- It is my intention to propose a new philosophical problem which I will call the problem of the many1. This problem concerns the number of entities, if any, that exist in actual ordinary situations and in counterfactual or hypothetical situations. The problem concerns the number even at a given moment of time, and it becomes only yet more baffling when durations of time, and changes, inevitably complicate the issue.
- It is a philosophical commonplace to note that, without any further specification, there is no definite finite answer to the question of how many entities a given ordinary situation contains. Considering my own present situation, for example, it might be said to contain a salt shaker, also each of the grains of salt in the shaker, also the atoms that compose the shaker, as well as each of those in the grains, and this is only to begin to enumerate what seems natural. Artificial or contrived entities, so to introduce them, greatly complicate the picture. There is the left half of the shaker, as viewed from right here, and also the right half; there is the scattered concrete entity whose salient parts are that left half of the shaker and the second largest grain of salt inside the shaker; perhaps, there is even relevantly in the situation, the abstract entity that is the set whose sole members are the two concrete items most recently specified; and so on, and so forth.
- To illustrate this commonplace is of course nothing new. But it is not even to rehearse any philosophical problem, about numbers of things. For, what is the problem here? On the contrary, it is natural to suppose that once an available category or sort of entities is specified, a definite answer frequently can be given, often in the form of a small positive finite number. Thus, for example, if the question is how many salt shakers my present situation contains, the answer is one. And, for another example, if the question is how many human bands are in that situation, then the answer is two. Supposedly without any serious problem, this is what one is given to think. What is new, I believe, is to suggest that even here, with such ordinary kinds purporting to delimit things, no such manageable answers are tenable. And, insofar as there is something to it, this suggestion does mean a problem.
- Perhaps "the problem of the many2" is a somewhat misleading name for the problem I mean to introduce. Perhaps it might better be called "the problem of the many3 or the none." For I shall not suggest that various considerations simply lead us to an extraordinarily high accounting, for example, to the idea that in my present situation, in what I take to be my dining area, there are millions of salt shakers. No; what these considerations lead to, I shall suggest, is a difficult dilemma:
Insofar as I find the latter of these alternatives rather absurd, I am that far inclined toward the first, to the nihilistic, or Parmenidian, option. But of course most philosophers will wish to avoid both these alternatives. So, insofar as it can be motivated, such a dilemma will be quite a problem for most philosophers.
- Either there really are no salt shakers at all,
- or else, in my dining area, there are millions of these things.
- In addition to informal discussion of it, I mean to motivate this problem in two main ways. First, I shall offer certain arguments, whose conclusion is our problematic dilemma, or else a proposition to the same effect. Along this line, I shall suggest that there are no adequate objections to these arguments. I shall try to support this suggestion, in part, by considering what appear the most plausible of objections and by showing that even these miss their mark. In part, also, I shall disarm any objections by examining the implications of my arguments' premises, by trying to understand what underlies them.
- These arguments will be presented first in terms of clouds, those putative ordinary things which, so often, seem to be up in the sky. As our problem is one that concerns vagueness, beginning with clouds is natural; it should be helpful in promoting some initial understanding, and sympathy, for my argumentation. Later, I shall extend my arguments, in fairly obvious ways, from clouds to many other sorts of ordinary things: stones, tables, hands, and so on.
- Although I think arguments are important in philosophy, my arguments here will be only the more assertive way for me to introduce the new problem, not the only way. To complement that reasoning, I shall ask certain questions. To avoid our problematic dilemma rationally, these questions must receive an adequate answer. But, it will be my suggestion, there really is no adequate answer to be given here.
- Concerning vagueness, as it does, the problem of the many4 is a problem in the philosophy of language as much as in metaphysics. Once the problem itself is presented in detail, I shall sketch certain further problems that it implies. While these implied problems also concern the aforesaid two philosophic areas, they do not end there. Rather, they also concern, or give rise to, certain problems in epistemology. Accordingly, it is my belief, the problem of the many5 should prove quite fertile for philosophical investigation.
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