[codebolt]

Alright, I’ll bite. I challenge your assertion that math is without objective meaning.

First I want to make an observation. Do you know the history of how the study of complex algebra/calculus came about? If so, I assume you will agree that it was initially a completely abstract thought experiment with no connection to anything in the “real” world.

Given your assertion that math is without meaning, it would seem to me that mathematical ideas that originate purely out of human imagination would just be arbitrary semantics.

Then how can it be that complex analysis only several decades after it was formulated turned out to be not only useful, but necessary to formulate the theory of quantum mechanics in a way that agrees with physical observation?

I can name numerous other examples of the same phenomenon; namely that a purely abstract mathematical idea is long after its formulation shown to be profoundly reflected in physical reality.

To me it seems obvious that the way these phenomena occur implies that part of the process by which humans use their imagination and reasoning to come up with abstract mathematical ideas, is more akin to using their intuition to map out objective ‘structures’ of logic (that are also reflected in the underlying structure of physical reality) than to simply play with semantics, as it seems you are asserting.

Tl;dr Post modernist philosophers are fools and they should be ashamed. Qed

[sova]

I agree with you that there are many incredible and useful insights based on mathematics and the equals sign, but the main point of contention is that not every mathematical truth has a co-responding physical phenomenon. Nor can we adequately explain how an equals sign works, or why it works. Mathematics and [im]material reality are not one-to-one and assuming that mathematics supersedes the imagination or is a superset of human language and expression negates human experience and renders our lives as secondary to "almighty math." Mathematics is a tool, would you agree? Philosophy is also a tool. Mathematics without a human user is like a video game without a player. I am not asserting that mathematics has no "objective meaning" it _only_ has objective meaning (because for every "object" we must have a "subject" namely, the observing consciousness).

Thanks for biting =)

[codebolt]

I'm always up for a discussion on this topic, because I find it very interesting and I think there is a major (dare I say it) metaphysical point here that is overlooked by mainstream intellectuals. However I've argued with enough post-modernists online over the years (which is usually like arguing with a wall) that I might have become a bit snarky- sorry about that, I appreciate the graceful tone in your response.

I agree that the symbolic language we call mathematics and reality are not one-to-one as you say. But the fact that we can use abstract reasoning around these symbols to uncover new ways of understanding of the physical world, especially in cases like the one I lined out in my example, implies to me that there must be some objective reality that is in some way captured by these symbols, in a way that plain philosophy cannot.

Personally I subscribe to Roger Penrose's lines of thought on these matters: http://theeternaluniverse.blogspot.no/2012/09/penrose-on-whe...

So to answer your question, I agree that math is a tool, but I think in some sense it also more than a tool. I believe it can also be seen as a map into a platonic reality, and that there is some element of our mind that is able to observe this realm which allows us to draw the map (using mathematical symbolic language) and come to an agreement about how it should be drawn. And that elements of this platonic realm are for some mysterious reason also reflected in the structure of our physical reality.

[sova]

Splendid, I really appreciate your taking the time to formulate a response -- it's very interesting to consider a metaphysical or Platonic realm where maths, although it may not exist in isolation, ends up arriving at the same points and valleys and landscapes and landforms time and time again. That is actually quite peculiar, the regularity with which mathematics works. I spent some time at the end of my university studies [the first go-round] trying to understand how we as humans came to discover multiplication and division. There are many possible operations we can do on numbers but only some yield a useful symmetry whereas others result in a jumbled chaos.

A close friend of mine refers to humans as "symbol makers" and I hold firmly that everything in the flow of life is meaningful, but it's really astounding that we can filter out useful patterns from our surroundings. Your point alludes to me in a similar way the beauty of a leaf or a tree: it's been speculated and suggested that over many millennia our sensory systems (namely sight) have tuned in and honed in on being able to find tasty ripe fruits and berries (why they may appear red and bright or purple and bright when in full ripeness and before ruin .. to pilfer an Alt-J lyric).

In that way, perhaps maths is some sort of tree or leaf or forest that is naturally existent, not actually separate from the earth or the forest or the consciousness of man, but still somehow a useful set of patterns our [mind] intellect-sense has been able to pick out and find the tasty and juicy bits of.

One very fascinating part of the whole narrative of mathematics is Progress. For example, Kepler and his assistant's calculated observations of the planets, mathematicians dedicating their lives to figuring out n-many decimal places of logarithms and creating reference books, and also equations and derivations. Although maths may somehow "exist" naturally because a set of equations or a set of inferences or physical phenomena may have a mathematical representation, they still need to be discovered (and often re-discovered) to stick around and be of any use to us. To me it still echoes of the personal mission of understanding and critical thinking -- one must come to the solution on their own and verify it in their personal experience to truly feel it and know it to be truthful.

Would you categorize maths as more of an invention or as a discovery? Pure discovery would imply that maths exists on its own like a tree does (or "might" if we consider that a perceiving consciousness must also be part of the 'tree'). Whereas, an invention is something deliberately put together to solve a functional need in the life of man.