Abstract
A deep-rooted assumption concerning indiscriminability between visual appearances is the following: two things are indiscriminable in look to an observer at a particular instant of time if and only if they look the same to that observer at that particular instant of time. I argue that this deep-rooted assumption may be false. The argument is in two steps. First, it is argued that indiscriminability between appearances may be non-transitive. Then it is argued that non-transitive indiscriminability between appearances is inconsistent with the deep-rooted assumption. It is therefore deduced that the deep-rooted assumption may be false.
Finally, I argue that if the deep-rooted assumption may be false, then one of the premises of the phenomenal sorites paradox may be false too. And this leaves open the possibility that vague phenomenal predicates are coherent and that phenomenal properties are ontologically legitimate.
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Notes
- 1.
From now on, when I write that objects are indiscriminable, I mean that they are indiscriminable in look, and when I write about indiscriminability, I mean to consider indiscriminability between visual appearances.
- 2.
It is useful to distinguish any objection to (IND) from Goodman’s (1951) claim that indiscriminability between qualia (“matching qualia” in his terms) is not identity between qualia. Goodman’s claim concerns qualia and a quale is defined as a “presented quality” or as a “quality of a presentation of a thing” (p. 96); a quale is therefore an abstract entity. (IND) concerns instead the appearances of things acknowledged by an observer at a particular time, i.e., instantiated phenomenal properties. Other philosophers – following Goodman – argued for the difference between indiscriminability and identity of abstract phenomenal qualities; see, for example, Dummett (1975), Wright (1975), Peacocke (1981, p. 125), Parikh (1983), and Linsky (1984).
- 3.
Mills (2002) seems to argue against the left to right implication in (IND), that is, he claims “that pairwise indistinguishability does not entail sameness of phenomenal appearances” (p. 392). He considers two line drawings with seven small differences and claims that “even if I never succeed in distinguishing the two drawings – even if they are pairwise indistinguishable – still it is perfectly intelligible to suppose that they look different to me” (p. 392). I believe that even if I never succeed in distinguishing the two drawings, they may still be distinguishable to me (it may even be physically possible for me to distinguish the two drawings). In my opinion, Mills’ observation shows that actually non-distinguished drawings may look different to an observer, but does not support the stronger thesis that indistinguishable drawings may look different to an observer (i.e., he does not succeed in giving a counterexample to the left to right implication in (IND)).
- 4.
I am indebted to Alfredo Tomasetta for helping me to stress the modal character of my argument.
- 5.
An interesting question is: what is it like to have such an experience? I suppose that the observer will see a difference in shade, for example, at the border between slice 1 and slice 3 but does not acknowledge any other difference in shade for the rest of the figure.
- 6.
As a referee observed, the reader may wonder why I do not assume (DIFF) to be true. In order to follow my reasoning, reconsider the previously presented case of the two indiscriminable vases, one porcelain and the other plastic. In such a case, the difference between the physical bases of the look of the two vases is certainly greater than any reasonable threshold, but they are indiscriminable anyway. Therefore, it is not always true that if the difference between the physical bases of certain looks is greater than a certain threshold, the looks are discriminable. Having in mind examples like this one, I maintain that (DIFF) is not always granted to be true, but it is still possible that (DIFF) holds at least in a restricted range of cases, analogous to the previously mentioned case of the black sticks on a white background.
- 7.
I am assuming bivalent classical logic in this work.
- 8.
The adopted rules are universal elimination (∀E), modus ponens (MP), conjunction introduction (∧I), and existential introduction (∃I).
- 9.
It is very difficult for me to retrace the history of this type of argument as requested by an anonymous referee. I think that something similar to this argument inspired Goodman’s (1951) distinction between indiscriminability (“matching” in his terms) and identity of qualia. Analogies with my argument may be found in arguments or reflections in Dummett (1975), Wright (1975), and Linsky (1984). As will be clear in Sect. 6.3, when writing up this argument I particularly had in mind specific arguments in Fara (2001), Chuard (2010), and Keefe (2011).
- 10.
As a referee observed, the reader may wonder why I assume (DIFF*–CONV) to be possibly true in a restricted range of situations and not simply true. As will be clear in Sect. 6.3, Fara (2001) argued that an assumption similar to (DIFF*–CONV) is not true. But her argument does not exclude that (DIFF*–CONV) may be true at least in a restricted range of cases. See also footnote 18.
- 11.
Some philosophers have offered reasons for non-transitive indiscriminability which are not my present concern because they are not similar to the arguments I have presented here. Among such lines of reasoning, it is worth mentioning an argument from phenomenal continua presented by Wright (1975) and discussed by Fara (2001) and an argument from inexact representation offered by Hellie (2005) and discussed by Pelling (2008).
- 12.
Fara (2001), p. 917, note 15 – emphasis in the original. It may be observed that the assumption proposed by Fara presupposes that the physical bases which elicit the appearances of an object in an interval are circumscribed to the object itself and do not extend to the environment in which it is positioned. This assumption does not seem to be justified. I am indebted to Andrea Bonomi and Clotilde Calabi for this interesting objection.
- 13.
Fara (2001), p. 918.
- 14.
Fara (2001), p. 919.
- 15.
Keefe (2011), p. 335, emphasis in the original.
- 16.
Chuard (2010), p. 180, my emphasis.
- 17.
Chuard (2010), p. 179, note 32.
- 18.
It may be not clear why I assume (DIFF*–CONV) to be possible in a restricted range of circumstances. The reason has to do with the fact that it is quite plausible to assume that (DIFF*–CONV) is not always true in the actual world: there may be stimuli, characterized by no difference in the physical bases, yet producing appearances distinguishable to an observer, as Fara (2001) observes (see quotation referred to in footnote 14). Notwithstanding this, it may be the case that at least in certain circumstances (DIFF*–CONV) holds. I am not arguing that (DIFF*–CONV) is true in a restricted range of cases, I am just maintaining that it is metaphysically possible that (DIFF*–CONV) is true in a restricted range of cases, without excluding that this restricted metaphysical possibility should actually occur. And the metaphysical possibility that (DIFF*–CONV) is true in a restricted range of cases is itself sufficient to make it possible that indiscriminability is non-transitive.
- 19.
A marginal difference between my argument and any of the others considered is the following: in the antecedent of the crucial implication, the others assume that the difference between the physical bases of two perceptual appearances is below a certain threshold, while in the antecedent of (DIFF*–CONV), I assume that the difference is either below or equal to the threshold. The reason for my assumption is that I want to stress the fact that (DIFF*–CONV) is the converse of (DIFF*). Nothing relevant for my claim depends on this difference between my presentation of the argument and the others.
- 20.
I am indebted to Sandro Zucchi for giving some helpful advice concerning this schematic translation.
- 21.
Moreover, in order to introduce the argument, some new rules, besides the ones already adopted, should be introduced. They are existential elimination (∃E) and conjunction elimination (∧E).
- 22.
- 23.
By “phenomenal predicates’ coherence,” I mean that the rules governing the use of phenomenal predicates allow such uses to be coherent. This is the “governing view” on the coherence of vague predicates according to Wright (1975, pp. 326–27). I use the shorter expression “phenomenal predicates’ coherence” for the sake of simplicity and because it is now quite widespread.
- 24.
- 25.
- 26.
- 27.
This is argued by a supporter of a semantic theory of vagueness like Fine (1975).
- 28.
- 29.
See, for example, Koons (1994) who distinguishes between “observational indistinguishability” and “absolute indistinguishability,” Mills (2002) who argues that “pairwise indistinguishability does not generally entail that two things ‘look the same’” (p. 392), Hellie (2005) who argues that “there can be indiscriminability without sameness of representation” (p. 485), and Pelling (2008) who offers his argument for non-transitivity of perceptual indiscriminability. See also Chuard (2010) and Keefe (2011) for arguing in favor of non-transitive indiscriminability.
- 30.
- 31.
In footnote 11 some different argumentative strategies in favor of (and against) non-transitive indiscriminability are mentioned.
- 32.
The argument assumes rules of logical equivalence between formulas with different connectives, a logical consequence demonstrated in footnote 33, biconditional elimination (↔E), and associativity of conjunction (∧ associativity).
- 33.
33Proof by contradiction that 3 is a logical consequence of 2:
1
¬∀x∀y (Ix, y → ∀X (Xx → Xy))
1
Assumption (2)
2
∀x∀y∀X (Ix, y → (Xx → Xy))
2
Assumption
3
∃x∃y¬(Ix, y → ∀X (Xx → Xy))
1
∃/∀ log. eq. from 1
4
¬(Is1,s2 → ∀X (Xs1 → Xs2))
4
Assumption
5
(Is1,s2 ∧ ¬∀X (Xs1 → Xs2))
4
→/∧ log. eq. from 4
6
Is1,s2
4
∧E from 5
7
¬∀X (Xs1 → Xs2)
4
∧E from 5
8
∃X¬(Xs1 → Xs2)
4
∃/∀ log. eq. from 7
9
¬(Ps1 → Ps2)
9
Assumption
10
(Is1,s2 → (Ps1 → Ps2))
2
∀E from 2
11
Ps1 → Ps2
2, 4
MP from 6 and 10
12
Contradiction
2, 4, 9
From 9 and 11
13
Contradiction
2, 4
∃E from 8 and [9–12]
14
Contradiction
1, 2
∃E from 3 and [4–13]
15
¬∀x∀y∀X (Ix,y → (Xx → Xy))
1
¬I from 2 and 14
I am indebted to Andrea Bonomi for highlighting this logical consequence to me and to Sandro Zucchi for helping me with this proof.
- 34.
This work improved greatly after the exchanges I had with Ken Akiba, an anonymous referee, Sandro Zucchi, Clotilde Calabi, Andrea Bonomi, Alfredo Tomasetta, Luca Barlassina, Giuliano Torrengo, Aldo Frigerio, and Bianca Cepollaro. I thank them all for the time they spent discussing it with me and for their helpful advice.
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Paganini, E. (2014). Indiscriminable but Not Identical Looks: Non-vague Phenomenal Predicates and Phenomenal Properties. In: Akiba, K., Abasnezhad, A. (eds) Vague Objects and Vague Identity. Logic, Epistemology, and the Unity of Science, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7978-5_6
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