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Response To Macula, Re. Platonism

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Posted by Paul R. Martin on May 26, 2003 20:04:14 UTC

(In response to:

Hi Kyle,

Sorry to be so late with my responses to you. I owe you quite a few. I'll start with this.

"we could also argue that music is more of a "sensation" than anything else, or a transduction of sound pressure waves which do not actually become music until our sensory apparatus translate them into the conscious state corresponding to music."


"I would therefore submit that 'color', like 'music', is a sensation that exists in the perceptual realm of consciousness rather than an independent "thing out there"."

I agree completely with your analyses. I think that rather than consider those things as being "out there", it is more appropriate to consider them to be "in here", meaning that they are somehow part of what we call consciousness. Taking this to an extreme, my speculation is that "consciousness" is all there is. I am an idealist who buys into Berkeley's thesis.

"When you say, "Three is the set of all triples" what you are saying, if I interpret you correctly, is that "three" is a property of collections of objects, ie. it is a property of sets. So we could say that a set has the property of threeness if and only if that set has precisely three members."

Not quite. You have described cardinality, not number. Cardinality is the property of threeness, for example. We say that a set has cardinality three, or a cardinality of three, if and only if the set has precisely three members.

"We know what the property of 'threeness' is, but what exactly is three itself? We can certainly consider 'three' as an adjective as in three apples or three sticks, but can we have a 'noun-object-thing' that is "three"?

I don't think we can any more so than we can have a 'noun-object-thing' that is red. I don't think that there is any such thing as three 'out there', independent of us.

But we can. That was the genius of Frege. The problem was, as you say, coming up with a 'noun-object-thing' that is "out there", i.e. extant, and unambiguous, to which we can assign the name 'three'. The set of all triples fills this bill. The definition is meaningful if there is even one set in existence containing three elements.

"So the answer to the question, "what is three?" we could say that the number three is a 'set of sets'; three is the set of all sets with this property of threeness."

You got it. That is what we do say.

"I think Frege considered numbers to be related not to empirical objects but rather to empirical concepts... these empirical concepts are used to describe the world... numbers are used to characterize those very descriptions (as 'names'). In this sense, I suppose Frege actually would have argued against mathematical Platonism."

You could be right about Frege. I don't know much about what he thought. But Whitehead and Russell used his definition of number without specifying what constitutes the sets which constitute natural numbers. In Zermelo's axiomatic system, sets are taken as undefined, so it doesn't matter how you think of them. You may think of them as containing empirical objects, or empirical concepts, or strictly ideal concepts, or a duke's mixture of all of them. None of it enters into the formal use of the term 'set' as a primitive concept.

"As funny as this might sound after having said all of that, my tentative conclusion after considering your post on the question of mathematical Platonism is that perhaps you are right when you say that it is all really just a matter of semantic distinction. (...or perhaps a philosophical exercise). Perhaps we are better off to just leave it at that for now!"

Okay, but one last thing before we leave it. I want to point out that even though there might be a set of three things "out there", independent of any and all minds, the concept of threeness, or the recognition of the existence of any set of cardinality three, requires a conscious mind of some sort. So in my view, Platonic reality cannot exist absent a consciousness. In that sense it is the same as music or color, as you pointed out, and it fits in with my extreme speculation.

"[Alan] said : "Math + Consciousness = Physics"

I thought that was a good quote (despite it's implied Platonism!)

I think it is a good quote, and I am pleased that you noted the fact that it is implied Platonism.

(Sorry for having fun with your "it's". I thought about using the '(sic)'. Then, I thought, "Naaa" I can interpret what you said literally to mean the same thing you intended. I think that even Mike would have to agree that both interpretations yield the same result.).

Back to Alan's equation. To me it says that God (Consciousness) produced the Universe (Physics) by doing Math (as Dr. Dick has shown he must). That will, no doubt, attract a lot of arrows flying my way, but it is a good succinct summary of my world view at the moment.

Warm regards,


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