Facts of identity

ABSTRACT

In The Philosophy of Logical Atomism Russell held the view that facts in the world are formally structured complexes, the structure of which matches the logical structure of correspondent propositions. Russell also seems to have denied that there are facts of identity and of diversity. This paper argues that Identity and Diversity can be understood as purely formal structures in Russellian facts. It considers Russell’s possible reasons for denying the existence of facts of identity and diversity and shows how problematic these reasons are. In particular, I argue that identity statements are not tautologies, and their denial does not result into a contradiction. An important consequence of this thesis is that Metaphysics and Logic are not as tied up as Russell took them to be, but nevertheless these are good news for the old formal program for Metaphysics that lies at the very heart of what he called philosophical logic.

KEYWORDS:

• Russell
• facts
• identity
• diversity
• tautology

Acknowledgements

This paper was written as part of Reseach Project PID2019-108870GB-I00, Spanish Ministry of Science and Innovation. Thanks to the Anonymous referees for Inquiry, and to the audience at the Workshop on The Philosophy of Logical Atomism Madrid 2019, for their comments on previous versions. Thanks to Fernando Martínez-Manrique for always helping me with my basic English. And special thanks to Mathew McKeever, the editor for Inquiry who followed the arduous process leading to the publication of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 A previous version of this paper was presented at a Workshop about Russell in The Philosophy of Logical Atomism in Madrid in 2019, and its main thesis was the same one as here. When re-writing the paper for Inquiry, I considered the possibility of also considering more recent theorists of identity, thus changing the direction of paper. I have finally decided to leave its purpose as it was because I saw in it an opportunity to decide whether there was a crucial point in history at which philosophical logic changed the subject. I think it did.

2 Other important theorists of facts, such as D.M. Armstrong, also believe that there are not facts of identity. In a sense that affects a main background point in this paper but which I cannot consider with sufficient care here, Armstrong’s philosophy shows the progressive transformation, initiated by Quine and Carnap, of Metaphysics into a question of Ontology, and of Logic into a question of Language. Thus, where Russell and Wittgenstein had worried about the logical structure of reality – or outlined a ‘certain kind of logical doctrine, and on the basis of this a certain kind of metaphysics’ (PLA, 2)–, Armstrong proposed ontological universal relations: nomological, causal, instantiation relations, etc. holding between universal properties, or between properties and things. That he dismissed talk about strict identity, and mainly cared about identity over time (e.g., Armstrong 1997, ch. 2), is just another example of this progressive change in subject in the Metaphysics of Facts, from logical structures to universal relations. Other philosophers of facts, such as Mulligan, Simons and Barry Smith also deny facts of identity: ‘Provided we can account for the truth and falsehood of atomic sentences, we can dispense with special truth-makers [facts] for e.g., negative, conjunctive, disjunctive and identity sentences.’ (1984, 289; my italics); and then they significantly write that the ‘idea of a perfect parallelism of logical and ontological complexity is the misery of logical atomism’ (1984, 298). This paper is written within opposite spirit.

3 As it also happens in Physics, the usual image of Russell’s atomism is a view of the world consisting ‘of many independent entities that exhibit qualities and stand in relations to one another’ (Klement 2019). Even if this is not clearly wrong, it can be misleading: one runs the risk of visualizing plenty of balls floating in empty space instead of a complex distribution of patterns of energy. In a parallel way, Russellian facts are complex structures made up by serial metaphysical relations, and other sorts of classes. The importance of serial relations, and of an ultimate order, constituting facts is also underlined by Paul Hager (1994).

4 One referee for Inquiry has pointed out to me that it is wrong to say that the logical structure of propositions corresponds to the structure of the world, because Russell says that there is not a complexity in the facts corresponding to molecular propositions such as conjunction or disjunction. Russell writes: ‘I do not see any reason to suppose that there is a complexity in the facts corresponding to these molecular propositions, because, as I was saying, the correspondence of a molecular proposition with facts is of a different sort from the correspondence of an atomic proposition with a fact.’ (PLA, 41) Now, I do not think that Russell is denying that there is formal correspondence between these facts and reality. The idea, I think, is that molecular propositions can be decomposed into ontologically independent components, which are atomic facts. Atomic facts cannot be thus divided, and, therefore, they are ultimate complexities and not logical compounds. Nevertheless, if there are identity facts, they should be atomic facts. The discussion in the paper concerns these only.

5 See e.g. the entry about Identity in The Stanford, by Noonan and Curtis (2018).

6 It also seems to me that Kripke’s version of the puzzle about belief is a form of telling why the puzzle about identity (about discoveries of identity) cannot be solved in terms of beliefs about the entity in question. That is, it is another form of denying that proper names stand for descriptions or modes of presentation: their cognitive value, if any, does not explain their contribution to the proposition.

7 I am following Kripke’s reading (1971/2011, 6) of Quine, and of Marcus/Barcan. For a more precise and developed analysis of this answer, and the next, see my García-Encinas (2017); the present paper attempts to develop some of the ideas there but within the Russellian framework of facts in PLA.

8 For a recent summary of the advantages and difficulties of metalinguistic views on proper names, see Gray (2018).

9 I will not attempt to defend the necessity of identity here. However, it is my purpose to show that the acceptance that identity is necessary does not imply that it is contradictory to deny true identity statements. In a sense, this could count as an indirect argument for the defence of its necessity, as denial of contradiction has traditionally been used against its necessity.

10 This difficulty also reveals why imagination cannot be the source of modal metaphysical knowledge. It is not only that the roads of imagination would make metaphysical knowledge ultimately private, but that in its dealings imagination will use contingent descriptions or representations of things (I have considered this problem more carefully in García-Encinas 2015).

11 Thanks to an anonymous referee for Inquiry for posing this difficulty.

12 On a parallel case, where Jane is unaware that two apples are the same one and thinks of ‘one of them’ that it is wholesome at the time she denies that ‘the other’ is wholesome, Boghossian writes that: ‘Two things are true of Jane in this case. First, her de re beliefs about the apple logically contradict each other: the (Millian) proposition subtended by the one is p and the one subtended by the other is not-p. And, second, she cannot recover from this condition on an a priori basis; to discover that the beliefs contradict each other she would have to learn an empirical fact, namely, that the apple involved in the first thought is identical to the apple involved in the second. That the two thoughts logically contradict each other is not introspectively accessible to her.’ (Boghossian 1994, 41. My italics.)

13 Kripke (1979, 146) also writes that is clear that Pierre ‘lacks information, not logical acumen. He cannot be convicted of inconsistency.’ One anonymous referee for Inquiry insists that Kripke’s remark can be taken to mean that while Pierre is in fact entertaining logically contradictory beliefs, he is not in an epistemic situation which allows him to see that this is so. Thus, the implication is not that Pierre’s denial of an identity statement isn’t contradictory, but that he does not see (and cannot see) that it is contradictory. But, again, if the negation that London is Londres is logically self-contradictory, then that London is Londres must be a logical truth, which it is not.

14 In ‘On Denoting’ Russell (1905) writes: ‘If a is identical with b, whatever is true of one is true of the other, and either may be substituted for the other in any proposition without altering the truth of falsehood of that proposition.’ (485) This, however, does not imply that identity is tautological for this reason. I have not really found any place where Russell accounts for the tautological character of identity in terms of substitution salva veritate.

15 See Muehlmann’s (1969) nice discussion for the thesis that Russell did hold that identity and diversity could be instances of properties in LII, thus making LII necessarily true and, thus, according to Russell, an axiom of Logic (LII would be necessarily true because nothing would fail to fulfil it. The difficulty is that one could ask, once more, why would nothing fail to. And to answer why, you would need to presuppose LII again).

16 See a recent work by Shumener (2017) on the difficulties of grounding identity on qualitative indiscernibility. Her paper also includes a nice discussion on the im/possibility of grounding identity on existence.

17 In the Preface to Naming and Necessity Kripke (1980) writes that (i) that identical objects are necessarily identical, and (ii) that true identity statements between rigid designators are necessary, and self-evident thesis; and (ii) roughly follows from (i) using substitution of rigid designators for universal quantifiers (4). Also in the proof, in (1971/2011), that if a is b then a is necessarily b, the thesis that every entity is necessarily identical to itself is an explicit premise.

18 This does not mean that Russell identified tautologies with uninformative statements. Logical propositions such as ‘If p implies q and q implies r, then p implies r’ are also ‘in some sense or other like a tautology,’ and a priori (PLA, 76). But it is not clear that these propositions are uninformative. However it might be, Russell did believe that any uninformative statement is a tautology.

Additional information

Funding

This work was supported by the Spanish Ministry of Science and Innovation [grant number PID2019-108870GB-I00].