Mathematics is not a science

@kennethamy,

kennethamy wrote:

TuringEquivalent wrote:

bject matters.

I said "science is inductive". I never said "all" of science is inductive. This original statement is true even if there is a tiny part that is inductive.
I also never said "science is partly deductive, and party inductive", so, it is out of scope.

Yes, but the distinction between math. and the empirical sciences seemed to be being drawn by the deductive/inductive criterion. But, I agree that the issue is whether mathematics is a science, even if it is not an empirical science. And I don't see that your original argument that since mathematical propositions are necessary and not contingent (as are the propositions of empirical science) shows that mathematics is not a science. All it shows is that it is not an empirical science. But we cannot simply assume that only empirical science is science, can we? Etymology is never decisive, but it is sometimes a guide, and the etymology of "science" is that it is from the Latin, "scientia" which means "knowledge". Now, there is certainly empirical knowledge. But isn't there also mathematical knowledge too? So, maybe that is a point in favor of saying that mathematics is a science.

And, as I pointed out, mathematics is certainly a disciplined inquiry in search of truth (as is empirical science). So, maybe that is another point. Perhaps the question comes down to the question of what kind of truth mathematical truth is. If mathematical truths are necessary truths as you say, then what kind of truth is a necessary truth?
[/quote]

1. You make good sense. If "science" means "a certain body of truth", then i agree with you that math is a science. Obviously, Math is not an empirical science. Yet, it seems to me that if we define science to be what you claim it to be, then you are stretch beyond the conception of science that most people hold. I think most people hold that science is distinct from other studies by it empirical method.

2. unnecessary divergences to talk about "math truth". All we need to agree is that math tell us truths. It might not be the scientific kind, but they are surely truths.

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Why does it matter if we consider mathematics a science or not? What do we gain from pondering mathematics' classification? Is there an epistemological interest here?

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@Zetherin,

Zetherin wrote:

Why does it matter if we consider mathematics a science or not? What do we gain from pondering mathematics' classification? Is there an epistemological interest here?

since when is doing something productive, necessary for doing something?

1 Reply

@TuringEquivalent,

What? I would just like to know what we gain, intellectually, from the classification of mathematics. Would there, for instance, be implications for it being classified as a science, or anything else for that matter? What problems would this solve, or what does this clarify?

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@Zetherin,

Zetherin wrote:

What? I would just like to know what we gain, intellectually, from the classification of mathematics. Would there, for instance, be implications for it being classified as a science, or anything else for that matter? What problems would this solve, or what does this clarify?

Your question implies there need something be gain from a certain act, if we are to do the act. Why else would you ask "what could be gain?", unless, you think something need to be gain. This is a fallacy. Obtaining something from doing a certain act is not necessary for doing a certain act.

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@TuringEquivalent,

But I never said that for one to do a certain act, one must gain from said act.

However, when a thread is posted on a philosophy forum, I would expect that the thread was posted for a reason - and that reason being that the issue is philosophically relevant. And if an issue is philosophically relevant, that generally means that there is something of substance we can learn/gain/clarify/solve by discussing the issue. And I want to know what that issue is for this thread.

Would the classification of mathematics have epistemological implications? Would there be scientific implications? Linguistic? What?

Oh, and if you're going to nonchalantly toss around the word "fallacy" in your next response, don't even bother typing. I'm not quibbling with you.

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@Zetherin,

Of particular philosophical interest is perhaps the fact that a mathematical model can direct observation of hitherto unobserved "data". Significantly mathematical models such as "group theory" now directs the search for sub-atomic particles. It is difficult to see where any boundary can be drawn between "mathematics" and "science" at that level.

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@Zetherin,

Zetherin wrote:

Why does it matter if we consider mathematics a science or not? What do we gain from pondering mathematics' classification? Is there an epistemological interest here?

As I mentioned, the relation between the physical sciences and the social sciences (the sciences of Man) have often been discussed. And, certainly, the question. "what is science" is a philosophical question. And to ask that question would be to ask what makes mathematics (or logic, for that matter) a science (if they are). Then too. as I suggested, if science has anything to do with inquiry for truth. mathematical and logical truth seems to be very different from empirical truth. The former is necessary truth, the latter contingent truth. So, there is that consideration too. As for epistemology (which you mention) it has been argued that mathematics bestows certainty, and science doesn't, so that mathematics has been thought of as the paradigm of knowledge to with science as only aspire, but never achieve.

So, yes, It seems to me that that there are several philosophical issues raised by asking whether mathematics is a science?

1 Reply

@Zetherin,

Zetherin wrote:

But I never said that for one to do a certain act, one must gain from said act.

However, when a thread is posted on a philosophy forum, I would expect that the thread was posted for a reason - and that reason being that the issue is philosophically relevant. And if an issue is philosophically relevant, that generally means that there is something of substance we can learn/gain/clarify/solve by discussing the issue. And I want to know what that issue is for this thread.

Would the classification of mathematics have epistemological implications? Would there be scientific implications? Linguistic? What?

Oh, and if you're going to nonchalantly toss around the word "fallacy" in your next response, don't even bother typing. I'm not quibbling with you.

You are a ******* idiot. The thesis is the first sentence in the op post. Also, by asking for "philosophical relevant", you assume it needs to be relevant, which is unjustified. How many ******* times do you want me to repeat it for you, idiot?

1 Reply

@kennethamy,

kennethamy wrote:

Zetherin wrote:

Why does it matter if we consider mathematics a science or not? What do we gain from pondering mathematics' classification? Is there an epistemological interest here?

As I mentioned, the relation between the physical sciences and the social sciences (the sciences of Man) have often been discussed. And, certainly, the question. "what is science" is a philosophical question. And to ask that question would be to ask what makes mathematics (or logic, for that matter) a science (if they are). Then too. as I suggested, if science has anything to do with inquiry for truth. mathematical and logical truth seems to be very different from empirical truth. The former is necessary truth, the latter contingent truth. So, there is that consideration too. As for epistemology (which you mention) it has been argued that mathematics bestows certainty, and science doesn't, so that mathematics has been thought of as the paradigm of knowledge to with science as only aspire, but never achieve.

So, yes, It seems to me that that there are several philosophical issues raised by asking whether mathematics is a science?

It has been argued that mathematics bestows certainty? Well, what kind of certainty? And what is the argument that science does not? Often times science is based on mathematics, so would we not call a scientific conclusion based on mathematics, if proved true, certain?

Your point however was that if mathematics were considered a science, it would lose some of its "certainty"? And there would be epistemological implications from that. I see. Let's detail this further.

1 Reply

@TuringEquivalent,

TuringEquivalent wrote:

You are a ******* idiot. The thesis is the first sentence in the op post. Also, by asking for "philosophical relevant", you assume it needs to be relevant, which is unjustified. How many ******* times do you want me to repeat it for you, idiot?

Blah blah blah. Go play somewhere else.

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@Zetherin,

Zetherin wrote:

kennethamy wrote:

Zetherin wrote:

Why does it matter if we consider mathematics a science or not? What do we gain from pondering mathematics' classification? Is there an epistemological interest here?

As I mentioned, the relation between the physical sciences and the social sciences (the sciences of Man) have often been discussed. And, certainly, the question. "what is science" is a philosophical question. And to ask that question would be to ask what makes mathematics (or logic, for that matter) a science (if they are). Then too. as I suggested, if science has anything to do with inquiry for truth. mathematical and logical truth seems to be very different from empirical truth. The former is necessary truth, the latter contingent truth. So, there is that consideration too. As for epistemology (which you mention) it has been argued that mathematics bestows certainty, and science doesn't, so that mathematics has been thought of as the paradigm of knowledge to with science as only aspire, but never achieve.

So, yes, It seems to me that that there are several philosophical issues raised by asking whether mathematics is a science?

It has been argued that mathematics bestows certainty? Well, what kind of certainty? And what is the argument that science does not? Often times science is based on mathematics, so would we not call a scientific conclusion based on mathematics, if proved true, certain?

Your point however was that if mathematics were considered a science, it would lose some of its "certainty"? And there would be epistemological implications from that. I see. Let's detail this further.

The certainty that stems from necessary truth. The negation of the proposition that The angles of a triangle add up to 180 degrees is logically impossible, and therefore that proposition is a necessary truth. It is impossible that a necessary truth be false. For this reason, mathematics was considered the paradigm of knowledge,

I don't know how something could lose some certainty since I don't think that certainty is a matter of degree. And if mathematics is a science, and if mathematics is certain, then it would follow that some sciences were certain. You seem to be assuming that all sciences are empirical sciences. But that begs the question, since it assumes that mathematics is not a science. And that is where we began. Mathematics has always been considered a science, but a formal science as contrasted with the empirical sciences. There is a distinction, of course, between pure (or theoretical mathematics) and applied mathematics. It is only pure mathematics that is thought to be certain, and consist of necessary truths. Not applied mathematics, which is what you mean when you talk about science being based on mathematics. 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".

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@TuringEquivalent,

Hold on there Newt, a mathematical proposition is not true by default as per your claim "math propositions are true, necessarily".

In fact a mathematical proposition is only valid to the extent it can be shown to be.

However a mathematical axiom is a proposition that is assumed to be true, but even in this special case your word "necessarily" would be in error (strictly speaking).

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@Chumly,

Chumly wrote:

Hold on there Newt, a mathematical proposition is not true by default as per your claim "math propositions are true, necessarily".

In fact a mathematical proposition is only valid to the extent it can be shown to be.

However a mathematical axiom is a proposition that is assumed to be true, but even in this special case your word "necessarily" would be in error (strictly speaking).

A necessary truth is not a truth that is "true by default" (whatever that may mean). A necessary truth is a truth whose negation is impossible.

1 Reply

@kennethamy,

kennethamy wrote:

Chumly wrote:
Hold on there Newt, a mathematical proposition is not true by default as per your claim "math propositions are true, necessarily".

In fact a mathematical proposition is only valid to the extent it can be shown to be.

However a mathematical axiom is a proposition that is assumed to be true, but even in this special case your word "necessarily" would be in error (strictly speaking).
A necessary truth is not a truth that is "true by default" (whatever that may mean). A necessary truth is a truth whose negation is impossible.

Firstly it makes no sense for you to claim a necessary truth is not a truth by default when you admit you have no understating what "true by default" means.

Further it makes no sense for you to then claim a necessary truth is a truth whose negation is impossible when you previously claimed math propositions are true, necessarily. Now, true by default means true automatically. As such when you said math propositions are true, necessarily you in fact said math propositions are true automatically. This is not the case because a proposition is not a proof.

Finally I challenge you to mathematically demonstrate that all necessary truths must must be true under all circumstances. If you cannot do this then I question your usage of the term necessary truth.

1 Reply

@Chumly,

Chumly wrote:

kennethamy wrote:
Chumly wrote:
Hold on there Newt, a mathematical proposition is not true by default as per your claim "math propositions are true, necessarily".

In fact a mathematical proposition is only valid to the extent it can be shown to be.

However a mathematical axiom is a proposition that is assumed to be true, but even in this special case your word "necessarily" would be in error (strictly speaking).
A necessary truth is not a truth that is "true by default" (whatever that may mean). A necessary truth is a truth whose negation is impossible.
Firstly it makes no sense for you to claim a necessary truth is not a truth by default without understating what the term means.

Further it makes no sense for you to then claim a necessary truth is a truth whose negation is impossible when you previously claimed math propositions are true, necessarily. Now, true by default means true automatically. As such when you said math propositions are true, necessarily you in fact said math propositions are true automatically... this is not the case. A proposition is not proof.

I challenge you to mathematically demonstrate that all necessary truths must must be true under all circumstances. If you cannot do this then I question your use of this term.

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.

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Without math, there is no science.

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@kennethamy,

kennethamy wrote:

Chumly wrote:
kennethamy wrote:
Chumly wrote:
Hold on there Newt, a mathematical proposition is not true by default as per your claim "math propositions are true, necessarily".

In fact a mathematical proposition is only valid to the extent it can be shown to be.

However a mathematical axiom is a proposition that is assumed to be true, but even in this special case your word "necessarily" would be in error (strictly speaking).
A necessary truth is not a truth that is "true by default" (whatever that may mean). A necessary truth is a truth whose negation is impossible.
Firstly it makes no sense for you to claim a necessary truth is not a truth by default without understating what the term means.

Further it makes no sense for you to then claim a necessary truth is a truth whose negation is impossible when you previously claimed math propositions are true, necessarily. Now, true by default means true automatically. As such when you said math propositions are true, necessarily you in fact said math propositions are true automatically... this is not the case. A proposition is not proof.

I challenge you to mathematically demonstrate that all necessary truths must must be true under all circumstances. If you cannot do this then I question your use of this term.

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.

1) You did not address my first point at all as per it makes no sense for you to claim a necessary truth is not a truth by default without understating what the term means.

2) You did not address my second point at all as per it makes no sense for you to then claim a necessary truth is a truth whose negation is impossible when you previously claimed math propositions are true, necessarily. Now, true by default means true automatically. As such when you said math propositions are true, necessarily you in fact said math propositions are true automatically... this is not the case. A proposition is not proof.

3) Nope, you did not mathematically demonstrate that all necessary truths must must be true under all circumstances as such I question your usage of the term necessary truth. Where is your proof that all dogs are dogs...that is axiomatic at best. And even if I accept all dogs are dogs as being axiomatic, that is no argument that all molecules are all molecules. What is next, you gonna argue that X = X simply because they are both named X!

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Chumly wrote:

Nope, you did not mathematically demonstrate that all necessary truths must must be true under all circumstances as such I question your usage of the term necessary truth. Where is your proof that all dogs are dogs...that is axiomatic at best. And even if I accept all dogs are dogs as being axiomatic, that is no argument that all molecules are all molecules. What is next, you gonna argue that X = X simply because they are both named X!

He just explained why X=X is considered a necessary truth, and of course it doesn't matter what you replace the variable "X" with. Maybe you don't know what a necessary truth is.

"A necessary truth must be true and could not be false, whatever way the world is"
http://www.blackwellreference.com/public/tocnode?id=g9781405106795_chunk_g978140510679515_ss1-41

So, yes, a necessary truth must be true under all circumstances. That is what the term means.

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@kennethamy,

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.

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Mathematics is not a science

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