Negative truths from positive facts

Abstract

According to the truthmaker theory that we favour, all contingent truths are made true by existing facts or states of affairs. But if that is so, then it appears that we must accept the existence of the negative facts that are required to make negative truths (such as ‘There is no hippopotamus in the room.’) true. We deny the existence of negative facts, show how negative truths are made true by positive facts, point out where the (reluctant) advocates of negative facts (Russell, Armstrong, et al.) went wrong, and demonstrate the superiority of our solution to the alternatives.

Notes

¹In 1911 Wittgenstein refused to agree with Russell that there was no rhinoceros in the room, perhaps because he feared that an absent rhinoceros would commit him to negative facts [Monk 1990: 39 – 40]. Later on the absent beast metamorphosed into a hippopotamus [Russell 1956a: 214; 1986a: 189; 1997: 178].

²Excepting those readers who like to take their philosophy out-of-doors, in corridors, at the zoo, etc.

³When we read this paper at the Australasian Association of Philosophy Conference 2005, University of Sydney.

⁴Demos's solution is discussed in Russell 1956a: 212 – 15; 1956b: 287 – 89; 1986a: 187 – 9; 1986b: 280 – 1].

⁵First-order facts are roughly those facts that do not involve semantic relations. Thus being accurately described by (NH) is a fact about Room S223 but it is not a first order fact. Unless we specify that the totality proposition T refers to first-order facts the very existence of proposition T would falsify T itself. If T were of the form

‘Propositions A₁ … A_n describe all the positive facts involving S223 on 4/7/05 that there are’

then there would be another fact about Room S223, not listed in A₁ … A_n, namely the fact that Room S223 is described by T. Suppose that the corresponding proposition T₁ ‘Room S223 is described by T’ were included in the propositions A₁ … A_n. Then there would be a further fact about Room S223 not described by the propositions A₁ … A_n namely the fact that Room S223 is described by T ₁. And so ad infinitum. Thus we must stick to first-order facts if totality propositions about lecture rooms are not to be self-refuting.

⁶After Porky the Pig's once famous valediction at the end of Loony-Toons cartoons. See Gale 1976: 43], but note that Gale mistakenly attributes the cartoons to Disney.

⁷According to Russell, ‘If I say “There is not a hippopotamus in this room”, it is quite clear that there is some way of interpreting that statement according to which there is a corresponding fact, and the fact cannot merely be that every part of this room is filled up with something that is not a hippopotamus. You would come back to the necessity for some kind or other of fact of the sort we have been trying to avoid’ [Russell 1956a: 213-14; 1986a: 189].

⁸It is Heil's belief that the same fallacy leads to other philosophical mistakes specifically the postulation of ‘levels of reality’. Because ‘Gus has neurological condition X’ does not entail ‘Gus is in pain’, Gus's being in neurological condition X cannot be the truthmaker for ‘Gus is in pain’ and we must postulate some higher-order property possessed by Gus, whose statement does entail that Gus is in pain. Thus confusing the truthmaker relation with entailment leads to ontological inflation all round. See Heil 2003: 65 – 6].

⁹The subscripted ‘what?’ is a gesture to the idea that the number of propositions in this list would be of a very high cardinality and, very likely, transfinite.

¹⁰We note that incompatibility truths would seem to be non-contingent, and that we have put to one side the issue of truthmakers for non-contingent truths. It may be that the correct account of non-contingent truthmaking would fortuitously make good Demos's second defect. In the meantime, the first defect is serious and the second is a hostage to fortune. Our solution, on the other hand, suffers from neither defect.

¹¹This objection was suggested by Josh Parsons.

¹²We thank Stephen Mumford, John Heil and Josh Parsons, and audiences at the University of Otago Philosophy Department Seminar and the Australasian Association of Philosophy Conference 2005 for their helpful comments.