Mathematics is not a science

Iam done.

TuringEquivalent wrote:

Iam done.

I'm not even sure you're ripe yet.

Who is this post addressing? What kind of preemptive strawman is this?

A
R
T

I'm inclined to believe that very few are interested in debating you. Perhaps you're very good at it. Other theories may exist.

A
R
T

Mathematics is not a science.

TuringEquivalent wrote:

Mathematics is not a science.

I expect the truth or otherwise of this assertion depends on whether mathematics is discovery or invention. As you're a Platonist, I take it you hold that all mathematical truths exist, and always have existed, independent of the existence of any mathematising agents. In short, Platonism puts you in the discovery camp. As discovery is the unearthing of empirical facts, it seems to me that Platonism commits you to the view that maths is a science. So, your views appear to be inconsistent.
Or, have you given up Platonism?

depends on whether mathematics is discovery or invention. As you're a Platonist, I take it you hold that all mathematical truths exist, and always have existed, independent of the existence of any mathematising agents. In short, Platonism puts you in the discovery camp. As discovery is the unearthing of empirical facts, it seems to me that Platonism commits you to the view that maths is a science.

Mathematics is not a science. This is actually a trivial point for anyone ever took a philosophy class. I am motivate to write this because it is common for people to think math is a science. The difference between mathematical propositions, and scientific theories is that math propositions are true, necessarily, while scientific theories are true, contingently. Notions such as "necessity", and "contingently" are modal notions. If you know know what i means, here is another way to look at the difference. Science uses "induction" and math uses " deduction". If you ever open a textbook in physics, you probably realize there are a lot of math. You probable would make the stupid inference that physics is math. Here is why it is wrong. It is true that a lot of the physics is deductive, but the base of the theory( ie: laws of nature) are inductive generalizations of the world, and those inductive generalization need not be necessary. This is why no scientific theory can never be certain. Mathematics is certain, because the base of any math theory are made up of axioms( assumed, not based on reality), and rules of inference. Another common objection is slogans. Perhaps you heard the slogan "mathematic is the queen of sciences", and make the inference that math is a science. You are probably retarded. It is not instructive to learn from a ******* slogans. Another objection is that "mathematical inductive" is induction. No, Mathematical induction is actually deduction. This concludes all the objections. I am done.




peace.

The Platonic conception of discovering mathematical objects is by mean of "intuition", while, the process of discovery in science is by mean of induction.

TuringEquivalent wrote:

Mathematics is not a science. This is actually a trivial point for anyone ever took a philosophy class. I am motivate to write this because it is common for people to think math is a science. The difference between mathematical propositions, and scientific theories is that math propositions are true, necessarily, while scientific theories are true, contingently. Notions such as "necessity", and "contingently" are modal notions. If you know know what i means, here is another way to look at the difference. Science uses "induction" and math uses " deduction". If you ever open a textbook in physics, you probably realize there are a lot of math. You probable would make the stupid inference that physics is math. Here is why it is wrong. It is true that a lot of the physics is deductive, but the base of the theory( ie: laws of nature) are inductive generalizations of the world, and those inductive generalization need not be necessary. This is why no scientific theory can never be certain. Mathematics is certain, because the base of any math theory are made up of axioms( assumed, not based on reality), and rules of inference. Another common objection is slogans. Perhaps you heard the slogan "mathematic is the queen of sciences", and make the inference that math is a science. You are probably retarded. It is not instructive to learn from a ******* slogans. Another objection is that "mathematical inductive" is induction. No, Mathematical induction is actually deduction. This concludes all the objections. I am done.




peace.

Since Quine's demolition of the analytic-synthetic distinction, I don't think we can be so sure that mathematical propositions are so different from empirical propositions, at least not from certain propositions that have the form of empirical propositions. Clearly, 2+2=4 is different from something like, the "cat is on the mat", but different in what way? No more different than Moore propositions (the sentences Moore gives in his "A defence of common sense") such as, "I have a body", "The earth has existed for more than five minutes", etc. Deduction is no explanation, given the right axioms and inference rules, everyone will agree that I can deductively infer anything I like, but this is no guarantee that my axioms are true, or that my inference rules 'generate' truths, let alone necessary truths.

schizophrenic delusions came to him in the same way as his mathematical ideas. Is this proof that aliens exist?

In a certain sense, math, and physics can be defined by a set of axioms, and rules of inference, but the difference lies is in the basic axioms that defines physics are inductive generalizations from the world, and the axioms in math are picked without regard to the world at all. This difference tell us that there is a distinct difference between math, and science. They are not the same.

The inductive generalizations( form the base of physics) are contingently true. The axioms of math are assumed to be true, and thus, necessary true.

Quote:

schizophrenic delusions came to him in the same way as his mathematical ideas. Is this proof that aliens exist?

You are equating "aliens" with "abstract objects", but they are not the same.
The way you find out if there are "aliens" is different from the way you finding a prove of some math conjuncture. Since, the two are incompatible, you cannot use a parallel argument to support your case.

Mathematics is not a science. This is actually a trivial point for anyone ever took a philosophy class. I am motivate to write this because it is common for people to think math is a science. The difference between mathematical propositions, and scientific theories is that math propositions are true, necessarily, while scientific theories are true, contingently. Notions such as "necessity", and "contingently" are modal notions. If you know know what i means, here is another way to look at the difference. Science uses "induction" and math uses " deduction". If you ever open a textbook in physics, you probably realize there are a lot of math. You probable would make the stupid inference that physics is math. Here is why it is wrong. It is true that a lot of the physics is deductive, but the base of the theory( ie: laws of nature) are inductive generalizations of the world, and those inductive generalization need not be necessary. This is why no scientific theory can never be certain. Mathematics is certain, because the base of any math theory are made up of axioms( assumed, not based on reality), and rules of inference. Another common objection is slogans. Perhaps you heard the slogan "mathematic is the queen of sciences", and make the inference that math is a science. You are probably retarded. It is not instructive to learn from a ******* slogans. Another objection is that "mathematical inductive" is induction. No, Mathematical induction is actually deduction. This concludes all the objections. I am done.




peace.

TuringEquivalent wrote:

In a certain sense, math, and physics can be defined by a set of axioms, and rules of inference, but the difference lies is in the basic axioms that defines physics are inductive generalizations from the world, and the axioms in math are picked without regard to the world at all. This difference tell us that there is a distinct difference between math, and science. They are not the same.

This does not make them unrevisable. To paraphrase Quine, our sentences face tribunal not individually, but only as a corporate body. Why should it matter whether some of them mention the world or not? We could revise either if it makes our entire system of beliefs more plausible. It just so happens that mathematical propositions, along with propositions like "The earth is more than five minutes old", lie at the centre of our web of belief, and are held fixed.

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The inductive generalizations( form the base of physics) are contingently true. The axioms of math are assumed to be true, and thus, necessary true.

It's past midnight in Britain, and the Queen, despite being a very busy woman, is 84 years old. I, therefore, assume the truth of the statement, the Queen of England is in bed at present.

Assumption does not make a statement true, and certainly not necessarily true.

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schizophrenic delusions came to him in the same way as his mathematical ideas. Is this proof that aliens exist?

You are equating "aliens" with "abstract objects", but they are not the same.
The way you find out if there are "aliens" is different from the way you finding a prove of some math conjuncture. Since, the two are incompatible, you cannot use a parallel argument to support your case.

I think the notion of an abstract object is completely incoherent and nonsensical; I do not equate them with anything. I equate (or rather, John Nash. himself, equates) the way he came to believe mathematical with the way he came to believe certain non-mathematical propositions, which are putatively false. Clearly this is an unrealiable method. Indeed, an argument from intuition comes down to: if it seems right it is right. Without an independent, accessible criterion of correctness we can know nothing about maths.

TuringEquivalent wrote:

Mathematics is not a science. This is actually a trivial point for anyone ever took a philosophy class. I am motivate to write this because it is common for people to think math is a science. The difference between mathematical propositions, and scientific theories is that math propositions are true, necessarily, while scientific theories are true, contingently. Notions such as "necessity", and "contingently" are modal notions. If you know know what i means, here is another way to look at the difference. Science uses "induction" and math uses " deduction". If you ever open a textbook in physics, you probably realize there are a lot of math. You probable would make the stupid inference that physics is math. Here is why it is wrong. It is true that a lot of the physics is deductive, but the base of the theory( ie: laws of nature) are inductive generalizations of the world, and those inductive generalization need not be necessary. This is why no scientific theory can never be certain. Mathematics is certain, because the base of any math theory are made up of axioms( assumed, not based on reality), and rules of inference. Another common objection is slogans. Perhaps you heard the slogan "mathematic is the queen of sciences", and make the inference that math is a science. You are probably retarded. It is not instructive to learn from a ******* slogans. Another objection is that "mathematical inductive" is induction. No, Mathematical induction is actually deduction. This concludes all the objections. I am done.




peace.

Math is not an empirical science (as you point out) but it is what is called, a formal science. The question you are raising is what it is that makes both empirical and formal sciences, sciences. One similarity is that both are disciplined inquiries into their subjects. Another is that both are attempts to discover what is true in their respective subject matters.

kennethamy wrote:

TuringEquivalent wrote:

Mathematics is not a science. This is actually a trivial point for anyone ever took a philosophy class. I am motivate to write this because it is common for people to think math is a science. The difference between mathematical propositions, and scientific theories is that math propositions are true, necessarily, while scientific theories are true, contingently. Notions such as "necessity", and "contingently" are modal notions. If you know know what i means, here is another way to look at the difference. Science uses "induction" and math uses " deduction". If you ever open a textbook in physics, you probably realize there are a lot of math. You probable would make the stupid inference that physics is math. Here is why it is wrong. It is true that a lot of the physics is deductive, but the base of the theory( ie: laws of nature) are inductive generalizations of the world, and those inductive generalization need not be necessary. This is why no scientific theory can never be certain. Mathematics is certain, because the base of any math theory are made up of axioms( assumed, not based on reality), and rules of inference. Another common objection is slogans. Perhaps you heard the slogan "mathematic is the queen of sciences", and make the inference that math is a science. You are probably retarded. It is not instructive to learn from a ******* slogans. Another objection is that "mathematical inductive" is induction. No, Mathematical induction is actually deduction. This concludes all the objections. I am done.




peace.

Math is not an empirical science (as you point out) but it is what is called, a formal science. The question you are raising is what it is that makes both empirical and formal sciences, sciences. One similarity is that both are disciplined inquiries into their subjects. Another is that both are attempts to discover what is true in their respective subject matters.

This is a trivial point. I perfer to think science is non-deductive, and math is deductive. This is more fundamental, and gets to the heart of the distinction. Don` t you agree?

TuringEquivalent wrote:

kennethamy wrote:

TuringEquivalent wrote:

Mathematics is not a science. This is actually a trivial point for anyone ever took a philosophy class. I am motivate to write this because it is common for people to think math is a science. The difference between mathematical propositions, and scientific theories is that math propositions are true, necessarily, while scientific theories are true, contingently. Notions such as "necessity", and "contingently" are modal notions. If you know know what i means, here is another way to look at the difference. Science uses "induction" and math uses " deduction". If you ever open a textbook in physics, you probably realize there are a lot of math. You probable would make the stupid inference that physics is math. Here is why it is wrong. It is true that a lot of the physics is deductive, but the base of the theory( ie: laws of nature) are inductive generalizations of the world, and those inductive generalization need not be necessary. This is why no scientific theory can never be certain. Mathematics is certain, because the base of any math theory are made up of axioms( assumed, not based on reality), and rules of inference. Another common objection is slogans. Perhaps you heard the slogan "mathematic is the queen of sciences", and make the inference that math is a science. You are probably retarded. It is not instructive to learn from a ******* slogans. Another objection is that "mathematical inductive" is induction. No, Mathematical induction is actually deduction. This concludes all the objections. I am done.




peace.

Math is not an empirical science (as you point out) but it is what is called, a formal science. The question you are raising is what it is that makes both empirical and formal sciences, sciences. One similarity is that both are disciplined inquiries into their subjects. Another is that both are attempts to discover what is true in their respective subject matters.

This is a trivial point. I perfer to think science is non-deductive, and math is deductive. This is more fundamental, and gets to the heart of the distinction. Don` t you agree?

But isn't physics deductive? Don't we talk about what (deductively) follows from Newton's laws? And how various physical theories are logically connected, so that Newton's laws follow from relativity theory? Natural laws are established inductively, although not simply by enumerative induction. Theoretical science does not proceed by sampling and then generalizing. It proceeds by what is called the hypothetical-deductive method: that is forming hypotheses, and then deducing from the hypothesis, observation statements which we then test. So, it isn't as if the division between the empirical and the formal sciences is all that sharp, for the empirical sciences are (partly) deductive too. I think that it is a philosophical question what a science is, and how the formal, the physical, and the social, sciences all fit together.

kennethamy wrote:

TuringEquivalent wrote:

kennethamy wrote:

TuringEquivalent wrote:

Mathematics is not a science. This is actually a trivial point for anyone ever took a philosophy class. I am motivate to write this because it is common for people to think math is a science. The difference between mathematical propositions, and scientific theories is that math propositions are true, necessarily, while scientific theories are true, contingently. Notions such as "necessity", and "contingently" are modal notions. If you know know what i means, here is another way to look at the difference. Science uses "induction" and math uses " deduction". If you ever open a textbook in physics, you probably realize there are a lot of math. You probable would make the stupid inference that physics is math. Here is why it is wrong. It is true that a lot of the physics is deductive, but the base of the theory( ie: laws of nature) are inductive generalizations of the world, and those inductive generalization need not be necessary. This is why no scientific theory can never be certain. Mathematics is certain, because the base of any math theory are made up of axioms( assumed, not based on reality), and rules of inference. Another common objection is slogans. Perhaps you heard the slogan "mathematic is the queen of sciences", and make the inference that math is a science. You are probably retarded. It is not instructive to learn from a ******* slogans. Another objection is that "mathematical inductive" is induction. No, Mathematical induction is actually deduction. This concludes all the objections. I am done.




peace.

Math is not an empirical science (as you point out) but it is what is called, a formal science. The question you are raising is what it is that makes both empirical and formal sciences, sciences. One similarity is that both are disciplined inquiries into their subjects. Another is that both are attempts to discover what is true in their respective subject matters.

This is a trivial point. I perfer to think science is non-deductive, and math is deductive. This is more fundamental, and gets to the heart of the distinction. Don` t you agree?

But isn't physics deductive? Don't we talk about what (deductively) follows from Newton's laws? And how various physical theories are logically connected, so that Newton's laws follow from relativity theory? Natural laws are established inductively, although not simply by enumerative induction. Theoretical science does not proceed by sampling and then generalizing. It proceeds by what is called the hypothetical-deductive method: that is forming hypotheses, and then deducing from the hypothesis, observation statements which we then test. So, it isn't as if the division between the empirical and the formal sciences is all that sharp, for the empirical sciences are (partly) deductive too. I think that it is a philosophical question what a science is, and how the formal, the physical, and the social, sciences all fit together.

What is wrong with saying "physics is non-deductive"? It would still be true if there is a .0001 % of physics that is inductive, even if all, or most of it is deductive. The portion that are inductive are the inductive generalizations, and those are contingent. Any hypothesis that are based on those generalizations would also be contingent. It is this contingency that distinquish science from math.


To show that science is deductive, you need to show there is zero element in science that is inductive. This is falses, since the laws are inductive.

TuringEquivalent wrote:

kennethamy wrote:

TuringEquivalent wrote:

kennethamy wrote:

TuringEquivalent wrote:

Mathematics is not a science. This is actually a trivial point for anyone ever took a philosophy class. I am motivate to write this because it is common for people to think math is a science. The difference between mathematical propositions, and scientific theories is that math propositions are true, necessarily, while scientific theories are true, contingently. Notions such as "necessity", and "contingently" are modal notions. If you know know what i means, here is another way to look at the difference. Science uses "induction" and math uses " deduction". If you ever open a textbook in physics, you probably realize there are a lot of math. You probable would make the stupid inference that physics is math. Here is why it is wrong. It is true that a lot of the physics is deductive, but the base of the theory( ie: laws of nature) are inductive generalizations of the world, and those inductive generalization need not be necessary. This is why no scientific theory can never be certain. Mathematics is certain, because the base of any math theory are made up of axioms( assumed, not based on reality), and rules of inference. Another common objection is slogans. Perhaps you heard the slogan "mathematic is the queen of sciences", and make the inference that math is a science. You are probably retarded. It is not instructive to learn from a ******* slogans. Another objection is that "mathematical inductive" is induction. No, Mathematical induction is actually deduction. This concludes all the objections. I am done.




peace.

Math is not an empirical science (as you point out) but it is what is called, a formal science. The question you are raising is what it is that makes both empirical and formal sciences, sciences. One similarity is that both are disciplined inquiries into their subjects. Another is that both are attempts to discover what is true in their respective subject matters.

This is a trivial point. I perfer to think science is non-deductive, and math is deductive. This is more fundamental, and gets to the heart of the distinction. Don` t you agree?

But isn't physics deductive? Don't we talk about what (deductively) follows from Newton's laws? And how various physical theories are logically connected, so that Newton's laws follow from relativity theory? Natural laws are established inductively, although not simply by enumerative induction. Theoretical science does not proceed by sampling and then generalizing. It proceeds by what is called the hypothetical-deductive method: that is forming hypotheses, and then deducing from the hypothesis, observation statements which we then test. So, it isn't as if the division between the empirical and the formal sciences is all that sharp, for the empirical sciences are (partly) deductive too. I think that it is a philosophical question what a science is, and how the formal, the physical, and the social, sciences all fit together.

What is wrong with saying "physics is non-deductive"? It would still be true if there is a .0001 % of physics that is inductive, even if all, or most of it is deductive. The portion that are inductive are the inductive generalizations, and those are contingent. Any hypothesis that are based on those generalizations would also be contingent. It is this contingency that distinquish science from math.


To show that science is deductive, you need to show there is zero element in science that is inductive. This is falses, since the laws are inductive.

I agree that the propositions of physics are contingent, but that is not the same as saying that they are all arrived at inductively. To call them contingent is to say that their negations are not self-contradictory. But to say that they are arrived at, or tested inductively is to talk about something quite different. Anyway, why must you show that there is nothing inductive about science to say that it is partly deductive and partly inductive? Why cannot the physical sciences be both? Indeed, they are. I didn't claim that science was deductive, after all. I just pointed out that it was not only inductive. It may just be that the formal sciences are purely deductive, but that the empirical sciences are partly inductive and partly deductive. What is the matter with that?

1. There are two ways to answer you. One, is to note that the different modal status between math, and science is distinct, fundamental, and irreducible. Case close.

The second way is to show that there is a statement in the "web of belief" that is immune from refutation. In the second case, we must ask "Are there propositions that we are so certain, we cannot doubt?". The answer is obviously "yes". If you disagree, then tell me under what condition can we say " bachelor is unmarry" falses?

2. Who said anything about "assumptions"? I said the axioms of math is necessary. What is necessary? It is necessary because it is true in all possible worlds. It is true, because the axioms have extensions in every possible world to some abstract object.

3. The fact that you find abstract object "nonsensical" just means you are not putting the work to understand it. It is not an argument of any kind. To show that the notion of abstract object is incoherent, you need to assume the properties of abstract objects, and derive a condition. Did you do that? no!

bject matters.

TuringEquivalent wrote:

1. There are two ways to answer you. One, is to note that the different modal status between math, and science is distinct, fundamental, and irreducible. Case close.

You mean bare assertion? From my, thankfully limited, interaction with you up to this point, that does seem to be a favourite of yours.

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The second way is to show that there is a statement in the "web of belief" that is immune from refutation. In the second case, we must ask "Are there propositions that we are so certain, we cannot doubt?". The answer is obviously "yes". If you disagree, then tell me under what condition can we say " bachelor is unmarry" falses?

All beliefs are revisable in principle, that is the essence of believing, we can take up and discard any of them in the face of recalcitrant thoughts and experiences. Certainly, there are beliefs that I cannot doubt: there is an external world, I have a body, 2+2=4, etc. However, it is a mistake to see our inability to doubt these propositions as the result of somekind of special feeling I have towards them. My relationship to these kinds of propositions is not epistemic, there is no process by which I may make sure of them (except in exceptional circumstances, e.g. You might look down to see which bits of you may be missing if you were to tread on a landmine, perish the thought!), rather, they are the hinges upon which all my other activities turn. I may well doubt that I have a body, or that 2+2=4, they are completely ungrounded in any justification that I can think of (or at least, they result in an infinite justificatory regress or justifications terminate in an ungrounded belief) but my way of life would drastically alter.

Consider, for example, if I were to count out the fruit in a bowl. I count the oranges first, and get three. Then I count out the apples, and I get two; however, when I count them all together I get four. Clearly in this situation I am presented with a range of options for revision. Usually, I say that I must have miscounted, or I have misplaced a piece of fruit, but there is nothing to stop me revising my belief that 2+2=4, indeed, if this sort of thing happened all the time (and people do miscount all the time!), then revising or qualifying 2+2=4 would no doubt be a very useful course of action. To sum up, of course there are propositions of which no revision is permitted, that is exactly what Quine is trying to get across with his web metaphor, his point is that it is our decision as to which propositions to hold fixed.

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2. Who said anything about "assumptions"? I said the axioms of math is necessary. What is necessary? It is necessary because it is true in all possible worlds. It is true, because the axioms have extensions in every possible world to some abstract object.

3. The fact that you find abstract object "nonsensical" just means you are not putting the work to understand it. It is not an argument of any kind. To show that the notion of abstract object is incoherent, you need to assume the properties of abstract objects, and derive a condition. Did you do that? no!

TuringEquivalent: "The axioms of math are assumed to be true, and thus, necessary true."

As to your comments about abstract objects, I refer you to this three page thread of sustained argument: http://able2know.org/topic/158212-1

I'm sure you remember, but if you have nothing new to add, I don't care to talk about abstract objects with you any more, you aren't very good at it. Though, issues of their coherence, indeed, existence, aside, I don't see how your belief in them squares with your view that mathematics is not a science. On the platonic view, the mathematician is a discoverer. He is engaged in the investigation of the properties of independently existing objects, and their relations to other objects... Sounds a lot like natural science to me. The same is true, of course, of people who subscribe to logicism, formalism, or something similar, who take a platonic view of rules. More sophisticated views of mathematics, however, view the mathematician more like an inventor than a discoverer; making new decisions in each new case, rather than simply moving along the pre-laid tracks of the platonist rail road.