcube;76114 wrote:

I am the kind of guy that if i don` t know something, I don `t really waste my time on it.

vectorcube;76114 wrote:

I don` t know about you but i see it as a gift for me to go study.

vectorcube

Thu 9 Jul, 2009 02:25 pm
@goapy,
Quote:
Perhaps. Although you would be obligated to provide an argument for validity and truth being semantic primes. And for the concept of semantic primitives in general.

definition of semantic primitive is here:

Semantic primitives

why are they primes. Because truth is a property of a proposition.

Truth (Stanford Encyclopedia of Philosophy)

Given that truth is a property of propositions( above), but validity is not a property of a proposition( Why?). We see they are distinct notions.

Another way of seeing how they are distinct notion is that neither one effects the other.
E.g:

1. The truth of individual propositions in argument does not imply validity of the argument.

2. The validity of a argument does not fix the truth of individual propositions

Peter Suber, "Truth and Validity"

Suppose validity is a property of propositions. Which proposition makes argument valid? How does the properties individual proposition fixs the form of a set of propositons? Best explanation is that they don ` t have anything to do with one another. Thus, they are semantic primitives.

---------- Post added 07-09-2009 at 03:47 PM ----------

Quote:

And also how it is that you're able to provide instances of valid forms without having an "explication/definition".

Why not? I can show y is not a solution of f(x)=E without giving a solution at all.

Quote:

How do you make this assessment? How are you able to pick them out? You've picked them out, so there must be some way in which you've picked them out. So, you should be able to tell us how you picked them out?

why do i need to? Do we pick out defintions? Obviously not. If so, from where? It is not like picking out apples from a box. Do we pick out out numbers? No, they just exist. Do we pick out the universe we live in ? No. We are stick in this universe.

goapy

Thu 9 Jul, 2009 04:10 pm
@vectorcube,
vectorcube;76126 wrote:

A quote from Suber, from the link you provided above:

"We cannot say that truth and validity are utterly independent because the impossibility of "case zero" (a valid argument with true premises and false conclusion) shows that one combination of truth-values is an absolute bar to validity. When an argument has true premises and a false conclusion, it must be invalid. In fact, this is how we define invalidity"

Suber goes on to make a distinction between a semantic concept of validity and a syntactic concept of validity. He is able to dispense with notions of truth only in the syntactic concept. Well, of course! This is just the same as what I said earlier:

goapy;76066 wrote:
Validity is a semantic notion: an inference (argument) is valid if and only if it is not possible for the premises to be true and the conclusion false; whereas derivability is a syntactic notion. A logic is said to be complete if those inferences that are valid are derivable; it is said to be sound if those inferences that are derivable are valid.

goapy;76066 wrote:

How do you make this assessment? How are you able to pick them out? You've picked them out, so there must be some way in which you've picked them out. So, you should be able to tell us how you picked them out?
vectorcube;76126 wrote:

why do i need to? ... they just exist...

Because I'm assuming that you aren't claiming that your assertions are a direct pathway to what exists and what is the case.

When you put forth instances of forms and claim that they are valid, these are your assertions. If your justification for your assertion that the forms that you have put forth are valid is "they just are" or "they just exist", you are saying that their validity is self-evident. Is this what you're claiming? Or do we need to go to you anytime we need to know whether a form is valid or invalid, or if there even are any?

No, you don't need to provide justification for your assertions. But don't expect to convince anyone except possibly yourself.

kennethamy

Thu 9 Jul, 2009 05:41 pm
@vectorcube,
vectorcube;76114 wrote:
Right. I said validity is based on form. It is true that it is not an explication, for you can question why the forms of logic hold, and not some other from that holds. I am the kind of guy that if i don` t know something, I don `t really waste my time on it. All i know is that your definition is wrong, because validity, and truth are distinctive semantic primitives. You cannot explained one in terms of another. Saying that your definition in incorrect does not follow that i need to give you an explication/definition.

Tho, distinquishing form from semantic is not at all uncommon in formal language in computer science.

[URL="file://%5C%5CTake"]Take[/URL] the case of physics. A set of equations would not be a model( or description ) of anything if not for the fact that each variables has a corresponding meaning. In this case, the meaning is the referent.

But it is not wrong. Every elementary logic book defines "validity" in that way. That is what "validity" means. The test of validity is a formal one, but there is no other definition of "validity". Look it up, and find out. Then you will know something, and you won't waste your time on it. No need to remain in ignorance, and deny any answer. Won't that be nice?

---------- Post added 07-09-2009 at 07:45 PM ----------

goapy;76154 wrote:
A quote from Suber, from the link you provided above:

"We cannot say that truth and validity are utterly independent because the impossibility of "case zero" (a valid argument with true premises and false conclusion) shows that one combination of truth-values is an absolute bar to validity. When an argument has true premises and a false conclusion, it must be invalid. In fact, this is how we define invalidity"

Suber goes on to make a distinction between a semantic concept of validity and a syntactic concept of validity. He is able to dispense with notions of truth only in the syntactic concept. Well, of course! This is just the same as what I said earlier:

Because I'm assuming that you aren't claiming that your assertions are a direct pathway to what exists and what is the case.

When you put forth instances of forms and claim that they are valid, these are your assertions. If your justification for your assertion that the forms that you have put forth are valid is "they just are" or "they just exist", you are saying that their validity is self-evident. Is this what you're claiming? Or do we need to go to you anytime we need to know whether a form is valid or invalid, or if there even are any?

No, you don't need to provide justification for your assertions. But don't expect to convince anyone except possibly yourself.

But, those are not just my assertions. They are the assertions which professional logicians make. No, validity is not self-evident. To find out whether an argument is valid you have to find out what the premises and the conclusion are, and then figure out whether it is possible for the premises to be true, and for the conclusion false. It is because of this, all argument with self-contradictory premises are valid, and all argument with tautologies as conclusions are valid. You do see that, don't you?

vectorcube

Thu 9 Jul, 2009 06:24 pm
@kennethamy,
Quote:
. No need to remain in ignorance, and deny any answer. Won't that be nice?

I am sorry, but you have me confused with you. Validity is a purely formal notion. Validity, and truth are different things. Truth is a property of propositions. They don ` t determine argument form. I suspect most authors don`t really want to make clear the distinction by trying to appeal to the readers intuition. I suspect more advanced books might do a better job. My gut feeling is that they don` t know anything about this issue. I even personally know a logician who is the author of a famous textbook in logic. You can ` t trust everything you read.

Quote:

But it is not wrong. Every elementary logic book defines "validity" in that way. That is what "validity" means. The test of validity is a formal one, but there is no other definition of "validity".

Most people know validity is based on form. I don ` t think anyone knows why. People don` t know, so that is why they gave that incorrect definition of validity like you. Of course, they are wrong. Formal language is all about separation between semantics and syntax. They are separate , distinct notions.

kennethamy

Thu 9 Jul, 2009 06:40 pm
@vectorcube,
vectorcube;76187 wrote:
I am sorry, but you have me confused with you. Validity is a purely formal notion. Validity, and truth are different things. Truth is a property of propositions. They don ` t determine argument form. I suspect most authors don`t really want to make clear the distinction by trying to appeal to the readers intuition. I suspect more advanced books might do a better job. My gut feeling is that they don` t know anything about this issue. I even personally know a logician who is the author of a famous textbook in logic. You can ` t trust everything you read.

Most people know validity is based on form. I don ` t think anyone knows why. People don` t know, so that is why they gave that incorrect definition of validity like you. Of course, they are wrong. Formal language is all about separation between semantics and syntax. They are separate , distinct notions.

Why not read a book or something, and inform yourself, so that you do not sound as if you are talking straight out of your hat?

An argument is valid if and only if the truth of its premises entails the truth of its conclusion, it would be self-contradictory to affirm the premises and deny the conclusion. The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a logical consequence of its premises.

Wicki

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

Internet Encyclopedia of Philosophy.

goapy

Thu 9 Jul, 2009 08:05 pm
@vectorcube,
vectorcube;76187 wrote:
Validity is a purely formal notion. Validity, and truth are different things. Truth is a property of propositions. They don ` t determine argument form.

Suppose all of the above is granted. Since we apparently can identify valid forms, there must be some methodology by which we do this. Do you dispute this?

What about the kinds of forms that are of the set of valid forms? Do these kinds of forms have no properties?

Wiki has an attempt to identify the properties of such forms:

"An argument is formally valid if its form is one such that for each interpretation under which the premises are all true also the conclusion is true."

It seems that this does not reduce validity to truth, but rather to the properties of any valid form. And to the extent it does speak of truth, it speaks of a function on truth, not truth itself. Not the sort of truth that is a property of a proposition. This is why classical propositonal logic is often referred to as truth-functional logic. If the formal connectives (logical constants) are basically symbol manipulation, they perform a function (symbol manipulation) on the possible (or stipulated) values of the non-logical constants.

You've provided at least one instance where the (occurrence of) non-logical constants may be some factor in an expression that is true in all possible worlds. You started this thread by asking:

"What exactly is the relationship between the non-logical constants, and the logical constants?"

-----
But suppose all of this is just too much truth-talk for you when it comes to validity.

Validity has also been defined as having no counter-examples. You could, if you like, think of a counter example as a form, rather than as a truth-functional instance of true premises and a false conclusion.

But to the extent that you put forth valid forms, you must have a means to do so.

vectorcube

Thu 9 Jul, 2009 11:21 pm
@kennethamy,
kennethamy;76190 wrote:
Why not read a book or something, and inform yourself, so that you do not sound as if you are talking straight out of your hat?

What is "straight out of my hat" mean? The definitions are at best "not good", and at worst "completely wrong". Validity, and truth are completely different things.

---------- Post added 07-10-2009 at 12:52 AM ----------

goapy;76200 wrote:
Suppose all of the above is granted. Since we apparently can identify valid forms, there must be some methodology by which we do this. Do you dispute this?

Honestly, I don` t know. I suspect they come from pre-theoretic belief.

Pre-theoretic belief - Wikipedia, the free encyclopedia

Quote:

What about the kinds of forms that are of the set of valid forms? Do these kinds of forms have no properties?

I don ` t know. I suspect they have no properties. If they do have properties, then accordingly, you can defined a set that instantiate the property. The set of all valid forms, but i see problems.

Quote:

Wiki has an attempt to identify the properties of such forms:

"An argument is formally valid if its form is one such that for each interpretation under which the premises are all true also the conclusion is true."

I think this definition of validity would make sense if validity is a second order property. That is, if validity is a relation between properties, truth. This only works if i accept validity as a second order property.

Quote:
It seems that this does not reduce validity to truth, but rather to the properties of any valid form. And to the extent it does speak of truth, it speaks of a function on truth, not truth itself.

Yes, this is right. This is like thinking of validity as a second-order property. I like this idea, but like i said before, i don ` t need to accept it if i reject validity as a second-order property. Logic would still work if both notions are primitives. Tho, i have nothing againist people who hold such belief.

goapy

Fri 10 Jul, 2009 12:05 am
@vectorcube,
vectorcube;76232 wrote:
Validity, and truth are completely different things.

Maybe we could just dispense with the common traditional consensus notion of validity that bothers you so much. Derivability will get us there just as well. Derivability is proof theory down to the ground. It is formal and syntactical all the way. I've mentioned it three times now, and you've ignored it each time.

Unfortunately, your buddy Peter Suber calls derivability by another name; Syntactic validity, as he distinguishes from Semantic validity and Logical validity.

Peter Suber:

Syntactic validity. An inference is syntactically valid iff the conclusion can be derived from the premises by means of stipulated rules of inference. See semantic validity.

^Look, no mention of truth! And yet a fully formal method to demonstrate validity. What do you say?

vectorcube

Fri 10 Jul, 2009 12:17 am
@goapy,
goapy;76246 wrote:

^Look, no mention of truth! And yet a fully formal method to demonstrate validity. What do you say?

What do you think? I say great. There is an intuitive appeal in thinking of validity as a set of rules, and operations.

kennethamy

Fri 10 Jul, 2009 01:05 am
@goapy,
goapy;76246 wrote:
Maybe we could just dispense with the common traditional consensus notion of validity that bothers you so much. Derivability will get us there just as well. Derivability is proof theory down to the ground. It is formal and syntactical all the way. I've mentioned it three times now, and you've ignored it each time.

Unfortunately, your buddy Peter Suber calls derivability by another name; Syntactic validity, as he distinguishes from Semantic validity and Logical validity.

Peter Suber:

Syntactic validity. An inference is syntactically valid iff the conclusion can be derived from the premises by means of stipulated rules of inference. See semantic validity.

^Look, no mention of truth! And yet a fully formal method to demonstrate validity. What do you say?

That there is no mention of truth does not mean that truth isn't there anyway. What does it mean to say that the conclusion is derived from the premises? It could not be. "if the premises are true, then so must the conclusion be true" could it?

1. Philosophy Forum
2. » Logic
3. » logical constants fix the truth value of logical expressions.