There seems to be what I would call an “epidemic” the symptoms of which include the postulate that mathematical objects are material things. Are numbers material, such that they can be weighed, measured, or sensed? Oddly enough, I’ve seen people make this claim, and I just find it absurd. Accordingly, a mathematical object is identical to a collection of electrons and neurons in a certain state, itself grounded upon data given in sensation.
The problem, for me at least, is that it would imply that infinite sets, such as the set of natural numbers, or an axiom schema, to use another example, come from the natural world; hence, an actual infinitude of things would exist, which would be a slippery slope to all sorts of real absurdities. Further, people, the bearers of such mental experiences, often disagree; provided that mathematical truths are reducibly material, and all brains are different, who is anyone to say that 1 + 1 does not equal 17? Finally, if you also subscribe to determinism, then how we think of mathematics is determined anyway; how are we to discern truth from fiction in all instances where we are determined to be making such judgments?
Here we are again, the chicken vs the egg. Did numbers give rise to experience (subjectivism), or did experience give rise to numbers (objectivism)? Did God create man in his likeness or did man create God in his likeness? It never ends… on and on and on. Maybe both (dualism), maybe neither (nihilism). Maybe both and neither, maybe neither neither nor both. Well, I guess I’ll try and uphold objectivism, that’s what I do… usually.
The world gave rise to concepts such as numbers. We can see, no no no, we can percieve numbers in the world. Number isn’t a thing (qualitive), the way an apple is a thing, rather, it’s a relation between things (quantitive). Take the number 3. After witnessing numerous (lol) occasions where there was only 1, 2, 3 of something in a given area, say, 3 apples in a basket, or 3 turds in a toilet, we gave this recurring set of circumstances a name, 3. There is something similar between 3 apples in a basket, or 3 turds in a toilet, no? Therefore, this similarity desevers a name, 3, no, I think so. It’s out there friends, in the world.
This recurring set of circumstances exists, and we can distinguish it from another recurring set of circumstances such as 4 apples in a basket, or 4 turds in a toilet.
No one’s saying that numeric representations are material things, other than in as much as they happen to have a perfect correspondence with material things. Like if there are 4 rocks in front of me and I say, “those 4 are material objects”, I’m not actually talking about some abstract “4” that’s out there in the world someplace.
Also, for all intents and purposes, the universe is infinite to us. Whether it actually is or not has yet to be seen is one thing we know for sure. So I think it’s a safe bet to toy around w/ the notion of infinity if it’s helpful to our understanding of things. What’s the big deal here? Am I missing something huge?
It might help to realize that there are two very major camps in philosophy;
Mind determines Truth {The Copenhagen, Quantum Magi perspective)
Mind discovers Truth (The Logic, Science, Religion perspective)
Information theory, M-theory, Multiple world theories, and the like are centered on “Mind determines reality”. In such a manner of thinking, any identifiable concepts are objects. Numbers would be merely one of the vast number of items to be regarded as objects. To you, they would be merely “objects of thought”, but to the camp that accepts the ancient idea that reality is merely a state of mind, everything concerning the mind is “matter” (ie. it matters).
I think those two camps are roughly equivalent. What’s the hang up? You do realize that you can’t prove or disprove one any more so than you can the other right?
The Copenhagen interpretation of Schrodinger’s Cat. The cat actually IS both dead and alive, but merely in different realities.
And it becomes your reality only when you open the box.
I think it could be a little of both (1 and 2), after all, the same thing will leave a different imprint on different things. That doesn’t mean the thing isn’t out there, I reckon. The same thing will leave a similar imprint on similar things.
Shot in the dark here but maybe he doesn’t mean mind in the sense of “non-physical somewhat hokey entity that’s postulated for no good reason”, but instead means, “perception or at least perspective is a product of the mind and the only kinds of truths we can know are the ones that fit into the framework of it”. Maybe he’s not being a mystic at all?
Dude is your avatar really you? Or is that a random pic from the internet?
Yeah, the mentalism vs physicalism issue and the subjective vs objectivism issue are two separate but related problems. This is more about the latter than the former. I myself, am somewhere in the middle on these matters, and yourself?
I really like this paper on philosophy of mind. I think it covers the bases we’re dealing with here, especially if you could locate on online copy of another paper called “an argument for identity theory” and sorta crunch them together. This one is really good though. I can’t help it I’m just a big David Lewis fan. Check it out.
I’m not really familiar with the topic but from what I’ve read (just in this post) it seems to me that numbers themselves are the focal point of understanding information in that they are representative of other information such as you find in a binary system of code or within any language whatsoever. They are a man made system designed to interpret reality. Correct me if you believe I’m wrong but it is essentially irrelevant if you have 3 apples in a basket. There is no debate about the number of apples unless you wish to dissimulate the argument from where it should instead turn to which is the question of whether numbers themselves are useful conceived as material things. The question of having 3 apples in a basket perhaps should be turned to how many sub-atomic particles exist in each individual apple and how many particles of oxygen and other gas elements are in constant interaction with the particles that make up the whole of those three apples. Are those numbers, whatever they may be, material things? Can those numbers actually be known and if they cannot what value is there in conceiving of those numbers as material objects? Maybe I’m missing the point here.
James pointed out two schools of thought in Philosophy. Either mind determines truth or it discovers truth. Obviously the former is the more subjective in that the world is determined by psyiological and intellectual limitations that control perception which inturn creates a bias to perception and interpretation. Truth will be interpreted differently from one human mind to another and will definitely be perceived differently by a human mind as opposed to a sentient alien mind or even a dogs mind. So therefore even if the Universe and or the perception of numbers is what it is objectively the perception of that reality, filtered through a mind, will inevitably distort the perception of that reality and in consequence create an unintentional bias. The latter school of thought perceives the nature of reality to be constant and our perception to be able to be objective scientifically and so therefore mathematics itself becomes a universal language that transcends any kind of bias. So I think the question, in terms of whether or not numbers are material, becomes an understanding of mathematics as a representational language and so therefore numbers and mathematics as a whole are as equally material as any language. Perhaps I am wrong with that supposition though.
Lucis Trust, they are separate questions but there is a point at which they both converge and or diverge or rather intersect and, at least in part, that is the place were the question of whether numbers are material or immaterial is considered. I think my first time through the thread I did not read your initial post very carefully and so on a second reading I can now perceive the relevance of your statement more clearly and I think we are essentially in agreement. Before there was a definition for three, there was a need for a definition, and so that need led to the creation of a defined universal quantity, hence three of something. As for whether apples are more real than atoms, well I think that could be debated. Just because apples can be perceived more readily by our senses does not necessarily mean they are more real. What if I had senses that could more easily perceive the atoms in an apple more easily than I could perceive the apple as a whole. For me, at that point, the atoms would be more real. It is a question of perception and of unintentional bias.
Smears, I’m not exactly sure what you mean by: “I don’t think the mind determining truth is more subjective if you look at the mind in terms of what it does, rather than as if each one is unique.” Thanks for the D. Lewis link as well. He is more intelligent and eloquent but some of the things I mentioned follow along with his thought.
