Many epistemologists have claimed that there is such a thing as non-trivial higher-order evidence – in other words, potentially misleading higher-order evidence. According to this claim, sometimes your evidence may support giving at least some credence to false propositions about what your evidence is – or even to false propositions about what your evidence supports.
In this post, I try to cast doubt on the main argument that has been advanced for this claim.
The argument in question relies on our intuitions about cases like the following.
Case 1. Suppose that your evidence in fact supports believing p; but you learn that another thinker, who appears wonderfully reliable about such matters, has the same evidence as you but disbelieves p.
Case 2. Your evidence in fact supports believing p, but you learn that a seemingly infallible oracle has pronounced that your evidence does not support believing p.
In these cases, some philosophers claim, it is just intuitively clear that your evidence supports giving some credence to the false proposition that your evidence does not support believing p.
As I shall argue here, this argument is unsound. Our intuitions about these cases are in fact quite compatible with the view that there is only trivial higher-order evidence – i.e., with the view the only rational attitudes for you to have towards questions about what your evidence is, and what it supports, are attitudes of maximum confidence towards the true answers to these questions.
The argument under consideration here involves the semi-technical notions of “your evidence” and of what your evidence “supports”. There are many puzzles about the interpretation of these notions. To fix ideas, I shall assume here that, as these terms are being used in the context, the following theses are all equivalent:
- Your evidence supports having doxastic attitudes A1, … An towards p1, … pn.
- Having doxastic attitudes A1, … An towards p1, … pn fits optimally with your evidence.
- There is (ideal) propositional justification for you to have doxastic attitudes A1, … An towards p1, … pn.
- Having doxastic attitudes A1, … An towards p1, … pn is an ideally rational set of attitudes for you to have.
The idea that there is a problem with this argument for non-trivial higher-order evidence is suggested by Mike Titelbaum’s brilliant paper “Rationality’s Fixed Point”. In effect, Titelbaum’s argument shows that, if this argument is sound, then a certain strange sort of doxastic akrasia would be rational.
Suppose that in fact your evidence supports having an attitude of maximum confidence in p. (For example, suppose that p follows logically from your evidence, or something like that.) Even so (as in Case 1), you might learn that another thinker, who appears wonderfully reliable about such matters, has the same evidence as you but totally disbelieves p. Alternatively (as in Case 2), you might learn that a seemingly infallible oracle has pronounced that your evidence does not support having a high credence in p.
If the argument under consideration is sound, then in these cases, even though your evidence in fact supports having an attitude of maximum confidence in p, it also supports having high credence in the false proposition that your evidence does not support having a high credence in p.
Given the equivalences that I am assuming here, this conclusion implies that simultaneously having maximum confidence in p and high credence in ‘My evidence does not support having high credence in p’ is in this case an ideally rational pair of attitudes for you to have. But this seems like a crazy kind of doxastic akrasia – not an ideally rational pair of attitudes for you to have!
But how can we resist the argument? We need to distinguish two conclusions that we might draw about these cases
Conclusion 1: In these cases, your evidence supports giving high credence to the false proposition that your evidence does not support having high credence in p.
Conclusion 2: In these cases, if you were thinking as rationally as it is realistically possible for you to do, you would respond to acquiring this higher-order evidence by raising your credence in this false proposition.
I propose that in fact, our intuitions do not directly support Conclusion 1, but only Conclusion 2 instead. In effect, our intuitions directly support a conclusion about which of the available sets of attitudes would be as doxastically justified as possible – they do not directly support any conclusion about what sets of attitudes are propositionally justified.
To some philosophers, it might seem hopeless to rebut the argument in this way. After all, many philosophers assume that doxastic justification implies propositional justification. (Call this the “Doxastic Implies Propositional” assumption, or DIP assumption for short.) According to this DIP assumption, if you believe p in a doxastically justified manner, there must also be propositional justification for you to believe p. So, suppose that you would be responding in a doxastically justified manner if she raised your credence in these false propositions about what your evidence supports. Then, according to the DIP assumption, there would also have to be propositional justification for you to raise your credence in these false propositions.
However, I want to suggest that the DIP assumption is ambiguous. In one sense, this assumption is plausible: Ideal doxastic justification does indeed imply ideal propositional justification. But doxastic justification comes in degrees. So, in another sense, this assumption seems to be false: A thinker’s response can be as doxastically justified as it is possible for any normal person’s response to be without being ideally propositionally justified.
It should be possible to adapt this objection to the argument to fit with many different conceptions of this crucial idea of “degrees of doxastic justification”. To fix ideas, however, I shall sketch the conception of this idea that strikes me as most plausible.
According to this conception, for you to be thinking in the most doxastically-justified manner that is possible for you, you must be manifesting dispositions that are no less rational than any alternative dispositions available to you. For flesh-and-bone creatures like us, such dispositions will never be perfect. Even if such imperfect dispositions often lead us to the attitudes that there is ideal propositional justification for us to have, they will often also lead us to attitudes that are slightly less than ideally propositionally justified.
No doubt any thinker with normal rational dispositions will wobble a bit in the tricky cases that the argument focuses on. But this does not show that the thinker’s evidence itself supports giving any credence to these false higher-order propositions. The intuitions underlying the argument are compatible with a different diagnosis – namely, that the cases in question are ones where the highest degree of doxastic justification available to normal thinkers involves having attitudes that are less than perfectly rational.
For this reason, the intuitions underlying the argument under consideration do not really support the possibility of non-trivial higher-order evidence. These intuitions are compatible with the view that the only attitudes that your evidence genuinely supports towards questions about what your evidence is, and what it supports, are attitudes of maximum confidence towards the true answers to these questions. That is, they are compatible with the view that there is only trivial higher-order evidence.
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