Abstract
Williamson (2007) argues that philosophers acquire no philosophical knowledge at all by semantic understanding alone. He further argues that the most important method used for achieving philosophical knowledge is through the ‘imaginative simulation’ process some of whose products are neither a priori nor a posteriori but ‘armchair’ knowledge. We argue in this paper that the way Williamson argues against the claim that semantic understanding alone is enough to achieve philosophical knowledge can be paralleled by an exactly similar argument against his view that imaginative simulation alone is enough to achieve philosophical knowledge. Because of the parallel argument, we conclude that Williamson’s argument against semantic understanding shows at most that it is fallible, if used alone, as a method for achieving philosophical knowledge. We also point out a blind spot in Williamson’s argument for his epistemology of modality: a reliable method for achieving knowledge about subjunctive conditionals is not necessarily a reliable method for achieving knowledge about modal statements even if every modal statement is logically equivalent to some subjunctive conditional. Finally, we argue that, with a suitable understanding of ‘understanding the meaning,’ Williamson’s armchair knowledge is nothing but the a priori knowledge of those good-old-days philosophy.
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Notes
By ‘philosophical methodology’, Williamson means philosophy methodology of analytic philosophy, especially the analytic philosophy since the late nineteenth century.
In the book The Philosophy of Philosophy, Williamson’s elaborated discussion primarily consists of two parts, the linguistic part and the conceptual part. Given the great similarity of his discussions between the two, we will confine our discussion to the linguistic part.
Williamson, ibid., pp. 10–11.
Williamson, ibid., p. 77: ‘…what is epistemically available simply on the basis of linguistic and conceptual competence? To a first approximation, the answer is nothing.’
Williamson, ibid., p. 134.
See Williamson, ibid., p. 3. This also explains why Williamson thinks that the methodological differences between philosophy and other sciences are less deep than is often supposed. Williamson emphasizes, later in his (Williamson, 2016), that the philosophical method is abduction. However, he does not further explain whether abduction is different from the philosophical method mentioned in The Philosophy of Philosophy. To avoid deviation from the issue discussed in this paper, we will not discuss the differences between the two here.
You may also ask whether we actually have philosophical knowledge so circumscribed. Some philosophers, such as Williamson (2007) and Bealer (1996), believe that we do have such knowledge, while others, such as Beebee (2018) and Kornblith (n.d.), do not think so. Fortunately, this further question is irrelevant to our discussion below. If you disagree with us about this relevancy, perhaps because you think that this paper assumes, while you object, that we do have philosophical knowledge, we ask you kindly to prefix every conclusion we will assert in this paper with the phrase ‘If we have philosophical knowledge, ….’
Thus, Williamson (2007, p. 134): ‘Philosophers characteristically ask not just whether things are some way but whether they could have been otherwise. What could have been otherwise is metaphysically contingent; what could not is metaphysically necessary. We have some knowledge of such matters.’
We borrow the term ‘remote’ from Dretske (1981), by which we mean (and we believe that he means the same too) a non-actual, very unlikely (and even causally impossible) but still metaphysically possible event or state-of-affairs. It is certainly a vague term as used here, but its exact meaning is not crucial for the purpose of this paper. Readers can also take a remote possibility to be a possibility of ‘an uncommon type’, a phrase that we use in ‘The Reliability of Imaginative Simulation’ section.
Traditionally, analytic truths are in contrast with synthetic truths, and these two categories are supposed to jointly exhaust all truths. All analytic truths (e.g., ‘All bachelors are unmarried’) are traditionally regarded as true purely in virtue of meanings, while all synthetic truths (such as ‘Tom is a bachelor’) are traditionally regarded as true partly in virtue of meanings and partly in virtue of facts. Williamson (2007, “chapter 3”) actually opposes to this way of making the distinction because he thinks that no sentences or statements can be true purely in virtue of meanings. However, unlike Quine, he does not think that no distinction can be made among these truths. In fact, Williamson has a different triple distinction among truths. (See the ‘Modal Knowledge and Imaginative Simulation’ section for further details.)
Williamson, ibid., “chapter 4.”
Williamson, ibid., p. 85. V is intended simply to be an easy case showing you how a linguistically competent person can understand the meaning of a truth without believing or knowing it. It is, therefore, not important that V is NOT, or will NOT be, generally believed by modern analytic philosophers to be important for their business. That is to say, even if the knowledge about V will not be counted as, strictly speaking, a part of our philosophical knowledge at all, Williamson’s point still remains: all philosophically important analytic truths are just like V in this respect: they can be understood by a linguistically competent person without his or her believing or knowing it.
Aristotle may agree on (i).
What if V is ambiguous between V1 and V2, where the former implies the existence of a vixen while the latter does not? In this case, Williamson can disambiguate V as V2 and goes on his story? Yet, what if V is not ambiguous but means, unlike what most modern logicians and philosophers believe, exactly V1? In this case, Williamson can still go on his story without any trouble; for what is required for his argument is simply that Peter’s odd theory about the Association of Foxes leads him to disbelieve V (or V1).
A three-valued logician may agree on this.
Williamson, ibid., section 5.3.
Williamson, ibid., p. 97.
For example, you are not required to understand such trivial application conditions of the word ‘vixen’ as ‘The word “vixen” can be applied to x if and only if x is a female fox’, or ‘The word “vixen” can be applied to x if and only if x is a fox and has female sex organs’ or any other more complex application conditions in order to understand the word.
For the debates between Williams and Boghossian on related issues, also see Boghossian and Williamson (2020).
In contrast, Beebee (2018) and Kornblith (n.d.) argue that philosophical discussions and researches do not yield any substantial philosophical knowledge. Their view is now known as ‘philosophical skepticism.’ Although we are sympathetic to this view, we pretend to agree with Williamson in this section.
This is one of the two main questions in the field called ‘modal epistemology.’ For a general introduction to modal epistemology, see Vaidya (2015).
Williamson, ibid., p. 136.
These principles are (A) Necessarily (ϕ ⊃ φ) ⊃ (ϕ > φ), and (B) (ϕ > φ) ⊃ (Possibly ϕ ⊃ Possibly φ). In plain English, (A) says that if ‘ϕ’ necessarily implies ‘φ’, then the subjunctive conditional ‘φ > ϕ’ will be true, while (B) says that if the subjunctive conditional ‘φ > ϕ’ is true, then ‘φ’ will be possible giving that ‘ϕ’ is possible.
See Williamson, ibid., p. 162. But why are we equipped with such an evolutionary byproduct? Williamson’s answer to this question is that (see his (2016), pp. 113–123.) ‘Sometimes, for structural reasons, the easiest way for evolution to develop the capacity to do something useful involves developing the capacity to do something useless too.’
Williamson, ibid., p. 152-3. Williamson believes that this method is only typical but not necessary. But what are methods other than this one? On p. 165 of the book, Williamson says: ‘Some subjunctive conditionals look like paradigms of a priori knowability, for example (7) [i.e., “If twelve people had come to the party, more than eleven people would have come to the party”], whose consequent is a straightforward deductive consequence of its antecedent. Others look like paradigms of what can be known as a posteriori: for example, that if I had searched in my pocket five minutes ago, I would have found a coin. But these are easy cases.’ So, standard a priori and a posteriori methods can sometimes also be used to evaluate a subjunctive conditional.
The metaphor ‘offline’ here means that the initial input, i.e., the assumption, does not come from perception or testimony, but from the subject’s active assumption.
The following example may be helpful for understanding what an expectation-forming mechanism is: after we see (or visually imagine to see) a ball being thrown for 1/2 seconds, we will instinctively and involuntarily predict its trajectory and position after 1/2 seconds. Such prediction involves our built-in offline prediction- or expectation-forming mechanisms.
We may use part of our background knowledge to assist the development of a supposition. However, not all background knowledge can be used in this way; ‘which background knowledge can be used to develop a supposition and which cannot?’ This is the question about the cotenability theory of subjunctive conditionals that has been troubling Goodman. For more details, see Goodman (1955) and Wang (2007), pp. 109–145.
For the sake of being brief, we will only use the phrase ‘imaginative simulation’ in what follows, but it should be understood as an abbreviation of the longer phrase ‘either imaginative simulation alone or imaginative simulation plus semantic understanding.’ We emphasize the differences between these two arguments by italicizing the different parts within them.
Our argument here is different from Mallozzi (2021), though both try to cast doubt on imagination as a reliable pathway of philosophical knowledge. Mallozzi distinguishes two notions of imagination — sensory vs. belief-like imagination — and argues that sensory imagination is neither necessary nor sufficient for philosophical knowledge while belief-like imagination isn’t adequately disentangled from inference. Our argument does not appeal to such a distinction.
Notice that NV here, unlike the V before, is a modal claim. Again, NV is intended simply to be an easy case showing you how a person can understand the meaning of a modal truth and go through Williamson’s imaginative process without believing or knowing it. It is, therefore, not important that NV is NOT, or will NOT be, generally believed by modern analytic philosophers to be important for their business. That is to say, even if the knowledge about MV will not be counted as, strictly speaking, a part of our philosophical knowledge at all, our point still remains: all philosophically important modal truths are just like NV in this respect: they can be understood and well-tested by Williamson’s imaginative procedure by a person without his or her believing or knowing it.
This distinction between ‘being false’ (or the negation being true) and ‘being untrue’ (or not being true) is important for logicians who take a gappy three-valued logic, such as strong or weak K3, to be the right logic: if what Stephen assumes is that not-V is true or that V is false, he may, perhaps, still develop a contradiction from this assumption. So it might be objected that our example about Stephen crucially depends on a distinction hard to be grasped by most people. This objection, we think, actually has no force; however, in order to avoid this complication and possible objection, we can revise our current scenario a bit and turn it into the following one: Stephen assumes that not-V is true, yet he believes that the negation in the assumption of a reductio ad absurdum argument should be the so-called external negation rather than the more often seen ‘internal’ one. It is well-known (and Stephen knows very well) that, when an external negation prefixes a neither-true-nor-false sentence, the negative sentence thus formed as a whole will be true and hence won’t lead to a contradiction. Therefore, Stephen can still conclude that this assumption will not lead to a contradiction.
Note that in both Peter’s and Stephen’s examples we assume that they both understand V (and E) but conclude that V is not necessary after careful imaginative simulation. So what these two stories actually show is that simulation plus understanding-assent link does not necessarily hold. We think that the inference from this to the claim that the imaginative simulation-assent link does not necessarily hold either is obvious.
Williamson believes that the reason why the imaginative simulation is reliable but fallible is that the offline predictive mechanism (or expectation-forming mechanism, or offline folk physics) is reliable but fallible. However, Williamson does not provide any piece of empirical evidence to demonstrate that the offline predictive mechanism is reliable. But we will not probe deeper into this issue in this paper.
Williamson, ibid., p. 155.
See van Inwagen (1998), 69–70.
One reason for saying this is that mathematical modal claims and philosophical modal claims may be two essentially different kinds of modal claims. But this is a very controversial issue that cannot be discussed here.
According to van Inwagen (1998), the reason why philosophers lack knowledge of these statements is that, in order to have genuine knowledge about them, philosophers must be able to involve some details, such as the structural details of physics and the laws of physics, when conceiving them. However, such detailed knowledge is inaccessible to us at present; neither can these details be supplied by Williamson’s ‘offline predictive mechanisms.’ Van Inwagen therefore believes that, regardless of whether philosophers have modal mathematical knowledge or not, they lack sufficient justification for many important philosophical modal claims and therefore do not have knowledge about them.
So does van Inwagen (1998), see the previous footnote.
We would (and we think that Williamson should too) reject (Wa) if it is interpreted as saying that we cannot achieve any knowledge at all by the semantic understanding method alone. What is not denied by us is, however, the possibility that the sematic understanding method alone is not a reliable method for achieving philosophical knowledge.
Williamson undoubtedly believes that some modal knowledge is a posteriori. But does he also believe that some modal knowledge is a priori? According to footnote 25, we believe that Williamson will accept the possibility of a priori modal knowledge. However, we have also often heard other commentators of Williamson say that Williamson completely denies the possibility of a priori modal knowledge. We have not found any textual evidence to judge who is right and who is wrong about this. We can only briefly mention these two possible interpretations. Fortunately, this issue is only loosely connected to our discussion below.
Williamson, ibid., pp. 167–169.
Williamson does not tell us how we can ‘independently’ learn how to use these two words without understanding the precise conversion ratio between them. Perhaps the following imaginative example may help, or at least we hope. Your thumb happens to be about one inch wide, and your little finger happens to be about one centimeter wide. After using your thumb and little finger to measure various distances, you have learned, to a certain degree, how to judge the distance between objects by inches or centimeters.
See Brandom (2007).
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Acknowledgements
The first author Cong Wang is a lecturer from the College of Marxism, Henan Normal University, China, and the corresponding author Wen-fang Wang is a professor from the School of Philosophy and Social Development (Institute of Concept and Reasoning), Shandong University, Jinan, Shandong Province, China. For the publication of this paper, we would like to thank the support of the project ‘Shandong University International Scientific Cooperation Seed Fund’ (11090089395416) and the project Major Program of National Social Science Foundation of China (18ZDA031).
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Wang, C., Wang, Wf. On Williamson’s Armchair Philosophical Knowledge. SOPHIA 61, 737–756 (2022). https://doi.org/10.1007/s11841-022-00908-1
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DOI: https://doi.org/10.1007/s11841-022-00908-1