logical constants fix the truth value of logical expressions.

[vectorcube]

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]

"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]

Originally Posted by vectorcube

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 ----------

Originally Posted by jgweed

"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]

Originally Posted by jgweed

"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.

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.

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 ----------

Originally Posted by Kennethy

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 ----------

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]

Originally Posted by vectorcube

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]

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.

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]

Originally Posted by vectorcube

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]

Originally Posted by vectorcube

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]

Originally Posted by kennethamy

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.

Take 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]

Originally Posted by vectorcube

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?

Originally Posted by vectorcube

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

Originally Posted by vectorcube

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