Case for math antirealism

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I made a lot possible enemies, so tumbleweed may be rolling past this topic, however, after reading the 'Solipsism' thread, in which math antirealism arguments were presented, and it seemed math realism rested on whether real world objects can be discretized as identical , I was wishing to investigate this further ...

Background:

1. Math Realism - humans discover math, not invent it. Thus, math exits in reality.
2. Math Antirealism - humans invent math, not discover it. Thus, math is dependent on the human mind.

http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Major themes

Realist Argument:

The realists suppose that 1 + 1 = 2 is a truth about reality.

Some realists argue that math can only be known empirically or with "ontological commitments" to provide definitions for the objects. Thus, among math realists there are ones who believe in abstract math truth, or empirical math truth, as well as other variations.

Case for antirealism:

A. Argument against abstract math realism:

On another thread I presented from a legal perspective that I often have variations where a lawyer may argue that say 1 rod + 1 rod connected together is now 1 rod (1 + 1 = 1), because the abstract object of "rod" was not defined.

Further, the foundation of math - the postulates - do not postulate on the nature of abstract objects used within math. Thus, as described above, 1 + 1 = 2 in the abstractness of math appears to be clearly non-truth about reality.

B. Argument against empirical math realism and math realism with ontological commitments:

"2 apples + 2 apples = 4 apples" seems rational, yet, we know we must have a definition of what is an "apple" to know all four belong to the same group. There must be physical properties that define the commonality.

Empirical math realism and ontological commitments tells us that given an ontology for what is meant by "apple" (i.e., define the abstract concept of "apple"), then 1 + 1 =2 is truth about reality.

However, humans are subjective, for example, one human may think turquoise is green, and another thinks it is blue. Thus, a definition still makes the truthfulness of 1 + 1 = 2 rest with the opinion of a human, and as such cannot be truth about reality.

The big question:

As was mentioned in the Solipsism thread, the question of whether matter be discretized such that a definition can be provided that does not rely on human subjectivity? This is what I was wishing to explore. If so, then the math realists would have a much better argument.

Right now though, I am in the math antirealist camp.

Last edited by LoveNotHate on 19 Aug 2014, 10:26 pm, edited 2 times in total.

Math sucks.

That is all.

I wish I could use "I am philosophically opposed to taking this maths quiz as I am a math antirealist" as an excuse.

Well this is my first time earing this , so im just going to make a question here and please correct me if im wrong becouse i want to know more about this.

So if a schezofrinic was in a room and he saw more stuff in the room and someone said "count the stuff that is in the room" and he would count it with the ilusions that to him are real...wath is it ? I go for antirealist but since its his realaty it could be real too no?

LoveNotHate, I'm assuming you are a solipsist. What's your premise about reality?

- maths is a descriptive language (languages as signs and symbols also don't exist in the exterior world, but that doesn't mean that they aren't applicable). There are mathematical properties to everything that exists in your reality.

- maths, as a human problem-solving tool, is predictable: 1+1 is never 767868959. If it weren't, it would have no use in reality as a problem solving tool.

You could try it with the IRS, VISA, and your landlord though.

The argument that what you owe them isnt real because math itsself isnt real!

Very Funny, but true

Math antirealists say numbers do not exist objectively, so '$1000 debt' has no objective meaning. They would argue that what gives it subjective meaning is that the IRS/landlord/VISA identifies particular quantities and methods of payment, thus qualifying what the abstract concept of '$1000 debt' means.

One could pay the abstract term '$1000 debt' with 10 beach shells claiming the shells subjectively equate to the abstract concept of "$1000 debt'.

Math antirealists are confusing the map with the territory.

Exactly.

Anyone not accepting mathematics should stand 9 metres from the edge of a cliff and step towards it by 10 metres and see how unreal that feels.

I don't know much about economics, but is currency really that arbitrary? Also, currency always changes in value relative to something. Are you using this example to argue that 10=1000? I think the problem is with the abstractness of debt and not the tool per se.

Same goes for people arguing that there is no cliff!

Be warned LNH will find a real study. twist its meaning and context to show that a mathematician who has taken the 10m walk and found the cliff does not exist or rather they were able to conjure up a nice beach side cabana, because nothing exists outside of the mind. All this in spite of the actual evidence that the experiment failed due to the presence of gravity and a long drop.

She will then get really pissed as no one will take her seriously and demand we show just how she has taken the research out of context.

you have been warned, have fun

1/1 = 1
0/1 = 0
0/0 = 1
1/0 = error
..but..
1/0 x 0/1 = 0/0 = 1

hmmmm

I am not a solipsist. Math antirealism was discussed on that thread. The discussion ended with the assertion that perhaps matter can be discretized to identical things. It was mentioned that perhaps Quantum Mechanics would show us this (i.e., perhaps QM would give us some objective definition for matter that can be used in math).

This is relevant to the math realists because for 1 + 1 = 2 , then presumptuously real world objects must have some common properties. However, we know that real world objects, for example a dollar can be ripped or faded, and missing those properties, yet still be accepted subjectively as a dollar, so the math antirealists would argue that you only find those objects having those properties subjectively, thus, objective truth in reality has not been established.



Math is predicatable, but it can be meaningless.

I showed you above how 1 + 1 can equal 1. You can test this on your calculator. Imagine in the real world you take 1 rod and connect it with another rod to make 1 rod. When you type 1 + 1 on your calculator it shows 1 + 1 = 2, because it functions in the abstract.



Many places would let you pay a '$1000 debt' with 10 gold bars for sure.

Mathematics is only a language and tool.

Man created language to standardize known concepts: pig + pig = More pigs: More pigs = 2 (or II, etc.) pigs (a language is born).

We're still trying to explain our universe by inventing new mathematics (example: Non-Euclidian Geometry, meh).

And we're still developing math to help to understand quantum effects we're just now beginning to utilize.

And black mass and black energy calculations have just begun (even though we don't know what we're doing).

The more carefully you measure the better and more accurate the answer, assuming your math

is adjusted to match reality.

Otherwise it's over the cliff you'll be a goin'.

Agreed! It was absolutely my worst subject in school.