Are there abstract objects? Do numbers, for example, have an existence that is independent of our minds? This is one of the Big Questions, and has been a recent topic of debate over at Maverick Philosopher, where I have been outnumbered as usual. It’s a pretty tough room for materialists, that place.
What, exactly, have we been wrangling over? Consider the following proposition:
The statement “3 is prime” was true even before there were any minds to conceive it.
Is this true? Bill Vallicella and company say it is (and seemed a bit shocked that I might think otherwise), but I think the question is more subtle that they realize, and doesn’t have a simple yes-or-no answer. Here’s the view I am proposing:
I think the warring parties would all agree that there is an objective Reality that forms the ground of any possible perception. My point is that this Reality has sufficient regularities and complexities that it is parsable into all sorts of conceptual mappings, depending on one’s cognitive apparatus, or, shall we say, “viewing angle”. One such mapping, which we humans have found to be so useful that it has become almost impossible for us to imagine that it is not more than just our view of things, is the concept of “number”. But there may be infinitely many other ways, many isomorphic, to apprehend the objective World, with equal or even greater predictive and interpretive power. Perhaps our ability to reduce the multifarious complexity of the world to mathematics is only a blessing up to a point; it might be symptomatic of a limitation of our perception and cognition that we feel the need to insist on its ontological fundamentality.
In other words, minds can gerrymander the underlying truth of the world, and the boundaries and categorization of objects, in an infinite number of ways. How it is for any particular mind depends on the contingent history of how that mind came to be, and what the needs of its evolutionary ancestors were. If a developing species hits on a useful categorization, a selective advantage may be conferred, and the categorization thereby reinforced. The point is that all of these systems are simply different “views” of the same underlying world, and in principle, perhaps, many could therefore be transformed or mapped one into the other. But not all of these views are going to have equal power or extensibility. An alien mind, therefore, might not have or need a concept of “number”. Our own compelling intuition that this concept is a fundamental necessity, a preexisting and objectively real “abstract object”, might be due only to the highly contingent details, shaped over our evolutionary prehistory, of our mental architecture. So when somebody says “it was true that 3 is prime, even before there were any minds to know it”, they are right in a sense, in that the infinite complexity of the world allows itself to be parsed in such a way that the statement is true, but it was not a salient, or even discernable, feature of the world until a suitable mind came along to define the concepts ‘3’ and ‘prime’.
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A similar debate (partially inspired, it seems, by the one at Maverick Philosopher) has taken place at Consciousness and Culture (between myself and Steve Esser), starting in the comments to this post, and continuing with this little fable about an encounter between platonists and aliens.
I take your side of the dispute, as far as I can tell. I think a statement like “3 is prime” would be true if there were no minds only in the sense that a statement like “A five-legged horse has five legs” would be true if there were no minds, no horses, no legs, and no “5” — it wouldn’t be any evidence of the existence of an abstract object such as a “five-legged horse”. That is, these kinds of statements are true only (or very largely) by virtue of their own internal consistency, and not (like empirical assertions) because they correspond to something “objective”. Perhaps a simpler route would just be to say that if there were no minds there would be no “statements” to be either true or false.
Thanks for the comment, Ellis. I’ll take a look at the links.
It’s a slippery topic, but my feeling is that the statement “a five-legged horse has five legs” would have no existence of any sort prior to the existence of minds to frame it. A corollary of the point I am making here is that any reification of things like “3” is in a sense retroactive, in that once the concept has been defined one can examine the previous state of the world to see that it would have been true then also. But to say that the concept exists independently of minds, other than as merely being one element of the infinite set of available gerrymanderings of the World is, I think, a mistake.
Well, I’m not quite sure of the difference you find between the two statements, other than perhaps the point that “3” is a more abstract concept than “a five-legged horse”. Once the concept “3” has been defined, then arguably you could say that it would have had meaning (as opposed to “truth”) prior to minds, but then so, as far as I can see, would the concept “five-legged horse”. If we make statements out of such concepts, and those statments refer solely to their meanings, then it seems to me that both could be said to be true, but only in a way that tells us nothing about “objective reality” of any sort.
But, as you say, it is a slippery topic, and I’m in general agreement with your take on it. In particular, I like your phrase about the “gerrymandering of the world”.
Hi again Ellis,
No, I think you misunderstood – I wasn’t making any functional distinction between the two statements, just responding to your “only in the sense that…” remark by re-emphasizing that the statement carries no mind-independent ontological weight at all, really. I think we are very much in agreement here.
Gotcha — sorry for the misunderstanding.
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[…] The point Bill is making with regard to the theory of references is to distinguish between linguistic tokenings, such as “Santa Claus does not exist”, and the proposition expressed by the tokening, namely that Santa Claus does not exist. The latter, he argues, is true independently of the historical use of the phrase “Santa Claus”, the referent of which may have changed over time. Knowing Bill, I imagine he would say that the truth of the proposition itself is actually independent of whether anyone had ever expressed it, in any language tokening whatsoever. And in the comment thread, he makes just that point: Does the earth exist? Yes, and the fact that it does does not depend on the existence of the corresponding word or concept. The earth existed long before any languages did. Of course, no one could name it ‘earth’ or ‘Erde’ etc. until languages arose. I’ll try to explain what’s bugging me (and I’ve had at least one previous go at digging into this). […]