Credal sensitivism: threshold vs credence-one JIE GAO, KU LEUVEN - - PowerPoint PPT Presentation
Credal sensitivism: threshold vs credence-one JIE GAO, KU LEUVEN NEW TRENDS IN EPISTEMOLOGY, HAMBURG, 05/10/2017 Some background Clarke, Roger (2013), Belief Is Credence One (In Context), Philosophers Imprint Greco, Daniel (2015), How
JIE GAO, KU LEUVEN NEW TRENDS IN EPISTEMOLOGY, HAMBURG, 05/10/2017
Philosophical Perspective
the credence-one view
+
belief sensitivism (credal sensitivism) credence-one sensitivism They argue that credence-one sensitivism is better than the threshold view
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=
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Defend threshold credal sensitivism = the threshold view + credal sensitivism
credal sensitivism
the threshold view
sensitivism is better than credence-one sensitivism
1. A taxonomy
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Sensitivism Non-sensitivism Credal sensitivism Threshold sensitivism The credence-one view Credence-one sensitivism ___ The certainty view The non-credence-
Threshold credal sensitivism Threshold sensitivism The standard threshold view
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(Non-sensitivism) Belief is context insensitive. v The traditional position (Sensitivism) Belief is context sensitive in the sense that whether one believes that p depends
Defining contextual factors:
factors (interests, stakes, other anxiety-producing factors, etc.)
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(The credence-one view) beliefs require maximal confidence or credence 1. (The certainty view) the credence-one view + non-sensitivism Ø Stability of credence one (In the Bayesian framework, once a rational agent has assigned p probability 1, one’s credence in it can never drop any lower. ) Problems with the certainty view:
what evidence she receives against.
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(The non-credence-one view) Belief does not require maximal confidence or credence 1.
(Note: it doesn’t deny the reality of belief)
(The threshold view) Beliefs reduce to credences above some threshold (<1). (The standard threshold view) the threshold view + non-sensitivism
(2007)
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You own a lottery ticket. You know that there are n tickets in the lottery, that exactly one winner will be selected, that each ticket has an equal chance of winning, and that each ticket’s winning
For any ticket i, let Li be the proposition that i loses; then for all i, you have Cr(Li) = !"#
! .
On the standard threshold view, if n is sufficiently high, it is impossible for you not to believe that your ticket will lose, which is strikingly counterintuitive.
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As Robert Stalnaker (1984: 91) emphasised, any number r [the threshold] is bound to seem arbitrary. Unless these numbers are made salient by the environment, there is no special difference between believing p to degree 0.9786 and believing it to degree 0.9875. But if r is 0.98755, this will be the difference between believing p and not believing it, which is an important difference. (Weatherson 2005: 420) There doesn't seem to be a non-arbitrary way of identifying a threshold, even a vague one.
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i. Behavioural dispositions: Believing p involves simply take p for granted, but a change
difference to one’s dispositions.
having credence in p just meeting a threshold less than 1 implies assigning a positive credence to the negation of p.
any qualitative difference, while changes passing the threshold make big differences in
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The credence-one view can easily solve problems for the threshold view:
1) The lottery problem ü There is no lottery large enough to make !"#
! = 1.
2) The arbitrariness problem ü Believing p to degree 1. 3) The problem with qualitative commitments involved in beliefs ü If one believes p to degree 1, she will not engage in any activities of taking not-p into consideration.
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Sensitivism solves standard problems for the credence-one view:
ü Belief to degree 1 should not be taken to entail certainty. Certainty requires a stability of
ü Offering a bet means changing the context. When the practical importance of p changes, as it must when a bet is offered, the space of salient alternatives to p may also change.
ü New counter evidence changes the space of alternative possibilities and hence induce changes to the context.
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i. Functional properties of belief: Ganson (2008): in order to count as believing p in a range of circumstances, one must be willing to act as if p in those circumstances. (see also Weatherson 2005, Fantl & McGrath 2009)
Nagel (2008, 2010)’s analyses of belief regulation of normal human beings in different practical settings support sensitivism.
S’s assertion that p is sincere iff S believes that p. S’s sincere assertion takes place against a common ground. Common ground can be modeled as a set of possibilities taken seriously for the purposes of the conversation. (Clarke forthcoming, Greco 2015)
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Sensitivism Non-sensitivism Credal sensitivism Threshold sensitivism The credence-one view Credence-one sensitivism ___ The certainty view The non-credence-
Threshold credal sensitivism Threshold sensitivism The standard threshold view
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(Threshold sensitivism) Credence is context insensitive; the threshold on credence necessary for belief varies in accordance with relevant contextual factors; the contextual sensitivity of the threshold explains the contextual sensitivity of belief.
version of threshold sensitivism (threshold pragmatism). But they simply stipulate it without neither argument nor evidence. (Credal sensitivism) Credence is context sensitive; the contextual sensitivity of credence explains the contextual sensitivity of belief.
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Credal sensitivism is entailed by credence-one sensitivism: One’s credences in a particular context are given by a function assigning weights to each of the salient possibilities in that context. When salient possibilities become more or fewer, one’s credences are given by a different function. This implies that credence distributions vary contextually.
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Independent evidence:
When we’re deliberating, a largely unconscious, automatic decision set-up process filters
then credences will be assigned to those possibilities “on the spot”. Which possibilities get through the filter is a highly context-sensitive matter. (Norby 2015)
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Independent evidence (continues):
*Mayseless and Kruglanski (1987, Study 2), confidence is measured on a 0-100 scale
Unfounded confidence paradox: Rush-oriented practical factors generate higher confidence in less accurate judgments. (See Gao’s ‘Credal pragmatism’, ms for more details)
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Rush-oriented Neutral Caution-oriented Confidence for 1st piece of evidence 50.84 34.78 27.43 Confidence shift for each piece of evidence 38.49 20.44 13.46
Sensitivism Non-sensitivism Credal sensitivism Threshold sensitivism The credence-one view Credence-one sensitivism ___ The certainty view The non-credence-
Threshold credal sensitivism Threshold sensitivism The standard threshold view
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Sensitivism Non-sensitivism Credal sensitivism Threshold sensitivism The credence-one view Credence-one sensitivism ___ The certainty view The non-credence-
Threshold credal sensitivism Threshold sensitivism The standard threshold view
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(Credence-one sensitivism) credence-one view + credal sensitivism Low stakes: Cr(p)=1 High stakes: Cr(p)=0.8 (Threshold credal sensitivism) the threshold view + credal sensitivism Low stakes: Cr(p)=0.98 High stakes: Cr(p)= 0.9
(threshold: 0.97)
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p p p p p p not-p p p
p: 0.98 not-p: 0.02 p: 0.9 not-p: 0.1
Three main differences:
shifting set (tractable for working memory in each context); context sensitive.
consideration; a large and stable set; context insensitive. 2. The mechanism of credence shifts
the space of alternative possibilities.
(not mediated by changes in the set of error possibilities).
Stakes.
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Three main differences (continued):
Belief is a three-place relation, between a believer, a proposition, and a set of possibilities. It’s part of the nature of belief that it is individuated by a context.
Belief is a two-place relation, between a believer and a proposition. People’s degrees of confidence and beliefs are normally influenced by features of the context. But this is not part of the metaphysical nature of belief.
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According to credence-one sensitivism, if one believes p then one assigns credence zero to all salient error possibilities. In other words, if one assigns positive credences to error possibilities entailing not-p, then one cannot believe p. Credence-one sensitivism conflicts with the fact that in many cases one believes p in spite of assigning minimal positive credences to certain error possibilities entailing not-p. Two types of considered error possibilities compatible with beliefs:
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Far-fetched possibilities: those that from the subjective perspective are utterly unlikely to happen Examples:
e.g. Suppose that there is a desk in front of me. According to quantum mechanics, there is a possibility that within a short while, the particles belonging to the surface of the desk remain more or less unmoved but the material inside the desk unfolds in a bizarre enough way that the system no longer counts as a desk. (Hawthorne 2004: 4-5) Compare to mundane error possibilities: Your car has not been stolen in the driveway
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Cases of beliefs where far-fetched possibilities receive non-zero credence in one’s probability distribution: Presumably, those who are aware of the sceptical scenario registered the possibility that our cognition might be embedded in a virtual rather than real world. However, the sceptical attitudes normally don’t linger after initial recognition. Ø Even as I form the skeptical belief, I realize that I will not remain committed to it for long. If the skeptic is to maintain that his arguments provide us with a powerful reason to forever refrain from believing positive knowledge ascriptions, how is he to explain our willingness to lapse—doxastically as well as assertorically—into those very ascriptions? (Hawthorne 2004: 131)
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Ø Before students take epistemology, they typically affirm ‘‘I know that I have a hand’’ with no doubt or hesitation. After the professor explains the brain in the vat or evil demon hypothesis, they begin to wonder. Many come to deny that they really know they have a
435-36) Ø [E]ven when a counter-possibility is accepted (regarded as relevant), in radical cases the persuasion is often half-hearted. The student who is moved by your dreaming argument to sincerely deny that he knows that he is in the classroom does not cease to believe that he is in the classroom. (Adler 2012: 264)
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We can naturally interpret the student in Adler’s quote as having registered the sceptical scenario as an open possibility while leaving her ordinary beliefs intact. The explanation is that the sceptical scenario is treated as a merely stipulated and hence idle possibility. But still, the agent assigns positive credence to such possibilities for she cannot really deny its possibility no matter how improbable she thinks it is. This is contrary to the prediction of credence-one sensitivism.
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Non-far-fetched possibilities: not as improbable as sceptical scenarios but are still often treated as irrelevant for beliefs. E.g.: Fallibility of testimony Imagine that you just acquired some information from testimony, and you realise that testimony is wrong at least one in one thousand times. If the testimony turns out to be wrong, you wouldn’t be surprised. Intuitively, you would form and retain the belief acquired by testimony despite recognising an obvious error possibility. Note: My objection concerns the compatibility of belief and certain error possibilities at the psychological level, hence it is different from Worsnip (2015)’s point on belief assertions.
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Another bad consequence of credence-one sensitivism: Entertaining the fallibility of a belief-forming method would result in suspensions of all beliefs acquired by that method. Suppose one considers the error possibility that a belief forming method, such as perception or testimony, could be fallible. Since that error possibility is within spaces of alternative possibilities relevant for a large number of beliefs, by assigning a positive credence to that error possibility, it follows that credence for all these propositions go under 1, and the (rational) subject doesn’t believe them anymore. However, this is clearly not the case.
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Threshold credal sensitivism (and the non-credence-one view in general) can easily accommodate the above considered phenomena. In this view, we assign positive credence not only to possibilities that we deem to be relevant (i.e. live possibilities or those we take seriously) in a context, but also to those we take to be irrelevant for outright beliefs (i.e. far-fetched or more mundane possibilities). Anticipations of those irrelevant error possibilities are built in our doxastic states.
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Clarke (2013, §7.3) argues that both credence-one sensitivism and the threshold view are able to accommodate the platitude that credences are degrees of belief: to raise one’s credence that p is to increase the degree to which one believes that p. But this only applies to cases where outright beliefs are absent. Credence-one sensitivism cannot accommodate: 1) Outright beliefs with different strengths 2) Confidences in outright beliefs are strengthened.
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E.g. While I believe both that I have watched Matrix and my spouse has watched Matrix, I hold the former belief firmer than the latter. Credence-one sensitivists could explain the phenomenon that one holds a belief more firmly in terms of one’s endorsement of that belief in a more stringent context. Similarly, that one holds less firmly a belief is explained in terms of one’s abandonment of that belief in a more stringent context. But this explanation fails to provide a unified account of degrees of belief. It makes a distinction between two types of confidence, degrees of credence and counterfactual belief status, that doesn’t seem to exist. In contrast, the non-credence-one view provides a unified account of confidence in terms of degrees of credence.
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Imagine that one receives positive evidence for the truth of p while leaving the relevant context unchanged (i.e., the evidence doesn’t change the space of alternative possibilities in ways capable of affecting the probability of p). In this case, it seems obvious that one’s confidence in the belief in p is strengthened. Nonetheless according to credence-one sensitivism one’s credence in p remains the same (i.e., cr(p)=1). By contrast, the non-credence-one view can easily explain why the credence in p changes given the new evidence.
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According to credence-one sensitivism, in order to completely specify an agent’s beliefs, we need more than just a list of the propositions she believes: we need such a list for each context she might find herself in (Clarke 2013, 2017, forthcoming). Two problems:
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In order to specify dispositional beliefs, one needs to listing relevant contexts paired to a subject and proposition. Two problems:
very large number).
set of modal properties. The COS answer should be that the subject believe p in this and that contexts and doesn’t believe in this and that contexts. This is not the answer we expect from the question.
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We often attribute beliefs to unconscious agents (e.g., sleeping). In other words, whether the subject is sleeping or not doesn’t matter for our belief attributions. However, unconscious agents do not have a context because they are not considering any error
In contrast, threshold credal sensitivism allows ascribing beliefs to unconscious agents (no context needed).
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Recap of the problem: According to the threshold view, a binary belief that p is often accompanied by a binary belief that there’s some non-zero chance—no matter how slight—that not-p. The first belief will dispose us to take p for granted or treat it as a starting point. The second belief will dispose us to take “There’s a small chance that not-p” for granted or treat it as a starting point. What does it make one disposed to act on p rather than on the chance that not-p given that one assigns positive credences to both p and not-p?
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Reply: A hypothesis: treating as true propositions about which we are uncertain is a heuristic that helps us deal with our cognitive limitations. Wenhong Tang (2015)’s cournotian heuristic account: Cournotian heuristic When certain probability values (subjective confidence) are close to 1 (or 0), we are disposed to employ the heuristic of reasoning as if the value is 1 (or 0). Suppose that we have a credence close to 1 in p, by employing the cournotian heuristic, in our reasoning we’ll end up making as if we had credence 1 in “There is no chance that not-p”. This yields the disposition to treat p as true.
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Recap of the problem: How to identify the threshold in a non-arbitrary way? Reply: The threshold can be understood as the crucial point at which the agent is automatically and subconsciously disposed to treat the credence as if it equals 1. Reaching the threshold would mark a qualitative change in one’s attitudes including committing oneself to the truth of p in one’s reasoning.
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Recap of the problem: according to the threshold view, it is impossible for one not to believe that her lottery ticket is a loser before knowing the result. Reply:
the use of cournotian heuristics is inhibited. This is in accordance with Nagel (2011)’s proposal: the presentation of numerical odds of the lottery would be expected to trigger controlled processing, i.e. System 2 as opposed to System 1.
mere statistical evidence (e.g., Smith 2016).
q The lottery problem also applies to the credence-one view. This view cannot explain why it is possible for one to believe that one’s lottery ticket is a loser while at the same time forming a credence that one’s ticket will lose which matches the objective probability.
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Defend threshold credal sensitivism = the threshold view + credal sensitivism
credal sensitivism
the threshold view
sensitivism is better than credence-one sensitivism
Perspectives 29 (1): 179–201.
Stakes’. Australasian Journal of Philosophy 86 (2): 279–94.
(1): 407–35.
11 (5): 1–28.
Perspectives 19 (1): 417–43.
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