14

Mathematics is not a science

kennethamy

0
Sun 1 Aug, 2010 06:08 pm
@mickalos,
mickalos wrote:

kennethamy wrote:

That all dogs are dogs is a necessary truth, since it can be shown on a truth table that it is a tautology for it is a substitution instance of the propositional form, all X is X. Consult any elementary logic book for how to operate truth tables. All dogs are dogs is a logical truth, and all logical truths are necessary truths for their negations are logically impossible.

1. All dogs are dogs is a logical true
2. All logical truths are necessary truths.

Therefore, 3, all dogs are dogs is a necessary truth. QED.

The second premise clearly needs further treatment before it can be accepted as sound. For me, something more substantive than, 'it is impossible for a logical truth to be false', is required. An appeal to possible worlds does, after all, need to be grounded in something. Conceivability is appealed to quite a lot, but might we not have had different concepts? Concepts are a very tricky subject, but its a more than plausible claim that our concepts could have been different if certain biological, socialogical, or natural facts had been different. A presumable result of this may be that certain things we hold to be impossible might be perfectly conceivable. Pv~P is a necessary truth, but what if we only had paraconsistent logics?...

There are other reasons to reject conceivability and possibility as being co-extensive. The necessarily existing God used in the ontological argument seems to be conceivable using possible world semantics: a necessarily existing God simply exists in all possible worlds. However, the notion of a necessarily existing being seems impossible to most.

For me, something more substantive than, 'it is impossible for a logical truth to be false', is required.

I see. You don't know what a logical truth is. It is a technical term in logic. It means that if when a truth is subjected to a truth table test, it tests out to a tautology. Now, a tautology is a proposition which is true under all interpretations of its variables. Thus, for instance, any proposition of the form, A or not-A is not only true, but it must be true, since for all substitutions of A, the proposition is true. Thus, it is impossible for any proposition of that form to be false, and so, it is not only true, but it is a necessary truth. You may need to learn a little logic. We can put this into the language of possible worlds too (although I find that language cumbersome). But we can say that a logical truth is true in all possible worlds. Which is equivalent to saying that it is true under all possible interpretations of its variables.

The notion of "necessary truth" has been extended somewhat outside of the strict notion of logical truth. So that to call a proposition a necessary truth is to say that it is either a logical truth or it is reducible to a logical truth. Issues sometime arise about whether or not a proposition is reducible to a logical truth as famously discussed by Quine. But there is no issue that some truths are clearly logical truths, and that all logical truths are necessary truths. The only problem that arises is whether a truth is reducible to a logical truth and is, therefore, a necessary truth.
ughaibu

2
Sun 1 Aug, 2010 06:54 pm
@kennethamy,
kennethamy wrote:
mickalos wrote:
what if we only had paraconsistent logics?
any proposition of the form, A or not-A is not only true, but it must be true, since for all substitutions of A, the proposition is true.
Isn't Mickalos' point that something being true in a particular class of logics, doesn't make it true in all logics? Thus the idea of necessary truth isn't primary and cant be appealed to for primary distinctions.
kennethamy

1
Sun 1 Aug, 2010 07:26 pm
@ughaibu,
ughaibu wrote:

kennethamy wrote:
mickalos wrote:
what if we only had paraconsistent logics?
any proposition of the form, A or not-A is not only true, but it must be true, since for all substitutions of A, the proposition is true.
Isn't Mickalos' point that something being true in a particular class of logics, doesn't make it true in all logics? Thus the idea of necessary truth isn't primary and cant be appealed to for primary distinctions.

I see no reason to deny the correctness of standard logic just because there are peculiar logics floating about.
ughaibu

2
Sun 1 Aug, 2010 09:04 pm
@kennethamy,
kennethamy wrote:
ughaibu wrote:
Isn't Mickalos' point that something being true in a particular class of logics, doesn't make it true in all logics? Thus the idea of necessary truth isn't primary and cant be appealed to for primary distinctions.
I see no reason to deny the correctness of standard logic just because there are peculiar logics floating about.
Logics are independent of reality, something of which you seem to be aware:
kennethamy wrote:
When pure mathematics is applied to "the real world", funny things begin to happen. That is also true when theoretical logic is applied to "the real world".
You subscribe to a correspondence theory of truth, and I take it "correctness" is a notion concerned with truth. As the correctness of logics is independent of reality and what is correct in any particular logic is a matter of how the formalism is defined, I dont see how you can talk about the correctness of logics in any interestingly non-circular manner. So, what do you mean by "correctness"?
0 Replies

mickalos

1
Mon 2 Aug, 2010 07:14 am
@kennethamy,
kennethamy wrote:

For me, something more substantive than, 'it is impossible for a logical truth to be false', is required.

I see. You don't know what a logical truth is. It is a technical term in logic. It means that if when a truth is subjected to a truth table test, it tests out to a tautology. Now, a tautology is a proposition which is true under all interpretations of its variables. Thus, for instance, any proposition of the form, A or not-A is not only true, but it must be true, since for all substitutions of A, the proposition is true. Thus, it is impossible for any proposition of that form to be false, and so, it is not only true, but it is a necessary truth. You may need to learn a little logic. We can put this into the language of possible worlds too (although I find that language cumbersome). But we can say that a logical truth is true in all possible worlds. Which is equivalent to saying that it is true under all possible interpretations of its variables.

You have missed my point. Does a certain model/interpretation force a truth value? Certainly, we feel a psychological compulsion to say Pv~P is an eternal truth (I'm not trying to be technical), but I dispute that it is any more than that, which is what my point about paraconsistent logics was about. With certain sociological and historical developments or changes, and perhaps with certain things we learn about the world, we often break free of psychological compulsions. History is full of examples of primitively compelling claims and arguments that we now regard as false concerning God, politics, reality, and even, yes, patterns of reasoning. Is there any fact of the matter that distinguishes "logical compulsion" from mere dogma (this, I think, is one of the things that makes Quine's arguments against the analytic synthetic distinction so compelling)? I think it can only be a naturalistic/anthropocentric fact of the matter, e.g. "People do not allow ~(Pv~P) in classical logic", but this is a very different fact of the matter than most realists about necessity and logical truth think there is.

Quote:
The notion of "necessary truth" has been extended somewhat outside of the strict notion of logical truth. So that to call a proposition a necessary truth is to say that it is either a logical truth or it is reducible to a logical truth. Issues sometime arise about whether or not a proposition is reducible to a logical truth as famously discussed by Quine. But there is no issue that some truths are clearly logical truths, and that all logical truths are necessary truths. The only problem that arises is whether a truth is reducible to a logical truth and is, therefore, a necessary truth.

I'm not quite sure what is going on in this paragraph. Surely, the issue is whether or not it is possible for Pv~P to be false. If we assign role to our concepts in determining the (necessary) truth of this proposition, and we accept that our concepts might have been different, then it seems likely that the hardness of the logical must might be compromised.

There's a very good article by Quassim Cassam called "Necessity and Externality" on these issues that might interest you.

Quote:
I see no reason to deny the correctness of standard logic just because there are peculiar logics floating about.

These peculiar logics arose out of the peculiarities of classical logic, which is littered with paradoxes: the paradox of entailment, the paradoxes of the material conditional, the principle of explosion. But, I want to stress that I am not saying classical logic might be false, and another logic true, simply that with a different history of inferring we might not hold the law of the excluded middle in such high regard.
0 Replies

rosborne979

1
Mon 2 Aug, 2010 07:20 am
@TuringEquivalent,
TuringEquivalent wrote:
Mathematics is not a science.

Obviously. But would it be more accurately classified as a Philosophy or a Language?
Zetherin

1
Mon 2 Aug, 2010 10:33 pm
mickalos wrote:
You have missed my point. Does a certain model/interpretation force a truth value? Certainly, we feel a psychological compulsion to say Pv~P is an eternal truth (I'm not trying to be technical), but I dispute that it is any more than that, which is what my point about paraconsistent logics was about. With certain sociological and historical developments or changes, and perhaps with certain things we learn about the world, we often break free of psychological compulsions. History is full of examples of primitively compelling claims and arguments that we now regard as false concerning God, politics, reality, and even, yes, patterns of reasoning. Is there any fact of the matter that distinguishes "logical compulsion" from mere dogma (this, I think, is one of the things that makes Quine's arguments against the analytic synthetic distinction so compelling)? I think it can only be a naturalistic/anthropocentric fact of the matter, e.g. "People do not allow ~(Pv~P) in classical logic", but this is a very different fact of the matter than most realists about necessity and logical truth think there is.

But following this, where do you draw the line? When do we consider something an actual matter of fact, instead of *only* a matter of fact for X discipline or position?

May I ask what position on truth you take?

ughaibu wrote:
You subscribe to a correspondence theory of truth, and I take it "correctness" is a notion concerned with truth. As the correctness of logics is independent of reality and what is correct in any particular logic is a matter of how the formalism is defined, I dont see how you can talk about the correctness of logics in any interestingly non-circular manner. So, what do you mean by "correctness"?

Echoing my post above, where do you draw the line? What has led you to conclude that the correctness of a particular logic is independent of reality? Because"correct" is defined by the particular formalism in question, doesn't mean that "correctness" cannot be part of a proposition (describing reality), does it? If I told you that the correct way to move a pawn in the game of chess is to advance it a single square, except during the first time the pawn is moved where it can advance two squares, am I not expressing something about reality?

May I ask what position on truth you take?
mickalos

1
Tue 3 Aug, 2010 03:52 am
@Zetherin,
Zetherin wrote:

mickalos wrote:
You have missed my point. Does a certain model/interpretation force a truth value? Certainly, we feel a psychological compulsion to say Pv~P is an eternal truth (I'm not trying to be technical), but I dispute that it is any more than that, which is what my point about paraconsistent logics was about. With certain sociological and historical developments or changes, and perhaps with certain things we learn about the world, we often break free of psychological compulsions. History is full of examples of primitively compelling claims and arguments that we now regard as false concerning God, politics, reality, and even, yes, patterns of reasoning. Is there any fact of the matter that distinguishes "logical compulsion" from mere dogma (this, I think, is one of the things that makes Quine's arguments against the analytic synthetic distinction so compelling)? I think it can only be a naturalistic/anthropocentric fact of the matter, e.g. "People do not allow ~(Pv~P) in classical logic", but this is a very different fact of the matter than most realists about necessity and logical truth think there is.

But following this, where do you draw the line? When do we consider something an actual matter of fact, instead of *only* a matter of fact for X discipline or position?

May I ask what position on truth you take?

First of all, I wouldn't characterise my view as being that 'Pv~P is a fact only in classical logic'. Certainly, it is a theorem of classical logic, and not a theorem of other calculi, but that is uncontroversial. My view is a naturalistic scepticism about rule following and necessity. There is no fact of the matter that makes Pv~P follow from the rules of logical inference apart from the fact that we all agree that it does, i.e. no expression or interpretation of those rules forces a particular application on me; logic does not "grab you by the throat". We might have agreed on something different.

I don't understand what you mean when you distinguish between an "actual fact of the matter" and other facts. As far as truth is concerned, I don't think it's as important a concept as the history of philosophy makes it out to be, it is merely a pat on the back we give to sentences that pay their way. Certainly, I think the idea that a sentence is true because that's the way the world is, seems to me to be a metaphysical tip of the hat that ought not be taken too literally. We can say some things about truth: 'truth' is the predicate we apply to beliefs that we've justified, beliefs can be true without being justified, and justification is relative to a range of audiences and truth candidates while truth is not relative to anything. I don't think there is much more that you can say about truth, it's not a very interesting concept.

Quote:
ughaibu wrote:
You subscribe to a correspondence theory of truth, and I take it "correctness" is a notion concerned with truth. As the correctness of logics is independent of reality and what is correct in any particular logic is a matter of how the formalism is defined, I dont see how you can talk about the correctness of logics in any interestingly non-circular manner. So, what do you mean by "correctness"?

Echoing my post above, where do you draw the line? What has led you to conclude that the correctness of a particular logic is independent of reality? Because"correct" is defined by the particular formalism in question, doesn't mean that "correctness" cannot be part of a proposition (describing reality), does it? If I told you that the correct way to move a pawn in the game of chess is to advance it a single square, except during the first time the pawn is moved where it can advance two squares, am I not expressing something about reality?

Only if you take a platonic realist approach to rules. What is a rule? Well, the rules of chess establish criteria of correctness, but how? Are they "abstract entities" that sort correct action from incorrect action all by themselves? Seems a bit far fetched for my liking.
0 Replies

ughaibu

1
Tue 3 Aug, 2010 08:20 am
@Zetherin,
Zetherin wrote:
ughaibu wrote:
You subscribe to a correspondence theory of truth, and I take it "correctness" is a notion concerned with truth. As the correctness of logics is independent of reality and what is correct in any particular logic is a matter of how the formalism is defined, I dont see how you can talk about the correctness of logics in any interestingly non-circular manner.
Echoing my post above, where do you draw the line?
What line?
Zetherin wrote:
What has led you to conclude that the correctness of a particular logic is independent of reality?
Logics are linguistic systems which preserve truth values according to defined rules, that is to say that they are human inventions, and I hold that reality is not a subset of human invention.
Zetherin wrote:
Because"correct" is defined by the particular formalism in question, doesn't mean that "correctness" cannot be part of a proposition (describing reality), does it?
How is this meant to be relevant?
1) if some particular logic happens to always mimic reality, that logic will still be a human invention
2) if it is the case that a certain logic is derived from human interaction with reality, then that logic will have an irreducibly contingent inductive basis, so you can say good-bye to any ideas about necessity.
Zetherin wrote:
If I told you that the correct way to move a pawn in the game of chess is to advance it a single square, except during the first time the pawn is moved where it can advance two squares, am I not expressing something about reality?
I dont see why, this rule is quite modern, and even today doesn't apply in Chinese, Japanese, Thai or Burmese chess.
Zetherin wrote:
May I ask what position on truth you take?
It's clear enough that any claim of the truth about truth will either be circular or pluralist, I prefer the pluralist stance.
0 Replies

High Seas

1
Tue 3 Aug, 2010 09:23 am
@rosborne979,
rosborne979 wrote:

TuringEquivalent wrote:
Mathematics is not a science.

Obviously. But would it be more accurately classified as a Philosophy or a Language?

Ditto to your "obviously", but your other 2 options aren't quite correct. Formally, mathematics is an axiomatic system of logic, and like all axiomatic systems it's subject to certain limitations. There is NO sector of mathematical thought that can be supplied with a set of axioms sufficient for developing systematically the endless totality of true propositions about that sector. That is the essence of the great Gödel's incompleteness theorem.
ughaibu

1
Tue 3 Aug, 2010 09:28 am
@High Seas,
High Seas wrote:
There is NO sector of mathematical thought that can be supplied with a set of axioms sufficient for developing systematically the endless totality of true propositions about that sector. That is the essence of the great Gödel's incompleteness theorem.
This cant be stated as a fact: http://plato.stanford.edu/entries/mathematics-inconsistent/
Melbourne University is presently hosting a three year program aimed at extending para-consistent set theory.
High Seas

1
Tue 3 Aug, 2010 09:37 am
@ughaibu,
Gödel addressed at length the apparent set-theoretical paradoxes and found classical mathematics to be free of them. I'll have a look at the Melbourne study if you wish detail, but I'm an applied mathematician, not a theorist, so any contribution to the specific sets will of necessity be limited:
Quote:
.... It might seem at first that the set-theoretical paradoxes would doom to failure such an undertaking, but closer examination shows that they cause no trouble at all. They are a very serious problem, not for mathematics, however, but rather for logic and epistemology. As far as sets occur in mathematics (at least in the mathematics of today, including all of Cantor's set theory), they are sets of integers, or of rational numbers, (i.e., of pairs of integers), or of real numbers (i.e., sets of rational numbers), or of functions of real numbers (i.e., of sets of pairs of real numbers), etc. When theorems about all sets (or the existence of sets in general) are asserted, they can always be interpreted without any difficulty to mean that they hold for sets of integers as well as for sets of sets of integers, etc. (respectively, that there either exist sets of integers, or sets of sets of integers, or... etc., which have the asserted property). This concept of set, however, according to which a set is something obtainable from the integers (or some other well-defined objects) by iterated application of the operation 'set of', not something obtained by dividing the totality of all existing things into two categories, has never led to any antinomy whatsoever; that is, the perfectly 'naive' and uncritical working with this concept of set has so far proved completely self-consistent

http://www.friesian.com/goedel/chap-1.htm
0 Replies

Zetherin

1
Tue 3 Aug, 2010 12:49 pm
mickalos wrote:
First of all, I wouldn't characterise my view as being that 'Pv~P is a fact only in classical logic'. Certainly, it is a theorem of classical logic, and not a theorem of other calculi, but that is uncontroversial. My view is a naturalistic scepticism about rule following and necessity. There is no fact of the matter that makes Pv~P follow from the rules of logical inference apart from the fact that we all agree that it does, i.e. no expression or interpretation of those rules forces a particular application on me; logic does not "grab you by the throat". We might have agreed on something different.

Can you give me an example of something you consider to be a matter of fact, and then detail how, or why, this differs from a rule in logic? Is it because logic, as ughaibu proclaimed, is an invention of man?
mickalos wrote:
I don't understand what you mean when you distinguish between an "actual fact of the matter" and other facts.

You said, "...this is a very different fact of the matter...", and I thought that meant you believed there to be different sorts of facts of the matter. That is why I asked.
mickalos wrote:
Certainly, I think the idea that a sentence is true because that's the way the world is, seems to me to be a metaphysical tip of the hat that ought not be taken too literally

If my mother is in the kitchen, wouldn't we say that it is literally true my mother is in the kitchen? A metaphysical tip of the hat? I'm not sure where you got that idea.
mickalos wrote:
Only if you take a platonic realist approach to rules. What is a rule? Well, the rules of chess establish criteria of correctness, but how? Are they "abstract entities" that sort correct action from incorrect action all by themselves? Seems a bit far fetched for my liking.

I simply wish to know how you differentiate matter of facts, from matters which are not factual. I don't see how a rule is "independent of reality" as ughaibu states. I see no reason why a sentence, concerning rules, cannot express a proposition (that is, have relation to reality).
Zetherin

1
Tue 3 Aug, 2010 12:59 pm
ughaibu wrote:
Logics are linguistic systems which preserve truth values according to defined rules, that is to say that they are human inventions, and I hold that reality is not a subset of human invention.

Humans invented my air conditioner. The sentence, "There is an air conditioner in my room" expresses a proposition (that is, it has relation to reality), does it not?

The line I'm asking to be drawn is between where you consider something to be a matter of fact, and where you do not. Is it all that is mind-dependent that you do not believe is part of reality? That is, you would deny that things like ideas are part of reality?
Doubt doubt

0
Tue 3 Aug, 2010 01:22 pm
1+1= 2x1 or 1&1

2 is not a real thing. there can only be two ones or 2 things.

there can be 2 cars in a way but they will always be 2 different cars. there can only be one of this car and one of that car.

their is no 100 just 100 ones or 100 of this or that.

for two things to be the same, what is true of one must be true of the other. in this way there can not be 2 cars. you must define something in a extremely lax fashion to fit the concept of 2.

there is one me and many yous but only if i define yous as everyone that is not me. if i define you as the person reading this that has lived the amount of seconds and had the experiences you have had then there becomes one me and one you.

it is only by coincidence that anything to do with numbers relates to the physical world.
0 Replies

ughaibu

1
Tue 3 Aug, 2010 07:27 pm
@Zetherin,
Zetherin wrote:
Humans invented my air conditioner. The sentence, "There is an air conditioner in my room" expresses a proposition (that is, it has relation to reality), does it not?
Yes, now will you please spell out how this is meant to be relevant. "There are both classical and non-classical logics" expresses the same kind of proposition, doesn't it?
Zetherin wrote:
The line I'm asking to be drawn is between where you consider something to be a matter of fact, and where you do not.
I take a naive view that reality is that which human beings have in common, naturally this needs clarifying for various conditions such as deafness and hyperaesthesia, but such clarifications are irrelevant to the matter at hand.
Zetherin wrote:
Is it all that is mind-dependent that you do not believe is part of reality? That is, you would deny that things like ideas are part of reality?
I didn't write that either logics or mathematics aren't part of reality, I wrote that they're independent of reality, and as I did so in reply to Kennethamy, including a quote from his reply to you, I once again cant see what the difficulty is meant to be.
0 Replies

Zetherin

1
Tue 3 Aug, 2010 08:09 pm
ughaibu wrote:
Yes, now will you please spell out how this is meant to be relevant.

It's meant to be relevant because propositions, as far as I know, are a reflection of reality. They are not independent of reality.
ughaibu wrote:
I didn't write that either logics or mathematics aren't part of reality, I wrote that they're independent of reality

So, logics and mathematics are both part of reality, but also independent of reality? What does that mean?
ughaibu wrote:
I take a naive view that reality is that which human beings have in common...

That may explain things. I don't agree with your view here, as I don't believe reality is defined by human intersubjectivity. The moon, for instance, was around for millions of years before any human concurrence, and the moon, of course, is part of reality.

kennethamy

1
Tue 3 Aug, 2010 08:17 pm
@Zetherin,
Zetherin wrote:

ughaibu wrote:
Yes, now will you please spell out how this is meant to be relevant.

It's meant to be relevant because propositions, as far as I know, are a reflection of reality. They are not independent of reality.
ughaibu wrote:
I didn't write that either logics or mathematics aren't part of reality, I wrote that they're independent of reality

So, logics and mathematics are both part of reality, but also independent of reality? What does that mean?
ughaibu wrote:
I take a naive view that reality is that which human beings have in common...

That may explain things. I don't agree with your view here, as I don't believe reality is defined by human intersubjectivity. The moon, for instance, was around for millions of years before any human concurrence, and the moon, of course, is part of reality.

Billlions. About four billion. What anyone means by saying that reality is what human beings have in common I have no idea. It is not a naive view, it is no view at all. But if it implies that the Moon did not exist many years before human beings, then it is simply false.
0 Replies

mickalos

1
Tue 3 Aug, 2010 08:38 pm
@Zetherin,
Zetherin wrote:

mickalos wrote:
First of all, I wouldn't characterise my view as being that 'Pv~P is a fact only in classical logic'. Certainly, it is a theorem of classical logic, and not a theorem of other calculi, but that is uncontroversial. My view is a naturalistic scepticism about rule following and necessity. There is no fact of the matter that makes Pv~P follow from the rules of logical inference apart from the fact that we all agree that it does, i.e. no expression or interpretation of those rules forces a particular application on me; logic does not "grab you by the throat". We might have agreed on something different.

Can you give me an example of something you consider to be a matter of fact, and then detail how, or why, this differs from a rule in logic? Is it because logic, as ughaibu proclaimed, is an invention of man?

Okay, a matter of fact: there are things whose existence is causally independent of human mental states. Why is it a fact? Well, by definition, it expresses a truth that is independent of human mental states. On rules of logic, there are two ways we might consider logic to be a human invention, both of which I would agree with. Firstly, that logic was not somehow "out there" waiting to be discovered. Logic was no more out there than Monopoly; it is an invention. Somebody might reply by saying, logic was out there, we just had to find the right rules, and everything follows from there, but that brings me to my second point. There is a sceptical paradox concerning rule following on the platonic account of rules assumed by the objection I have just stated.

Any rule has a number of different interpretations for how we might go about applying them, including the rules of logical inference; people often misinterpret rules in every day situations, and practically every philosophy undergrad learning formal logic for the first time will have got a proof wrong at some point, so this claim shouldn't be objectionable. One might then say that grasping a rule is about simply about finding the correct interpretation, but the problem here is that an interpretation just hangs in the air with that which it interprets; an interpretation, too, stands in need of an interpretation. Imagine driving in a foreign country and being given a table for interpreting the foreign signs into the ones used at home. You need to know how to read the table if you are to use it correctly; a second table might be desirable. An expression of a rule does not force a course of action, and nor does any interpretation.

Quote:
mickalos wrote:
I don't understand what you mean when you distinguish between an "actual fact of the matter" and other facts.

You said, "...this is a very different fact of the matter...", and I thought that meant you believed there to be different sorts of facts of the matter. That is why I asked.

This is a direct continuation of the above. On the platonic account of rule following, it is assumed that there is a fact about a rule that makes a certain course of action correct or not. That the statements in a logic textbook themselves, or something to which they refer, mean that I should be able to prove Pv~P. However, the very question that is at stake is what indeed does follow from the statements in a logic textbook. The platonist is begging the question.

The naturalistic account of rules, on the other hand, notes that there are facts about our rule following practices: nothing but Pv~P (and the other theorems of logic) is allowed under any circumstances in actual pen and paper cases of inferring, and deviant behaviour is corrected. The essential point is that what makes the inference acceptable is not a fact about the rules, but a decision on the part of practitioners of logic as to what the correct answer to a problem is. Imagine a room of people are given a simple bit of addition that nobody had ever done before (perhaps because it involves very large numbers), x+y. Now, what if exactly half get one answer, and the other half a different answer? Is there any fact of the matter that determines who is correct? I say, no, because a criterion of correctness has not yet been established; a decision must first be made.

Perhaps my original wording was a bit sloppy, but I think the above brings out what I meant in my previous remarks. The difference was not in some kind of category of facts, but rather in the content.

Quote:
mickalos wrote:
Certainly, I think the idea that a sentence is true because that's the way the world is, seems to me to be a metaphysical tip of the hat that ought not be taken too literally

If my mother is in the kitchen, wouldn't we say that it is literally true my mother is in the kitchen? A metaphysical tip of the hat? I'm not sure where you got that idea.

I would say if your mother is in the kitchen, then it is literally true that your mother is in the kitchen, but this doesn't tell me anything substantive about truth. 'P' is true iff P. Big deal. I certainly don't want to deny a realist account of objects, but I do want to say that simply encountering bits of reality does not give me any specific beliefs about it. Before I can hold the appropriate beliefs I need to be taught a whole matrix of socio-linguistically constructed concepts. The mere encounter with a horse does not furnish us with any horse concepts. I can't simply read off the object the various ways in which it fits into my life, I need to see how it fits into my practices and those of others before I can even begin forming sentences or beliefs about horses. Moreover, the practices of my linguistic community may have been entirely different, and thus I may have been furnished with completely different concepts such that the only fact of the matter that makes it that the saddle is on a horse rather than the saddle preventing the horse floating off into space is my membership of a certain linguistic community.

Quote:
mickalos wrote:
Only if you take a platonic realist approach to rules. What is a rule? Well, the rules of chess establish criteria of correctness, but how? Are they "abstract entities" that sort correct action from incorrect action all by themselves? Seems a bit far fetched for my liking.

I simply wish to know how you differentiate matter of facts, from matters which are not factual. I don't see how a rule is "independent of reality" as ughaibu states. I see no reason why a sentence, concerning rules, cannot express a proposition (that is, have relation to reality).

Which bit of reality would be constitutive of a rule?
0 Replies

ughaibu

1
Tue 3 Aug, 2010 09:47 pm
@Zetherin,
Zetherin wrote:
It's meant to be relevant because propositions, as far as I know, are a reflection of reality. They are not independent of reality.
Fictions are part of reality but they are independent of reality, and some propositions are fictions.
Zetherin wrote:
So, logics and mathematics are both part of reality, but also independent of reality? What does that mean?
In classical logics the law of excluded middle is true, but in intuitionistic logics it is false. This means that if logics are not independent of reality, then within logic, as a whole, the law of excluded middle is false, and this means that classical logics are false and thus independent of reality. Intuitionistic logics are similarly independent by reversing the argument.
Zetherin wrote:
I don't agree with your view here, as I don't believe reality is defined by human intersubjectivity. The moon, for instance, was around for millions of years before any human concurrence, and the moon, of course, is part of reality.
And that the moon was around billions of years ago is information commonly available to all healthy human adults, so it isn't any kind of counter example.
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