Elijah Chudnoff, University of Miami
Intuition defends a traditional Platonic view of intuition according to which it is a form of intellectual perception. Thinking through Richard Manning’s comments has helped me get clearer on some crucial dialectical issues. Thinking through Gene Witmer’s comments has helped me get clearer on some crucial metaphysical issues. I am most appreciative of their efforts.
The book has three parts. The first part is about the nature of intuition experiences. The main claim there is that they are like perceptual experiences in possessing presentational phenomenology. More on this below. Manning challenges how I support this claim. The second part is about the nature of intuitive justification. There I argue for a form of phenomenal dogmatism about intuition: having an intuition as of p prima facie immediately justifies you in believing that p and does so because of its phenomenology. On my view the phenomenology grounds the epistemology. In his comments Manning suggests a way for the epistemology to ground the phenomenology. I address his challenge and his suggestion in the first section below.
The third part of the book is about the nature of intuitive knowledge. The main claims there are that intuitions make us aware of abstract objects and it is because of this that they give us knowledge about abstract reality such as mathematics, metaphysics, and morality. I think the claim that intuitions make us aware of abstract objects is essential to the Platonic conception of intuitions as a form of intellectual perception. It has also proven to be the main stumbling block to acceptance of this conception. Witmer develops a challenge to my attempt to overcome this traditional difficulty. I address this challenge in the second section below.
Presentational Phenomenology
One of the concepts that figures prominently in Intuition is that of presentational phenomenology. To get a grip on it, consider the following picture:
In Case A you have a visual experience that represents that the dog has a middle part. But your visual experience does not make it seem as if you see the bit of reality that makes this proposition true—the middle is occluded by a bar. In Case B you have a visual experience that represents that the dog has a middle part. And your visual experience does make it seem as if you see the bit of reality that makes this proposition true—the middle is right there before you.
I use the term “presentational phenomenology” to mark this contrast. In Case A your experience lacks presentational phenomenology with respect to the proposition that the dog has a middle. In Case B your experience has presentational phenomenology with respect to the proposition that the dog has a middle. Put generally though a bit roughly: an experience has presentational phenomenology with respect to the proposition that p just in case it both represents that p and makes it seem as if you are aware of a chunk of reality in virtue of which p is true (i.e., a truth-maker for p).
One of the central claims in Intuition is that intuitions have presentational phenomenology with respect to some of their representational contents. Manning pursues a number of points in his comments, but I’m going to focus on two, both concerned with this central claim. The first point is that the introspective evidence I cite in favor of it is unconvincing. The second point is that my case might be better served by a “transcendental argument” a la John McDowell’s for the claim that perceptual experiences have conceptual contents—if only such an argument were available. 1
Contrast the following two claims:
Similarities and Differences: Intuitions are like perceptual experiences and unlike conscious beliefs.
Veridicality Conditions: Intuitions have veridicality conditions associated with my gloss on presentational phenomenology (e.g., some intuitions that p are veridical only if they make you aware of a truth-maker for p).
Manning focuses on Veridicality Conditions. He says that his own introspective endeavors fail to support it. I’m happy to concede that. This might not have been so clear in the book, but my considered argumentative strategy is this: use examples to stimulate introspective endeavors that support Similarities and Differences, use Similarities and Differences as a premise in an inference to the best explanation argument in support of Veridicality Conditions.
Compare and contrast the following cases:
Case C: You believe that √7 + √10 > √3 + √17 by calculation.
Case D: You believe that there is mail in your mailbox by testimony. Case E: You intuit that if a < 1, then 2 – 2a > 0.
Case F: You see that there is mail in your mailbox.
In Case C you work out that the inequality is true, but it is not as if the arithmetical relations in virtue of which it is true become transparent to you. In Case D you find out that there is mail in your mailbox, but it is not as if the mail is there in front of you. In Case E, not only you do work out that the conditional is true, but in doing so it is, or at least can be, as if the arithmetical relations in virtue of which it is true become transparent to you. You can “see” how a’s being less than 1 makes 2a less than 2 and so 2 – 2a greater than 0. In Case F you find out that there is mail in your mailbox, and it is as if the mail is there in front of you.
The differences between Case C and E and between Case D and F should be introspectively manifest. I also think that the similarity between Case C and Case D is introspectively manifest. There is a common sense of getting information without gaining direct access to the reality that makes the information true. Further, I think the similarity between Case E and Case F is introspectively manifest. There is a common sense of getting information and also gaining direct access to the reality that makes the information true: the arithmetical relations and the mail are ostensible objects of awareness.
What I’d like to highlight is the limited role of introspection. The role of introspection is to support Similarities and Differences. Maybe there is some direct introspective support for Veridicality Conditions. But if there is, it is rather weak and it is not what I would emphasize. What I would emphasize is the indirect support that accrues to Veridicality Condition as an explanation of the similarities and differences recorded in Similarities and Differences. So I think the introspective evidence in favor of the claim that intuitions have presentational phenomenology with respect to some of their contents is sufficient so long as you do not try to overwork it.
Toward the end of his comments Manning makes an intriguing suggestion. He considers my claim that intuitions have presentational phenomenology with respect to some of their contents and McDowell’s claim that perceptual experiences have conceptual contents. Both are surprising. But while I support my claim on the basis of introspection, McDowell supports his claim on the basis of a transcendental argument. Roughly: ordinary thought and practice accord perceptual experiences a rational role they couldn’t play unless they had conceptual contents; so we have some reason to think they do have conceptual contents. Manning thinks this is a dialectically more effective approach and that my project would be better served if I could develop a similar argument. I think I can.
Return to Case A and Case B above and consider the proposition that the dog has a middle part. Plausibly the experience you have in Case A only mediately justifies believing this proposition: it immediately justifies believing there is a dog—that is what you see—and you know dogs have middles. But the experience you have in Case B immediately justifies believing this proposition: it immediately justifies believing that there is a dog and also immediately justified believing that the dog has a middle part—both are seen. This suggests the following: one’s perception that p immediately justifies believing that p only if its veridicality conditions include both p and awareness of a truth-maker for p. 2
Now here is a bit of transcendental reasoning:
- (1) One’s perception that p immediately justifies believing that p only if its veridicality conditions include both p and awareness of a truth-maker for p. [See foregoing]
- (2) In some cases one’s perception that p immediately justifies believing that p. [Reflect on ordinary thought and practice]
- (3) In some cases one’s perception that p is veridical only if it makes one aware of a truth-maker for p. [(1) and (2)]
- (4) Intuition and perception have similar veridicality conditions. [Similarities and Differences]
(5) In some cases one’s intuition that p is veridical only if it makes one aware of a truth-maker
for p. [(3) and (4)]
In this argument the inference to the best explanation is replaced by transcendental reasoning. I still rely on introspection in supporting Similarities and Differences however. But perhaps this can be remedied:
- (1) One’s intuition that p immediately justifies believing that p only if its veridicality conditions include both p and awareness of a truth-maker for p. [Analogous to case for perception]
- (2) In some cases one’s intuition that p immediately justifies believing that p. [Reflect on ordinary thought and practice]
- (3) In some cases one’s intuition that p is veridical only if it makes one aware of a truth-maker for p. [(1) and (2)]
No more introspection. Just transcendental reasoning. I’m not entirely convinced this is a
dialectical improvement. But I myself do find the arguments compelling and the issues they raise worth exploring further.
Awareness of Abstract Objects
In Intuition I argue that intuitions can make us aware of abstract objects and that intuitions can put us in a position to know about abstract objects. These claims raise “how possible?” questions. Ignoring details that are irrelevant for what follows, the gist of my answers to them can be put as follows:
Awareness: If one’s intuition makes one aware of an abstract object, then it does so because it essentially depends for its phenomenology on that object.
Knowledge: If one’s intuition that p puts one in a position to know that p, then it does so because it makes one aware of an abstract object that makes p true.
Witmer takes issues with this package of ideas. The worry is that the account of awareness indicated in Awareness fails to identify a relation between experience and object that can bear the burden placed on it in the account of knowledge indicated in Knowledge.
I’m going to simplify things a bit in my response. Let’s just stipulate that we’ll only use “awareness” to pick out a relation that will bear the burden placed on it in the account of knowledge indicated in Knowledge. Then Witmer’s challenge can be framed as a challenge to my account of that relation. Is the account indicated in Awareness adequate?
First, some warm up. I have a dog named Harry. Consider the following three cases:
Case 1: I see Harry and draw a picture of him.
Case 2: I draw a picture of any old dog and the dog I draw happens to look like Harry.Case 3: I draw a picture of any old dog and the dog I draw happens to look like Harry and there is an x such that what it is for x to exist is for this picture I just drew to exist and for Harry to exist. Let’s call x the image-Harry sum.
Here are some plausible judgments about the items introduced in these cases. The picture in Case 1 refers to Harry. The picture in Case 2 does not refer to Harry. And for all I have said about it, the image-Harry sum in Case 3 also does not refer to Harry. The image-Harry sum essentially depends on Harry. But, for all I have said about it, the image-Harry sum does not refer to Harry. It is not of him in the way that the picture in Case 1 is of him.
Addition is commutative. Here is an illustration:
Consider the following three cases:
Case 4: I grasp the commutativity of addition and illustrate it with a picture like the one above.
Case 5: I randomly doodle and produce a picture that looks like the one above.
Case 6: I randomly doodle and produce a picture that looks like the one above and there is an x such that what it is for x to exist is for this picture I just drew to exist and for addition to be commutative. Let’s call x the figure-commutativity sum.
Here are some plausible judgments about the items introduced in these cases. The picture in Case 4 refers to the commutativity of addition. The picture in Case 5 does not refer to the commutativity of addition. And for all I have said about it, the figure-commutativity sum in Case 6 also does not refer to the commutativity of addition. The figure-commutativity sum essentially depends on the commutativity of addition. But, for all I have said about it, the figure-commutativity sum does not refer to the commutativity of addition. It is not of that state of affairs in the way that the picture in Case 4 is of it.
These examples fit into a pattern that also contains Witmer’s example of Amy. Once again consider the following three cases:
Case 7: Amy sees a brown dog in front of her.
Case 8: Amy has a visual hallucination as of a brown dog in front of her and there happens to be a brown dog in front of her.
Case 9: Amy has a visual hallucination as of a brown dog in front of her and there happens to be a brown dog in front of her and there is an x such that what it is for x to exist is for this hallucination to occur and for there to be a brown dog in front of Amy. Let’s use Witmer’s term and call x VH+.
The pattern of plausible judgments continues: Amy’s experience in Case 7 refers to—makes Amy aware of—a particular brown dog. Amy’s experience in Case 8 does not. And, for all I have said about it, neither does VH+ in Case 9. VH+ essentially depends on the brown dog. But, for all I have said about it, VH+ does not refer to–make Amy aware of—the brown dog. It is not of the brown dog in the way that Amy’s experience in Case 7 is of him.
According to Witmer, the example motivates a bad company argument against the account of awareness of abstract objects that I offer in Intuition. Here is the basic idea:
(1) VH+ does not make Amy aware of the brown dog in front of her.
(2) There are no awareness relevant differences between VH+ and experiences that meet the conditions I place on awareness of abstract objects.
(3) So my account of awareness of abstract objects is inadequate.
I agree with (1). VH+ might just as well have been called the experience-dog sum, highlighting its similarity with the image-Harry sum and the figure-commutativity sum. 3 These sums yoke images, figures, and experiences together with objects in ways that fail to constitute images of, figures of, or experiences of those objects. I take issue with (2).
One relevant difference is that experiences that meet the conditions I place on awareness of objects in general and awareness of abstract objects in particular must depend for their phenomenology, not just their existence, on those objects. Notice that VH+ need not even be an experience that has a phenomenology. It is a sum one part of which is an experience that has a phenomenology. But that does not imply that it is an experience that has a phenomenology. Similar points hold for the image-Harry sum and the figure-commutativity sum: for all I have said about it, the image-Harry sum is not itself an image though it has an image as a part; for all I have said about it, the figure-commutativity sum is not itself a figure though it has a figure as a part. Presumably images of objects depend for their qualities on those objects. When I draw Harry I make something with certain qualities because of how I see Harry. Presumably figures of objects depend for their characteristics on those objects. When I illustrate the commutativity of addition I make something with certain characteristics because of how I grasp the commutativity of addition. Even if there are existential dependence relations between the image-Harry sum and Harry, and the figure- commutativity sum and the commutativity of addition, these other dependence for qualities and dependence for characteristics relations are lacking. The same goes for VH+, or the experience-dog sum, and the brown dog in front of Amy.
Due to an earlier exchange, Witmer recognizes that this is my likely reply to his challenge. Here is what he says about it:
I want to consider a suggestion Chudnoff made in response to an earlier version of this example. He suggested that there was indeed a relevant difference between VH+ and his kind of example, noting that it is one thing to say that the existence of an experience “depends for its existence” on the relevant object (the situation involving the dog, or some situation involving abstract objects) and saying that “its phenomenology depends on” the relevant object. The example as I’ve presented it here, at least, builds in such dependence of phenomenology on the object. Insofar as I understand what Chudnoff might have in mind by saying that the phenomenology of an intuition depends on the abstract object it allegedly makes us aware of, the phenomenology of Amy’s experience v also depends on the object it allegedly makes us aware of (the situation of the brown dog being in that location).
Recall that I stipulated, in describing VH+, that as part of its essence, v necessarily differentiates the dog situation from others that might be visually represented, so that the dog situation is a kind of principle of unity for v; no experience event could be v unless it had a phenomenology that provided for such contrasts. If this is what Chudnoff means by saying that the “phenomenology depends on” the object—and it seems to be all he could mean— then our v in VH+ indeed features such dependence, and the two cases do not yet differ in an epistemically significant way. I wonder if he might be thinking (surely unconsciously) of the dependence as a kind of causal dependence, where the abstract object as it were reaches down and shapes the phenomenology. Of course, he will not want to appeal to that as a relevant difference. 4
Witmer’s reply to my reply directs us back to his specification of VH+. So here it is:
In VH+, Amy’s particular experience v is essentially such that it could not occur unless the concrete situation of there being a brown dog in that location indeed existed. Another experience with the same content might occur without there being any such dog, but this one—the particular experience v—could not. That situation is, of course, a truth-maker for Amy’s belief that there is a brown dog in front of her. Further, in VH+, the essence of v is such that it necessarily differentiates that brown-dog situation from other kinds of situations of a sort that might be visually represented. So, if v occurs, it must be one that is different in salient ways from a visual experience representing a black cat up ahead, or one representing a region of space devoid of animals, or the like. The situation of there being a brown dog in that location is a principle of unity for v, in that v could not exist without its various elements being arranged in one of the ways that allow for such differentiation. 5
One preliminary calibration: Witmer uses “VH+” to name the case and “v” to name the thing introduced in the case, but I will continue to use “VH+” for that thing. I find a few problems with Witmer’s specification. First, VH+ is defined in terms of an experience—Amy’s hallucination as of a brown dog—but, as I pointed out above, VH+ need not itself be an experience. Second, since VH+ need not be an experience, it need not be the sort of thing that differentiates the brown dog from its background. When I talk about differentiation I have in mind the opposite of what results from camouflage. If the brown dog is camouflaged, Amy cannot see it. If the brown dog is differentiated, Amy can see it. Third, Amy’s hallucination is as of a brown dog, or as of a brown dog in front of her, or as of a brown dog in front of her causing this experience, or something along these lines. This is different from being a hallucination as of a cat. But this does not mean that it differentiates the brown dog from its background. Differentiation is a relation between an experience and a particular. Amy’s hallucination might be phenomenally like an experience that differentiates the brown dog in front of her from its background without itself differentiating the brown dog in front of her from its background.
So I do not think that Witmer is entitled to claim of VH+ that it is an experience that has phenomenology, and I do not think that Witmer is entitled to claim of VH+ that it differentiates the brown dog in front of Amy from its background. Premise (2) remains questionable.
There is more to say, however. When I draw Harry there is a causal relation between Harry and the image I produce. When I illustrate the commutativity of addition I do so in light of a presupposed grasp of the commutativity of addition. If we wanted to say what VH+ is missing, we could say that it is missing appropriate phenomenology appropriately caused by the dog in front of Amy. None of these examples helps in specifying what exactly intuitions making one aware of abstract objects have that Witmer is neglecting. How does the phenomenology of an intuition depend on the abstract objects it makes one aware of? Witmer is correct in discarding the possibility that the dependence is “a kind of causal dependence, where the abstract object as it were reaches down and shapes the phenomenology.” Rather, I think it is a kind of non-causal dependence, where the phenomenology as it were reaches up and conforms itself to the abstract object. This is just a picturesque way of saying that the phenomenology is so structured as to differentiate the abstract object from a background.
One might press further: but in virtue of what does an intuition experience differentiate an abstract object? 6 I cannot develop a full response to this question here, but I would like to make a tentative suggestion. It is that differentiation in the case of abstract objects has some crucial features in common with the relation of similarity. Two seem particularly relevant. First, in the case of abstract objects–though not in the case of concrete objects–it depends on generic properties rather than particularizing properties: it obtains in virtue of characters and not identities. Second, and related to this, it is an internal relation: it obtains in virtue of the essential properties of the relata. Suppose A and B are similar and I try to say in virtue of what. All there is to do is describe A and B. Suppose an intuition experience differentiates an abstract object and I try to say in virtue of what. Then, again, I suspect that all there is to do is describe the intuition experience and the abstract object.
Witmer concedes that there is nothing metaphysically suspect about this relation between experience and abstract object. If there is a worry, I think it is epistemological. The following is tempting: I imagine observing an intuition experience occur (e.g., an intuition as of the commutativity of addition), and I want to find something in the way that it occurs that will show me it is differentiating that state of affairs and not another state of affairs or no state of affairs at all. But I think we should reject this demand. Suppose you have an intuition as of the commutativity of addition. Why think it makes you aware of the commutativity of addition? A perfectly sensible answer to this question is that your experience puts you in a position to know that addition is commutative in a way that is analogous to perception and it couldn’t do that unless it made you aware of the commutativity of addition. We do not need to support claims about awareness from a position that does not presuppose intuitions put us in a position to have knowledge. If there is a question about awareness of abstract objects, then the question is a metaphysical “how possible?” question. Answering that question requires identifying a metaphysically respectable relation that might obtain between experiences and abstract objects and that might count as a form of awareness. It does not require identifying a relation we can show to obtain in particular cases without presupposing that those cases are ones in which an intuition puts us in a position to have knowledge.
- John McDowell, Mind and World (Harvard University Press, 1996).
- I develop an extended case for the epistemic asymmetry indicated in this paragraph in the first chapter of a book in progress provisionally titled The Cave.
- In personal communication Witmer has clarified that he does not intend VH+ to be a mere sum like the image-Harry sum and the figure-commutativity sum, but rather to be an experience of just the sort I pick out when I give examples of intuitions. This might be true about his intention. But my claim is that for all Witmer has said about VH+ he has not ensured it isn’t a mere sum. VH+ is introduced by a construction and our reasoning about VH+ should be guided by that construction. My central point is that the construction does not rule out the possibility that what it results in is a mere sum—does not sufficiently distinguish VH+ from the image-Harry sum and the figure- commutativity sum.
- D. Gene Witmer, “Chudnoff on the Awareness of Abstract Objects,” Florida Philosophical Review XVI.1 (Winter 2016), 113-114.
- Witmer, “Chudnoff on the Awareness of Abstract Objects,” 110.
- In personal communication Witmer pressed me to address this question.