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Perceptual Indiscriminability: In Defence of Wright's Proof
Abstract
A series of unnoticeably small changes in an observable property may add up to a noticeable change. Crispin Wright has used
this fact to prove that perceptual indiscriminability is a non‐transitive relation. Delia Graff has recently argued that there
is a ‘tension’ between Wright's assumptions. But Graff has misunderstood one of these, that ‘phenomenal continua’ are possible;
and the other, that our powers of discrimination are finite, is sound. If the first assumption is properly understood, it
is not in tension with but is actually implied by the second, given a plausible physical assumption.
... Williamson's methods can be somewhat improved upon by taking a quantitative point of view (De Clercq and Horsten 2005).⁹ Our task again is to approximate the indiscriminability graph as closely as possible by a transitive graph. ...
... Taking a quantitative view of the matter, we consider those transitive graphs that result from G by cutting and/or pasting a minimum number of edges from/in G. Equivalence ⁹ The method that we are about to discuss can be fairly straightforwardly extended to infinite domains. See again De Clercq and Horsten (2005). approximations in this sense are quantitative approximations. ...
This chapter investigates the connection between indiscriminability with respect to colour, and the concept of a colour shade. A crucial question is whether indiscriminability is a transitive relation. If it is, then a simple identity criterion for colour shades can be straightforwardly expressed in terms of indiscriminability. If it is not, then we are driven to a less immediate identity criterion for colour shades, which is however still intimately linked to indiscriminability. In this situation, there is a sense in which the concept of a colour shade must be taken to be a low-level theoretical notion.
... The transitivity or more more often the lack of transitivity of αδ ≈ have been studied extensively and proven or postulated in many human experiences, [Goo51,Wri75,Wil90,Gra01,DCH04,Hel05,Pel08,Far10,Raf12,Ars12,BRWS23]. ...
Many machine learning (ML) classifiers are claimed to outperform humans, but they still make mistakes that humans do not. The most notorious examples of such mistakes are adversarial visual metamers. This paper aims to define and investigate the phenomenon of adversarial Doppelgangers (AD), which includes adversarial visual metamers, and to compare the performance and robustness of ML classifiers to human performance. We find that AD are inputs that are close to each other with respect to a perceptual metric defined in this paper. AD are qualitatively different from the usual adversarial examples. The vast majority of classifiers are vulnerable to AD and robustness-accuracy trade-offs may not improve them. Some classification problems may not admit any AD robust classifiers because the underlying classes are ambiguous. We provide criteria that can be used to determine whether a classification problem is well defined or not; describe the structure and attributes of an AD-robust classifier; introduce and explore the notions of conceptual entropy and regions of conceptual ambiguity for classifiers that are vulnerable to AD attacks, along with methods to bound the AD fooling rate of an attack. We define the notion of classifiers that exhibit hypersensitive behavior, that is, classifiers whose only mistakes are adversarial Doppelgangers. Improving the AD robustness of hyper-sensitive classifiers is equivalent to improving accuracy. We identify conditions guaranteeing that all classifiers with sufficiently high accuracy are hyper-sensitive. Our findings are aimed at significant improvements in the reliability and security of machine learning systems.
... The non-transitivity of our phenomenal notion of indiscriminability is the center of (Williamson 1990). For a more recent defense of this position, see(De Clercq and Horsten 2004).Content courtesy of Springer Nature, terms of use apply. Rights reserved. ...
Recent years have witnessed a revival of interest in the method of explication as a procedure for conceptual engineering in philosophy and in science. In the philosophical literature, there has been a lively debate about the different desiderata that a good explicatum has to satisfy. In comparison, the goal of explicating the concept of explication itself has not been central to the philosophical debate. The main aim of this work is to suggest a way of filling this gap by explicating ‘explication’ by means of conceptual spaces theory. Specifically, I show how different, strictly-conceptual readings of explication desiderata can be made precise as geometrical or topological constraints over the conceptual spaces related to the explicandum and the explicatum. Moreover, I show also how the richness of the geometrical representation of concepts in conceptual spaces theory allows us to achieve more fine-grained readings of explication desiderata, thereby overcoming some alleged limitations of explication as a procedure of conceptual engineering.
Famously, the Church–Fitch paradox of knowability is a deductive argument from the thesis that all truths are knowable to the conclusion that all truths are known. In this argument, knowability is analyzed in terms of having the possibility to know. Several philosophers have objected to this analysis, because it turns knowability into a nonfactive notion. In addition, they claim that, if the knowability thesis is reformulated with the help of factive concepts of knowability, then omniscience can be avoided. In this article we will look closer at two proposals along these lines (Edgington in Mind 94(376):557–568, 1985; Fuhrmann in Synthese 191(7):1627–1648, 2014a), because there are formal models available for each. It will be argued that, even though the problem of omniscience can be averted, the problem of possible or potential omniscience cannot: there is an accessible state at which all (actual) truths are known. Furthermore, it will be argued that possible or potential omniscience is a price that is too high to pay. Others who have proposed to solve the paradox with the help of a factive concept of knowability should take note (Fara in Synthese 173(1):53–73, 2010; Spencer in Mind 126(502):466–497, 2017).
The non-transitivity of the relation looks the same as has been used to argue that the relation has the same phenomenal character as is non-transitive—a result that jeopardizes certain theories of consciousness. In this paper, I argue against this conclusion while granting the premise by dissociating lookings and phenomenology; an idea that some might find counter-intuitive. However, such an intuition is left unsupported once phenomenology and cognitive access are distinguished from each other; a distinction that is conceptually and empirically grounded.
The debate about cinematic motion revolves around the question of whether the movement of cinematic images is real. That the movement we perceive in film should be construed as the movement of images is taken for granted. But this is a mistake. There is no reason to suppose that cinematic images of moving objects are themselves perceived to be moving. All that is necessary is to perceive these images as continuously changing images of one and the same object.
It is common among philosophers who take an interest in the phenomenon of vagueness in natural language not merely to acknowledge higher-order vagueness but to take its existence as a basic datum; so that views that lack the resources to account for it, or that put obstacles in the way, are regarded as deficient just on that score. This chapter aims to loosen the hold of this deeply misconceived idea. Higher-order vagueness is no basic datum but an illusion, fostered by misunderstandings of the nature of ordinary (if you will, 'first-order') vagueness itself. To see through the illusion is to take a step that is prerequisite for a correct understanding of vagueness, and for any satisfying dissolution of its attendant paradoxes.
Since Nelson Goodman 19513.
Goodman , N. 1951. The Structure of Appearance, Cambridge, MA: Harvard University Press. View all references, the assumption that phenomenal indiscriminability is non-transitive is taken generally for granted. Moreover, this assumption was used (by Goodman 19513.
Goodman , N. 1951. The Structure of Appearance, Cambridge, MA: Harvard University Press. View all references, Travis 19859.
Travis , C. 1985. Vagueness, Observation and Sorites. Mind, 94: 345–366. View all references, Dummett 19752.
Dummett , M. 1975. Wang's Paradox. Synthese, 30: 301–324. [CrossRef]View all references and others) to argue against the existence or coherence of subjective and/or observational properties. Recently, however, the assumption has been questioned [Fara 20015.
Fara , Delia Graff . 2001. Phenomenal Continua and the Sorites. Mind, 110: 1–29. View all references] and I agree with Fara that the assumption is much more problematic than was thought, partly because it is not clear what is meant by the relation of phenomenal indiscriminability, and partly because it is not clear how to interpret ideas such as continuous change, and the limitations of our power of perceptual discrimination.In this paper I will bypass the question of the transitivity of phenomenal indiscriminability. I will use only the assumption about the existence (or even the possibility of existence) of a phenomenal sorites. This assumption is less controversial, and accepted (at least the version I will use) by opponents and defenders of transitivity alike. I will argue that the incoherence of ‘red’ (as response-dependent or purely observational) can be derived without committing ourselves to a view on the question of transitivity, and I will use this incoherence, to argue against the account of ‘red’ as a response-dependent concept.
It is obvious both that some changes are too small for us to perceive and that we can perceive constant motion. Yet according to Fara, these two facts are in conflict, and one must be rejected. I show that conflict arises only from accepting a ‘zoëtrope conception’ of change experience, according to which change experience is analysed in terms of a series of very short-lived sensory atoms, each lacking in dynamic content. On pain of denying the phenomenologically obvious, we must reject the zoëtrope conception. I offer an alternative account, according to which the dynamic content of our experience at short timescales is metaphysically dependent on the content of experience over longer timescales. Moreover, at short timescales such content is purely determinable.
Fallibilists about looks deny that the relation of looking the same as is non-transitive. Regarding familiar examples of coloured patches suggesting that such a relation is non-transitive, they
argue that, in fact, indiscriminable adjacent patches may well look different, despite their perceptual indiscriminability:
it’s just that we cannot notice the relevant differences in the chromatic appearances of such patches. In this paper, I present
an argument that fallibilism about looks requires commitment to an empirically false consequence. To succeed in deflecting
putative cases of non-transitivity, fallibilists would have to claim that there can’t be any perceptual limitations of any
kind on human chromatic discrimination. But there are good reasons to think such limitations exist.
KeywordsChromatic appearances-Looks-Non-transitivity-Phenomenal sorites arguments-Perceptual limitations-Veridical experience-Fallibilism-Colour-Colour perception-Perceptual discrimination
I defend, to a certain extent, the traditional view that perceptual indiscriminability is non-transitive. The argument proceeds
by considering important recent work by Benj Hellie: Hellie argues that colour perception represents ‘inexactly’, and that
this results in violations of the transitivity of colour indiscriminability. I show that Hellie’s argument remains inconclusive,
since he does not demonstrate conclusively that colour perception really does represent inexactly. My own argument for the
non-transitivity of perceptual indiscriminability uses inexactness instead as one horn of a dilemma: the key idea is that
there is a class of perceptual experiences which might plausibly be supposed either to represent inexactly or to represent
exactly—but which demonstrate the non-transitivity of perceptual indiscriminability either way.
We are no less directly acquainted with the temporal structure of the world than with its spatial structure. We hear one word succeeding another; feel two taps as simultaneous; or see the glow of a firework persisting, before it finally fizzles and fades. However, time is special, for we not only experience temporal properties; experience itself is structured in time.
Part One articulates a natural framework for thinking about experience in time. I claim (i) that experience in its experiential aspect has a realistically conceived temporal structure; (ii) that our judgements about that structure always go via judgements about the temporal structure of the apparent objects of perception; and (iii) that a subject undergoing perceptual experience of a given experiential kind is always in a position to know that they are undergoing experience of that kind simply in virtue of so undergoing. On this basis, I argue that the temporal structure of experience cannot systematically come apart from the temporal structure of its objects.
Part Two treats four puzzles relating to our experience of time. The first is Dennett’s notorious discussion of masking and apparent motion phenomena. The second is the traditional debate regarding the very possibility of perceiving temporal properties. The third is Fara’s recent contention that standard explanations of our experience of slow changes preclude us from perceiving constant motion. A common reaction to these three puzzles is to reject some element of the naïve picture of temporal experience developed in Part One. I resolve them instead by showing how each arises from mistakenly thinking that experience is homoeomerous down to very short durations or instants. That is, thinking that we can analyse experience into a series of independent short slices, and explain the nature of the stream of consciousness in terms of those slices. The final chapter discusses a fourth puzzle about visual motion perception which I diagnose as driven by a rather different, but equally misguided way of thinking about vision.
I argue that, contrary to widespread philosophical opinion, phenomenal indiscriminability is transitive. For if it were not transitive, we would be precluded from accepting the truisms that if two things look the same then the way they look is the same and that if two things look the same then if one looks red, so does the other. Nevertheless, it has seemed obvious to many philosopher (e.g., Goodman, Armstrong and Dummett) that phenomenal indiscriminability is not transitive; and, moreover, that this non-transitivity is straightforwardly revealed to us in experience. I show this thought to be wrong. All inference from the character of our experience to the non-transitivity of indiscriminability involve either a misunderstanding of continuity, a mistaken interpretation of the idea that we have limited powers of discrimination, or tendentious claims about what our our experience is really like; or such inferences are based on inadequately supported premisses, which though individually plausible are jointly implausible.