Buddhism and numbers incompatible?

[Dancing David]

Hmmm... Well damned if you do, damned if you don’t. That’s a safe, but ultimately a dead-end view. It may be the most correct, but it certainly doesn’t leave much to say... Perhaps you’re right in that I’m just being silly drKitten, hence the anonymous forum Regardless of how “silly” it may be, debate over the nature of numbers and mathematics has been a fiery subject form the time of the Greek and continues to rage (in fact, Santa’s opinion on the issue is quite enlightening ).

Below are just a sampling of philosophical school that focus on the nature of mathematics. So while this conversation may seem laughable there are some people out there who get paid to ponder on this stuff, and thus it is at least as good as porter potty cleaning, if not better.

From the Wiki page on Philosophy of Mathematics:

Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind.

Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the naive view most people have of numbers.

Logicism is the thesis that mathematics is reducible to logic, and hence nothing but a part of logic (Carnap 1931/1883, 41). Logicists hold that mathematics can be known a priori, but suggest that our knowledge of mathematics is just part of our knowledge of logic in general, and is thus analytic, not requiring any special faculty of mathematical intuition.

Empiricism is a form of realism that denies that mathematics can be known a priori at all. It says that we discovered mathematical facts by empirical research, just like facts in any of the other sciences

Formalism holds that mathematical statements may be thought of as statements about the consequences of certain string manipulation rules. For example, in the "game" of Euclidean geometry (which is seen as consisting of some strings called "axioms", and some "rules of inference" to generate new strings from given ones), one can prove that the Pythagorean theorem holds (that is, you can generate the string corresponding to the Pythagorean theorem). Mathematical truths are not about numbers and sets and triangles and the like — in fact, they aren't "about" anything at all!

Mathematical intuitionism: In mathematics, intuitionism is a program of methodological reform whose motto is that "there are no non-experienced mathematical truths" (L.E.J. Brouwer).

Constructivism: Like intuitionism, constructivism involves the regulative principle that only mathematical entities which can be explicitly constructed in a certain sense should be admitted to mathematical discourse. In this view, mathematics is an exercise of the human intuition, not a game played with meaningless symbols. Instead, it is about entities that we can create directly through mental activity. In addition, some adherents of these schools reject non-constructive proofs, such as a proof by contradiction.

Fictionalism was introduced in 1980 when Hartry Field published Science Without Numbers, which rejected and in fact reversed Quine's indispensability argument. Where Quine suggested that mathematics was indispensable for our best scientific theories, and therefore should be accepted as a body of truths talking about independently existing entities, Field suggested that mathematics was dispensable, and therefore should be considered as a body of falsehoods not talking about anything real.

***Embodied mind theories hold that mathematical thought is a natural outgrowth of the human cognitive apparatus which finds itself in our physical universe. For example, the abstract concept of number springs from the experience of counting discrete objects. It is held that mathematics is not universal and does not exist in any real sense, other than in human brains. Humans construct, but do not discover, mathematics.
*** this is the one I gather most people here ascribe to.

Social constructivism or social realism theories see mathematics primarily as a social construct, as a product of culture, subject to correction and change.


There were also “non-traditional schools listed but I though it best to keep this post in the category of “obnoxiously long” as opposed to “not worth the effort”.

Wow, Santa and the Tooth Fairy sure have a lot of time on their hands!

That was very enlightening, thank you.

 

[Loriciferan Universe]

Wow, Santa and the Tooth Fairy sure have a lot of time on their hands!

That was very enlightening, thank you.

Glad I could bring you something new .

drKitten (or anyone else), I have a question. The examples you listed were interesting, but they stemmed from several different sources so for now I’m going to pick just one point you made and go from there. You stated:

“Just because you can apply the label "two" to something doesn't mean that the two things are entirely separate and separable. Just because you can apply the label "one" to something doesn't mean that it's uniformly and homogenously the same.”

But isn’t it a mathematical axiom that if I am working an equation with x and y, that they are related so far as the equation shows, but no more so. In other words, x and y are completely different things and you are describing a relationship between them. Now, isn’t this kind of mathematics used to describe physical properties of the universe. And if you are correct that “Just because you can apply the label "two" to something doesn't mean that the two things are entirely separate and separable” doesn’t that present a problem for using math as a way to understand the universe?

 

[Dancing David]

The key word being describe, which means to write about. Do not mistake the map for the road?

 

[cyborg]

1) The metaphysical is not the physical.
2) Metaphysical concepts can be represented physically.

 

[drkitten]

“Just because you can apply the label "two" to something doesn't mean that the two things are entirely separate and separable. Just because you can apply the label "one" to something doesn't mean that it's uniformly and homogenously the same.”

But isn’t it a mathematical axiom that if I am working an equation with x and y, that they are related so far as the equation shows, but no more so.

Not at all; in fact, much of mathematical reasearch consists of showing that if two things are related in one way, then they must also be related in a second way. For example, if you have a set of objects that are related in such a way that they form a planar graph, then they must also be related in such a way that their chromatic number is four or less (this is the famous "Four-color theorem"). If you know that x and y are related by being relatively prime, then you also know that they are both related to the number xy in that xy is their least common multiple. If you know that three points are related in the form of an equilateral triangle, then they are also related in that their internal angles are each sixty degrees. And so forth.

Now, of course, if all you know is that x and y are related in one way, you can't assume without justification that they are related in another way as well -- I share a last name with a guy I've never met from Kansas, but I can't assume on that basis that we are genetically related as well. This applies to mathematics as well as to "raal life"; you don't get to make unfounded assumptions.

{QUOTE] And if you are correct that “Just because you can apply the label "two" to something doesn't mean that the two things are entirely separate and separable” doesn’t that present a problem for using math as a way to understand the universe?[/QUOTE]

Not at all. I assume (because I know it) that this guy in Kansas shares my name. But I also assume (with equal validity) that he's a different person from me. Can I assume that he's a relative? Not with any confidence. Now, it might be that he is. He might be part of my extended family and I will eventually inherit millions from him -- but that's not an assumption that I should make. My understanding of the universe is limited by what I know about it.

But because I know he's a different person than I, I also know that if we took a trip together, we would probably need to rent two hotel rooms. Two people = two rooms. Even if we're relatives, that doesn't mean that we should share a room. Even if he were my long-lost brother, that doesn't mean that we should share a room. One family (perhaps) -- but still two hotel rooms.

 

[blobru]

According to Herodetus it isn't. The water changes, the banks change, your presense changes the river, etc...

The Pre-Socratic philosopher Heraclitus is the source of the quote, "you can't step into the same river twice", though it may have been recorded in Herodotus' Histories.
His disciple Cratylus took it a step further and declared, "you can't step in the same river once!"
In opposition to the "change is all there is" school, Parmenides and Zeno (he of the paradoxes) argued change is impossible.
Of course Plato reconciles the two by saying universal Ideas don't change whereas particular objects do.

 

[Dancing David]

The Pre-Socratic philosopher Heraclitus is the source of the quote, "you can't step into the same river twice", though it may have been recorded in Herodotus' Histories.
His disciple Cratylus took it a step further and declared, "you can't step in the same river once!"
In opposition to the "change is all there is" school, Parmenides and Zeno (he of the paradoxes) argued change is impossible.
Of course Plato reconciles the two by saying universal Ideas don't change whereas particular objects do.

Ooops, it is Heraclites isn't it. Old brain.