You mean it wasn’t straight forward the first time?!?
Anywho (we’ll do, will due, will do)…
I have to say, off the top, that I’ll try to articulate this as best I can, but I admit that it is not entirely clear and precise in my head either. Here goes…
We have a finite set of words, many of which have sense on their own: dog, park, hat, slew, yellow, chance, Coca-Cola, for a scant few. These sorts of bits of language have sense that is more or less definite in the minds of most of the English speaking community; thus, we appear to have a more or less adequate grasp on the corresponding referent that these bits pick out. We have a set of finite words that have relations to seemingly discrete parts of reality. Now, it appears as if humans have a strong disposition to accept that discrete things are in themselves finite, and so, we believe/think/feel that these finite words we use are in some way connected to finite things in the world.
Now maybe this might be a biological fact, but it could also be a psychological fact—hardwired and/or software, and it might even be that it simply is the way of the world; however, and which+ever/other/none/all, it does seem as if we exist with, to quote Lurid, “…finitely biased brains.” We use finite words in our relating to what we—for whatever reason—experience as more or less definite and finite forms of differentiation: we are seemingly finite beings in a seemingly finite world.
Although I have an intuition that all things are infinite (where the math is more metaphor than an attempt to justify, validate or otherwise “prove”—all seemingly finite and discrete lines, plains, and solids are “composed” of the same infinite number of points), we typically experience differentiated and seemingly finite forms, but we do not appear to experience any infinite forms. Certainly we can conceive of infinity, even in respect to some of the finite words which refer to apparently finite things, take colours for example—red as pointed out by Lurid above—they can come in a conceptually infinite variety of shades, and perhaps any patch of red we experience is all the infinite shades of red in one, but we seem to, in any particular experience of red, interact with something that we interpret as finite and more or less definite. We do not generally interpret any experience as having an infinite content, and so, unlike most other words, infinity does not relate to a particular experience. So what does infinity relate to? It’s kind of like Grant pointed out, “You're left with a kind of sense-only, maybe.”
Infinity has to refer to something, I mean, we have a sense of infinity, we seem, after all, to be discussing something here, but it doesn’t seem as if we are discussing something that we experience in any direct way. So the referent of infinity has to be itself.
Now Quantum, you’ve stated that you don’t buy into the whole sense/reference thing, but think of it in terms that I’ve tried to sketch out: differentiated and discrete forms make up our interpretations of experiences and we have finite words and phrases that bear some relation with a perceived external reality; however, we don’t appear to have any direct experience of infinity insofar as we interpret any given experience. Thus, when we talk about infinity, we can’t be talking about something we’ve experienced, and yet, we are talking about something. So, unlike many words which seem to have a more or less definite relationship with our experience, ‘infinity’ has no such relationship.
I think it is important to take note that infinity is not a number, it is a set of relations—a bundle composed of an unending number of components all of which stand in relation to one and other. Now, it seems as if all of our experiences are relations to “sets” or bundles which are composed of components (again, we generally assume and interpret the differentiated forms we interact with as being composed of a finite number of components), and yet, we don’t seem to experience any particular bundle as being infinite. As I said before, I think all our words create an interpretation of events that “shield our minds” from direct contact with an infinite bundle of relations. Thus, steeped in our finite interpretation of experience, the immediate experience of an infinite number of relations must go interpreted as only itself; that is, infinity can only be itself—it is self-referencing, or, if you want, the sense of ‘infinity’ can only be its sense.
Now Quantum, you said, “Words are sense-only. (as are numbers- you can't point to a thing in the world and say 'that is 5').” And I entirely disagree, well OK, not entirely, but I do disagree. Words might be thought of as “sense-only,” but to me that’s buying into the whole sense/reference dichotomy. As I’ve sketched out above, our words bear some relation to our experiences: they are part of our interpretation of reality (whatever that may be). Whether we want to call that relation “reference” or not is unimportant, but we can’t deny that there are relations between our words and our experiences. Further, I do think we can point to a “thing” in the world that is five. We can point to five differentiated seemingly discrete and finite things and we experience the bundle, set, or group of relations that is five. It is exactly like pointing to a shovel and using the word ‘shovel’ in relation to a bundle, set, or group of components that make up the apparently discrete shovel. Numbers are no more or less “fictional” than shovels!
Anyway, I’ve spent much too much time on this (but it has been a great trip to the gymnasium)—I have to clean the dwelling. I know this is still probably muddled and muddy, but I am happy to attempt to address further inquiries in an attempt to be more clear!
eZ
Phew! |