I think some of you…cough…Mr. Rule…cough… haven’t been studying the history of philosophy like you should. If you did, then you’d be aware of a long and influencial history of the debate between nominalism and realism. In fact, the first big “throw-down” between these ideas came between Aristotle and his teacher Plato.
“Aristotle makes it obvious that, when a number of individuals share a predicate, this cannot be because of relation to something of the same kind as themselves, but more ideal. This much may be taken as proved, but Aristotle’s own doctrine is far from clear. It was this lack of clarity that made possible the medieval controversy between nominalists and realists.” - Bertrand Russell’s “History of Philosophy” pg 162.
Russel goes on to describe in detail what a “universal” is to Aristotle, then he critiques Aristotle’s position. To understand Russell’s critique, we have to look at an analogy he makes.
He says…suppose I say, “There is the game of football.” Most people he says would grant this as a truism…but, then, if he says…“football can exist without the players…” the statement becomes foolish. Or, another example he gives is, there is such a thing as “parenthood” only because there is such a thing as parents…and there is only sweetness, because there is such a thing as candy. There is “redness” he says, because there are “red” things…and we can add to this list…“there must be numerical concepts, because there are a numerous amount of things.”
Such is the nominalism of an Aristotle. But you see, Russell goes on to critique this position. He says that the real distinction is not a metaphysical distinction between universals and particulars (parenthood and actual parents) but rather, it is a linguistic distinction derived from syntax. He claims that we need a new philosophical language that will do away with such syntax errors and thus make the problem of the “one and the many” disappear.
But, does this work? Christian philosopher Greg Bahnsen points out that saying this is a “syntax” problem is simply pushing the problem back to the realm of language. We still have universal concepts being applied to particular objects despite how we choose to discuss them.
Therefore, for some of you…cough…Mr. Rule…cough…to arbitrarily assert a form of nominalism as “granted” is to ignore the history of the discussion and arbitrarily assert a well refuted position.
Lets my post run too long…I’ll quickly reply to Mr. Auf…
Again, I applaud your level headed response, but, I think you have a misunderstanding of angels… you see, they ARE necessary for science. In fact…if God ordains something to happen in the physical realm, he carries it out via the actions of his angels. (I’m being silly here, though I do hold to a form of angelic causation, I’m exaggerating the issue in order to demonstrate why the “non-physical” angels are just as necessary to science as your non-physical numbers. We could disagree over their necessity of course, but the point is, you cannot exclude them from the “natural” realm since they, and God as well, would meet the criteria you’ve established for “numbers.” Thus, if you include numbers, you have to include God and angels in the natural world as well.)