Analysis ‘Problem’ No. 19 Revisited: How to Look Yourself in the Mirror When There Are No Reflexive States of Affairs
The Analysis ‘Problem’ No. 19, reported on in the June issue of Analysis in 1983, is an intriguing and charming puzzle, which enables us to apply our view that there are no TM-irreducible reflexive relations:
(a) If I am looking at myself in a mirror I am directly facing, do I see myself looking at myself? (b) If so, do I also see myself looking at myself looking at myself—and so on?
Call (SLG) the ‘problem of self-mirroring’. I shall start by considering Haldane’s terse answer to this problem (1983
). The first question of (SLG), (a), in itself implies two separate questions:
Do I see myself in the mirror?
Do I see myself looking at myself?
Haldane answers (1) in the affirmative. This step might be doubted because of the idea that what one literally sees (when looking directly into a mirror) is not oneself, but a reflection of oneself. However, Haldane maintains that there is no question of one not literally seeing oneself, for, he claims (without argument), ‘[a] reflection of an object, or its appearance through various media, are not proxies for the thing itself. They are simply ways in which it is presented—what one might choose to call “object-environment composites”’ (ibid., p. 115).
To assess this claim would take us to epistemology far outside the scope of this work. But given the thesis that there are no TM-irreducible reflexive relations, the answer to (1) is ‘No’. For, I shall assume, an affirmative answer requires such relations (presumably, that seeing is one of them—or more precisely, that seeing is a ‘non-reflexive’ relation). More generally, because of this thesis, there is no TM-irreducible ‘reflection reflexivity’, to coin a phrase for the view that when an entity is, as we say, reflected in something, it instantiates a certain reflexive relation. Specifically, I deny that one can literally see oneself in a mirror. That is, I am denying that a proposition like ‘I see myself in a mirror’ has as (part of its) truthmaker the state of affairs S(I) or S(myself), where S = seeing (which, it may be noted, does not lessen its pragmatic value).
As to (2), Haldane also answers this in the affirmative. True, he says, unlike a thinker who is within the range of his own thought, a perceiver normally is not within his own range of perception: one normally cannot see oneself. But, he claims, cases with reflective surfaces provide the exception. This reasoning seems plausible, given Haldane’s acceptance of reflection reflexivity.
We come now to the second part, (b), of (SLG):
Do I see myself looking at myself looking at myself, etc.?
Haldane answers ‘Yes’ to this question too. The reason is, he thinks, that ‘I see myself looking at myself’ entails
‘I see myself looking at myself looking at myself, etc.’ Call this regress the ‘mirror regress’. However, he does not think the regress is vicious:
Just as the regress of entailments from an event’s being ‘present’ to its being ‘present in the present’ etc., does not require an infinity of times; neither does the truth of the entailed ‘looking’ sentences imply an infinity of acts and objects. Rather these iterations logically reduplicate those items actually involved: my seeing, and its object—myself looking at myself. (p. 116)
Thus, he thinks that, as he puts it, it is a ‘benign regress’, it is merely ‘logical’ (by which he seems to mean that each level is logically equivalent to any other level).
A similar conclusion is reached by Garrett (1983), in an equally terse answer to the problem of self-mirroring. In a diagnosis that is only terminologically different from Haldane’s, Garrett maintains that the regress is non-vicious, on the grounds that ‘the truth-value of every statement in the regress is determined simultaneously and the truth-conditions of each statement in the regressive series are identical’ (ibid., p. 117). Furthermore, like Haldane’s, Garrett’s answers to (1), (2), and (3) are affirmative. His main argument adds little of importance to that of Haldane’s, but one of his points is of particular interest to us. He formulates a version of the original problem of self-mirroring, which occurs even if one shares my view that strictly speaking one cannot see oneself in a mirror, only a reflection of oneself (i.e. if one rejects reflection reflexivity):
(a′) If I am looking at a reflection of myself, do I see a reflection of myself-looking-at-a-reflection-of-myself? (b′) If so, do I also see a reflection of myself-looking-at-reflection-of-myself-looking-at-a-reflection-of-myself—and so on?
Garrett maintains that this version of the problem of self-mirroring is just as serious as the original one. And he is prima facie right. Specifically, the regress of (b′), call it the reflection regress, is no less puzzling than the one of (b) in (SLG). (Garrett himself, however, nonetheless endorses the original problem, and since, as mentioned, his answer to (1) is ‘Yes’, he is also committed to reflection reflexivity.)
So (SLG′) is the problem I accept. How does state of affairs ontology deal with it? To answer this, let us first say that the initial reflection r is identical to the state of affairs R(I, m), where R = the relation (or ‘relation’) of ‘self-reflecting’, which holds between me and a reflection of myself when I see this reflection (understanding of course that the relevant reflection is a mirror reflection); ‘I’ = the first personal pronoun; and m = the mirror.11 The situation of self-mirroring and the reflection regress are now as follows:
S(I, r) (I see a reflection of myself),
S(I, r′) (I see a reflection of myself-looking-at-a-reflection-of-myself),
S(I, r′′) (I see a reflection of myself-looking-at-reflection-of-myself-looking- at- a-reflection-of-myself), and so on ad infinitum,
where S = seeing, r = R(I, m), r′ = R′(I, r), r′′ = R′′(I, r′), and so on ad infinitum; and R, R′, R′′, etc. is the corresponding series of relations of ‘self-reflecting’. By substitution, the series of reflections – r, r′, r′′, etc.—is in turn identical to the following series: r = R(I, m), r′ = R′[I, R(I, m)], r′′ = R′′[I, R′[I, R(I, m)]], and so on ad infinitum.
Is this regress vicious? It suffices to be brief here, since however vital the ability to look oneself in the mirror may be nowadays, the regress does not seem to be ontologically that important. Briefly, if an infinite regress is vicious, it is because it fails explanatorily, that is, if the explanation of any level n requires us to ascend to level n + 1 (Sect. 10.5) . I shall assume that involved notion of explanation is, roughly speaking, truthmaking: a truthmaker explains what it makes true. The reflection regress is thus not vicious, since the state of affairs at the first level, S(I, r), where S = seeing, and r = R(I, m), makes true and hence explains the first-level proposition ‘I see a reflection of myself.’ By the same token, since this proposition entails the propositions of the succeeding levels, ‘I see a reflection of myself-looking-at-a-reflection-of-myself’—‘I see a reflection of myself-looking-at-reflection-of-myself-looking-at-a-reflection-of-myself’, etc.—it makes true and hence explains them as well. For the same reason, by a now familiar argument, each putative state of affairs above level (1′) is only an apparent state of affairs (or equivalently, R, R′, R′′, etc. is a series of TM-reducible relations) In short, I maintain that the reflection regress is both (1) benign and (2) economically unproblematic.