In this post, I will address Aidan's second objection to my lottery argument. By his lights, even if we grant whatever closure (or conjunction) step I need to make the aforementioned inference, premise (A6) still seems in need of defence. For example, suppose that S, due to some introspective failure, does not recognise that what she may justifiably believe about this lottery has the form of (a*). This is consistent with S's recognizing that if she believed something which had the form (a*) she would be believing a set of inconsistent propositions.
The upshot, according to Aidan, is that (A3) and (A4) might be true, and my opponent might grant me whatever I need to conclude from that that what S may justifiably believe about this lottery is (by (A5)) inconsistent. But even in the presence of (A6) that's not enough for (A7); it's not enough that S recognize that something of the form (a*) would be inconsistent – she must also recognise that what she may justifiably believe about this lottery has the form (a*). And according to Aidan, therein lies the rub. The number of tickets n might be very large (and the larger n is, the more plausible (A1) and (A2) are). Why, then, should we accept that S is able to recognize that the huge set of beliefs she may justifiably have, has the form of (a*)?
Now, I take (A6) to be true by hypothesis. Moreover, I take it to be an intelligible hypothesis, a fact that our own ability to understand the lottery argument makes obvious. But just so that it is clear that I am not begging any questions in so doing, some clarification and defence of (A6) may be in order. I do not believe that it is impossible for a lottery subject, due perhaps to some sort of introspective failure, to fail to recognise that what she may believe about the lottery takes the form of (a*). However, it think that such an oversight is no-where as likely as Aidan makes it sound. Given the set-up of the lottery argument, the lottery subject knows all of the following:
Moreover, I think there is something misleading about Aidan’s claim that the likelihood of the lottery subject failing to realise that what she may believe about the lottery takes the form (a*) increases the larger we make the overall pool of tickets. After all, I have presented the argument with a million tickets, and this fact does not make the lottery argument any more difficult to understand than if I spoke instead of a hundred or a thousand tickets. That is to say, what is important is the formal structure of the reasoning implicated, rather than the individual application of the reasoning. S only needs to recognise that the inference she makes with regards to her own ticket may, by parity of reasoning, also be made regarding every other ticket, in order to recognise that what she believes about the lottery takes the form of (a*). She does not actually have to set about the arduous task of applying the relevant inference to each individual ticket. Thus, I see little motivation for thinking that a doxastically responsible subject may be mistaken on this question.
But let us grant that some given subject does not recognise that what she may justifiably believe about the lottery takes the form of (a*). I do not see how this poses a problem for the lottery argument. Notice, the conclusion of the lottery argument merely implicates what S may justifiably believe, not what she actually believes. To say that one may justifiably believe p is to say that it is rationally permissible to believe p. The question with which we are presently concerned, then, is a normative one regarding what is rationally permissible for S to believe. The conclusion of the reductio is that it is rationally permissible for S to believe something she recognises to be inconsistent, and this is a conclusion I take to be unacceptable. Whether or not S actually does recognise that her belief is inconsistent is, as far as the present argument is concerned, beside the point.
In this regard, the lottery argument employs a similar strategy to Boghossian-type arguments against the compatibility of self-knowledge and content externalism. For the Boghossian argument to be effective, a subject need not actually come to believe some fact about her environment, for example, that she inhabits a planet with H2O, by means of a priori introspection. In fact, given that people are not typically shuttled between Earth and Twin Earth, the scenario described by Boghossian arguments may turn out to be purely hypothetical. (Though some philosophers have argued that there are in fact real life slow-switch scenarios, such as a speaker switching between British to American English.) However, the mere fact that it is possible for the subject to acquire such knowledge is seen as sufficient to impugn the content externalist position. The intuition here is that certain epistemic achievement should not be possible. Analogously, the intuition underlying the lottery argument is that a certain epistemic achievement should not be permissible—namely, a subject believing something she recognises to be inconsistent. The point of the reductio is that we should reject (A1) since it, in conjunction with a number of other plausible premises, suggests that believing a set of propositions one knows to be inconsistent is permissible. (Again, whether or not some particular subject actually does come to believe something she recognises to be inconsistent is beside the point.)
Notice, in the above reply, I have interpreted Aidan as claiming that a subject may recognise that she is in a lottery type situation without realising that what she may justifiably believe about the lottery takes the form of (a*). But one may well ask, what about the case in which the subject fails to recognise that she is in a lottery-type case altogether. In such a case, (A6)—which my lottery argument simply assumes by hypothesis—does not even apply. The lottery argument would therefore (apparently) fail to cover such cases. This is the objection raised by Clayton Littlejohn, and will be the focus of my next post on this topic.
The upshot, according to Aidan, is that (A3) and (A4) might be true, and my opponent might grant me whatever I need to conclude from that that what S may justifiably believe about this lottery is (by (A5)) inconsistent. But even in the presence of (A6) that's not enough for (A7); it's not enough that S recognize that something of the form (a*) would be inconsistent – she must also recognise that what she may justifiably believe about this lottery has the form (a*). And according to Aidan, therein lies the rub. The number of tickets n might be very large (and the larger n is, the more plausible (A1) and (A2) are). Why, then, should we accept that S is able to recognize that the huge set of beliefs she may justifiably have, has the form of (a*)?
Now, I take (A6) to be true by hypothesis. Moreover, I take it to be an intelligible hypothesis, a fact that our own ability to understand the lottery argument makes obvious. But just so that it is clear that I am not begging any questions in so doing, some clarification and defence of (A6) may be in order. I do not believe that it is impossible for a lottery subject, due perhaps to some sort of introspective failure, to fail to recognise that what she may believe about the lottery takes the form of (a*). However, it think that such an oversight is no-where as likely as Aidan makes it sound. Given the set-up of the lottery argument, the lottery subject knows all of the following:
(i) That she is playing a lottery,Given that the subject is aware of (i)-(v), it would be odd for her not to realise that what she may justifiably believe about the lottery, given (A1), takes the form of (a*). More importantly, such an individual would most certainly be guilty of gross introspective and rational failure and may, eo ipso, count as doxastically irresponsible. Thus, we seem to have independent grounds for holding that such an individual is not justified.
(ii) That the lottery is composed of a million tickets,
(iii) That one ticket must win and only one ticket can win,
(iv) That the odds of her ticket losing are the same as that of any other ticket losing
(v) That she is no more justified in believing that her ticket will lose than any other
Moreover, I think there is something misleading about Aidan’s claim that the likelihood of the lottery subject failing to realise that what she may believe about the lottery takes the form (a*) increases the larger we make the overall pool of tickets. After all, I have presented the argument with a million tickets, and this fact does not make the lottery argument any more difficult to understand than if I spoke instead of a hundred or a thousand tickets. That is to say, what is important is the formal structure of the reasoning implicated, rather than the individual application of the reasoning. S only needs to recognise that the inference she makes with regards to her own ticket may, by parity of reasoning, also be made regarding every other ticket, in order to recognise that what she believes about the lottery takes the form of (a*). She does not actually have to set about the arduous task of applying the relevant inference to each individual ticket. Thus, I see little motivation for thinking that a doxastically responsible subject may be mistaken on this question.
But let us grant that some given subject does not recognise that what she may justifiably believe about the lottery takes the form of (a*). I do not see how this poses a problem for the lottery argument. Notice, the conclusion of the lottery argument merely implicates what S may justifiably believe, not what she actually believes. To say that one may justifiably believe p is to say that it is rationally permissible to believe p. The question with which we are presently concerned, then, is a normative one regarding what is rationally permissible for S to believe. The conclusion of the reductio is that it is rationally permissible for S to believe something she recognises to be inconsistent, and this is a conclusion I take to be unacceptable. Whether or not S actually does recognise that her belief is inconsistent is, as far as the present argument is concerned, beside the point.
In this regard, the lottery argument employs a similar strategy to Boghossian-type arguments against the compatibility of self-knowledge and content externalism. For the Boghossian argument to be effective, a subject need not actually come to believe some fact about her environment, for example, that she inhabits a planet with H2O, by means of a priori introspection. In fact, given that people are not typically shuttled between Earth and Twin Earth, the scenario described by Boghossian arguments may turn out to be purely hypothetical. (Though some philosophers have argued that there are in fact real life slow-switch scenarios, such as a speaker switching between British to American English.) However, the mere fact that it is possible for the subject to acquire such knowledge is seen as sufficient to impugn the content externalist position. The intuition here is that certain epistemic achievement should not be possible. Analogously, the intuition underlying the lottery argument is that a certain epistemic achievement should not be permissible—namely, a subject believing something she recognises to be inconsistent. The point of the reductio is that we should reject (A1) since it, in conjunction with a number of other plausible premises, suggests that believing a set of propositions one knows to be inconsistent is permissible. (Again, whether or not some particular subject actually does come to believe something she recognises to be inconsistent is beside the point.)
Notice, in the above reply, I have interpreted Aidan as claiming that a subject may recognise that she is in a lottery type situation without realising that what she may justifiably believe about the lottery takes the form of (a*). But one may well ask, what about the case in which the subject fails to recognise that she is in a lottery-type case altogether. In such a case, (A6)—which my lottery argument simply assumes by hypothesis—does not even apply. The lottery argument would therefore (apparently) fail to cover such cases. This is the objection raised by Clayton Littlejohn, and will be the focus of my next post on this topic.
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