Perspicuity Offline119 • Male •
Perspicuity: Are numbers real?
Part of the issue is what “real” means. Dumbledore tells Harry Potter that just because the events he experienced occurred in his head, that doesn’t mean they are not real. Things like tables are not, in some sense, part of the ultimate inventory of the universe as such—they are constructs from the world of quarks, or strings, or whatever turns out to be ultimate. There is no surface of a table, for example, since electrons part of the table (as opposed to the air above) are in superposition and might be observed anywhere in space. But tables ae “real,” as anyone knows who bangs his head against one. They produce real injuries.
The sense of real I will be talking about below is roughly like this: to say of something that it is real, in this sense, is to say that it is an inescapable feature of reality, that is, that no fully comprehensive and adequate description of the world can avoid containing it or something analogous to it.
In a sense we create the world, but we create a world that is there to be created. I mean something like this: reality has no specific form apart from a conscious being who imposes upon it a comprehensive theory (complete interpretation), but not all theories fit equally well, since reality has some sort of integrity, some intrinsic nature (otherwise conscious beings could not have evolved to create theories). Reality resists certain interpretations. Those complete interpretations that fit reality without resistance are objectively true.
Now, I cannot imagine any reasonably comprehensive and adequate theory of the world that does not include something analogous to numbers. I’m not saying it is impossible, but, try as I might, be as wild as I wish, I cannot escape something like number. For example, we can give up individual objects for something like a field in which everything is related, and we can give up space and time as we know it, but we still need the field or whatever to reflect different strengths or intensities, since the world is not completely uniform. [even if differences we perceive are an illusion, nonuniformity is required to explain the illusion, since the illusion is not uniform.] And those strengths or intensities are comparable, that is, one is greater in some dimension or respect than another. Hence something like ratios, hence something like numbers, enter into the complete description of reality.
Unless I am just missing a possibility for a complete and adequate description (possible but not likely), something akin to number is part of the any adequate conceptualization of the nature of reality itself. Thus, numbers are real in the sense defined earlier.
FistOfStone: so numbers are "real" in the sense that we cannot give a complete and adequate description of the world without them
then aren't prepositions real too? i cannot give a complete and adequate deacription of the world without employing prepositions; so, in your sense, prepositions are real (punctuation marks are not real however since as this parenthetical comment demonstrates i can form sentences without them)
Perspicuity: I doubt prepositions are "real" in my sense. Mathetmatics doesn't contain prepositions, for instance, and it is not inconceivable that a completely mathematical characterization is possible.
FlorSilvestre: Thank you so much! I loved your idea about maths and "reality"!
I'm a little obsessed with fractals and their boundaries to infinity... I need to work more on it ... thanks again
Amazing thoughts, dear professor
FistOfStone in reply to Perspicuity: i think that -is- inconceivable ... mathematics derives, both historically and -logically-, from ordinary spoken and written language - if it didn't implicitly occur as part of the practice of counting -objects- (for which there must be words), the sequence of signs "4 + 4 = 8" could be anything, or nothing
imagine a chimp scrawls that on a blackboard - what makes it a mathematical calculation, as opposed to an imitation of a human mathematician's sheer physical action, or a mating ritual, or a work of art? not the signs themselves but their use in a larger linguistic community, their use in connection with things like counting, weighing, economic transactions, measurements, etc
Perspicuity in reply to FistOfStone: But those activities are only possible because the world lends itself to them....and it does so because the possibility of number is built into the possibility of existence
FistOfStone in reply to Perspicuity: yes, that's true - if most objects were as transitory as soap bubbles, or if every time we tried to count objects we got different results and no amount of investigation revealed why, then the concept of number would have no use
but this doesn't mean that numbers are "real," it means that, as a contingent fact, the world is such that numbers, mathematics, counting, etc are useful
Perspicuity: First, number is not "about" material objects. Numbers are abstract concepts whose usefulness to us depends, in part, upon the fact that our world is best understood (for our purposes) in terms of longer-termed material objects. But see, if you put two bunnies and two more bunnies in a cage and come back in a while, you don't have four bunnies, you have quite a bit more. This doesn't show that 2 +2 doesn't equal four. It shows that bunnies left in a cage don't add....they multiply (so to speak). Now, that abstract concept may itself be viewed as a product of human cognition....but we develop concepts like number because the innate character of the world apart from us is congenial to such concepts, which is what I meant by the possibility of number. Hope that helps.
FistOfStone: yes, i can go along with all of that ... and i agree that, without number, we can't give an adequate account of the world - what i'm pushing back on is using the word "real" here, and i think that if you do, you have to call prepositions real too (if i'm right that you can't give a sheer mathematical description of the world, without natural language)
Perspicuity: Is it impossible to have a richly functional human language without prepositions? I would think so, although, perhaps, there might be something that is a rough analogue. Take the possessive "of"--a language might simply attach the name with a hyphen (Richard-book instead of "the book of Richard".