Belief, Reason & Logic
Scott Sturgeon
Birkbeck College London
(a)
(b)
(c)
(d)
Sketch a conception of belief
Apply epistemic norms to it in an orthodox way
Request more norms
Check the order of explanation between orthodox & requested
norms by looking at the role of logic in epistemology
--------------------------------------------------------Belief----------------------------------------------------[1]
Coarse and fine belief
[2]
The Threshold View
Ø
----------------------------------------100%
Belief
----------------------------------Threshold
*Suspended*
*Judgement*
---------------------------Anti-Threshold
Disbelief
-------------------------------------------0%
On this picture: to believe is to have sufficiently strong confidence; to disbelieve is have
sufficiently weak confidence; and to suspend judgement is to have confidence neither
sufficiently strong nor sufficiently weak. In all three cases “sufficiency” will doubtless
be vague and contextually-variable.
[3]
Confidence first!
--------------------------------------------------------Reason--------------------------------------------------[4]
The Two-Cell Partition Principle for Credence
If Ø1 and Ø2 form into a logical partition, and your point-valued subjective probability
for them—or "credence", as it's known— is cr1 & cr2, then cr1 plus cr2 should equal
100%.
For instance: credence in Ø and ¬Ø should add up to 100%.
The Logical Implication Principle for Credence
If Ø1 logically implies Ø2, and your rational credence in Ø1 is cr1, you should not invest
credence in Ø2 less than cr1.
For instance: When you are rationally 70% sure of Ø, you should not be 65% sure
of (Øv).
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[5]
Probabilism: ideally rational degrees of belief are measured by probability functions; and
such degrees of belief are updated by conditionalization (or perhaps Jeffrey's rule).
[6]
How does the epistemology of coarse belief fit into this picture? Probabilism invites the
view that coarse epistemology is at best a by-product of serious epistemology:
Richard Jeffrey: "By 'belief' I mean the thing that goes along with valuation in
decision-making: degree-of-belief, or subjective probability, or personal
probability, or grade of credence. I do not care what you call it because I can
tell you what it is, and how to measure it, within limits...Nor am I disturbed by
the fact that our ordinary notion of belief is only vestigially present in the
notion of degree of belief. I am inclined to think Ramsey sucked the marrow
out of the ordinary notion, and used it to nourish a more adequate view."
('Dracula meets Wolfman: Acceptance vs. Partial Belief', in Marshal Swain
(ed.) Induction, Acceptance & Rational Belief (Reidel: 1970), pp. 171-172.)
Robert Stalnaker: "One could easily enough define a concept of belief which
identified it with high subjective or epistemic probability (probability greater than
some specified number between one-half and one), but it is not clear what the
point of doing so would be. Once a subjective or epistemic probability value is
assigned to a proposition, there is nothing more to be said about its epistemic
status. Probabilist decision theory gives a complete account of how probability
values, including high ones, ought to guide behaviour, in both the context of
inquiry and the application of belief outside of this context. So what could be the
point of selecting an interval near the top of the probability scale and conferring
on the propositions whose probability falls in that interval the honorific title
‘believed’?" (Inquiry (MIT: 1984), p.138.)
[7]
The worry, then, is simple: if coarse epistemology springs from its fine cousin via a
belief-making threshold, coarse epistemology is pointless; it is at best a theoretical
shadow cast by real explanatory theory (i.e. Probabilism).
------------------------------------------------More Norms Please!-----------------------------------------[8]
My view is that Probabilism is an incomplete epistemology of confidence. To see why,
consider a few thought experiments.
[9]
Case 1. You are faced with a black box. You are rationally certain of this much: the box
is filled with a huge number of balls; they have been thoroughly mixed; exactly 85% of
them are red; touching a ball will not affect its colour. You reach into the box, grab a
ball, and wonder about its colour. You have no view about anything else relevant to your
question. How confident should you be that you hold a red ball?
You should be 85% confident, of course. Your confidence in the claim that you
hold a red ball is well modelled by a position in Probabilism’s "attitude space":
85%
|---------------------------------------------------------------|
0%
100%
con(R)
2
Here we have one attitude ruled in by evidence and others ruled out. The case suggests a
principle:
Out-by-In Attitudes get ruled out by evidence because others get ruled in.
In Case 1, after all, it seems intuitively right that everything but 70% credence is ruled
out by your evidence precisely because that very credence is itself ruled in.
[10]
Case 2. The set up is just as before save this time you know exactly 80-to-90% of balls in
the box are red. How confident should you be that you hold a red ball?
You should be exactly 80-to-90% confident, of course. Your confidence in the
claim that you hold a red ball cannot be well modelled with a position in Probabilism’s
attitude space. Your evidence is too rough for that. Certain attitudes within credal space
are ruled out by your evidence in Case 2; but no attitude in that space is itself ruled in.
This puts pressure on the Out-by-In principle.
[11]
I want to resist that pressure; for I want to insist that there are more attitudes in our
psychology than are dreamt of in Probabilism’s epistemology. There are more kinds of
confidence than credence. It seems to me this is both obvious after reflection and
important for epistemology. For one thing it means that Probabilism is an incomplete
epistemology of confidence. After all, it lacks an epistemology of non-credal confidence.
Or as I shall put the point: it lacks an epistemology of thick confidence.
[12]
To get a feel for this think back to Case 2. Evidence in it demands more than a point in
credal space. It demands something like an exact region instead. Evidence in Case 2
rules in a thick confidence like this:
80%
90%
|---------------------------------------------------------------|
0%
100%
con(R)
Everyday evidence is normally like this. It tends not to rule in credence, being too
coarse-grained to do so. This does not mean that everyday evidence tends not to rule in
confidence. It means that such evidence tends to rule in thick confidence.
[13]
The key point here is simple: evidence and attitude should match in character. Precision
in evidence should make for precision in attitude; and imprecision in evidence should
make for imprecision in attitude. Since evidence is normally imprecise, levels of
confidence normally warranted by it are thick.
[14]
This makes room for a reduction of coarse belief to confidence:
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t
|---------------------------------------------------------------|
0%
100%
con(R)
Probabilism may give a full view of rational credence; but it does not give a full view of
rational confidence. Probabilism entails that ideally rational agents always assign pointvalued subjective probability to questions of interest. It is clear that this is not so. Often
our evidence is too coarse for subjective probability. When that happens epistemic
perfection rules out credence in favour of thick confidence; and that is because there
should be character match between attitude and evidence on which it is based. Since we
deal in coarse evidence in everyday life, we should often adopt an attitude at the heart of
both coarse and fine epistemology. We should often adopt a thick confidence spreading
from the belief-making threshold to certainty. For this reason, coarse epistemology is of
theoretical moment even if Probabilism is the full story about credence. Coarse
epistemology captures the heart of everyday rationality.
--------------------------------------------------------Logic----------------------------------------------------[15] Where does logic fit in the theory of epistemic rationality? Probabilism invites the view
that logic's role is pinned down by probability theory. The basic idea is that logic helps
shape rational belief by helping to shape probability functions which measure rational
degree of belief. What do we say, though, once thick confidence shows up in theory?
[16]
David Christensen sticks to a Probabilist line even after thick confidence—or 'spread out
credence', as he calls it—is admitted into epistemic theory. He notes that thick
confidence is naturally modelled by richly-membered sets of probability functions rather
than single probability functions. And he infers from this that an epistemology of thick
confidence will preserve the central insights of Probabilism. "On any such view," he says
"ideally rational degrees of belief are constrained by the logical structure of
the propositions believed, and the constraints are based on the principles of
probability. Wherever an agent does have precise degrees of belief, those
degrees are constrained by probabilistic coherence in the standard way.
Where her credences are spread out, they are still constrained by coherence,
albeit in a more subtle way. Thus the normative claim that rationality
allows, or even requires, spread-out credences does not undermine the basic
position that I have been defending [in this book]: that logic constrains ideal
rationality by means of probabilistic conditions on degrees of confidence."
(Putting Logic in Its Place (OUP: 2004), p150.)
[17]
The Two-Cell Partition Principle for Confidence
If Ø1 and Ø2 form into a logical partition, and your confidence in them is [a,b] & [c,d]
respectively, then a plus d should equal 100%, and b plus c should equal 100%.
For instance: if you are 20-to-30% confident in Ø, you should be 70-to-80%
confident in ¯.
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But notice: the two-celled principle for credence is simply a limit case of the two-celled
principle for confidence. The latter does not hold because the former holds. It is rather
the other way around. The order of explanation goes from general fact to limit-case
instance.
The Logical Implication Principle for Confidence
If Ø1 logically implies Ø2, and your rational confidence in Ø1 is [a,b], then you should
not invest confidence [c, d] in Ø2 when c is less than a.
For instance: When you are 70-to-80% sure of Ø, you should not invest a confidence
[c, d] in (Øv) when c is less than 70%.
Here too the general principle is explanatorily fundamental. The logical implication
principle for credence holds because it is a limit case of more general fact. That more
general fact is captured by the logical implication principle for confidence.
[18]
Christensen notes that thick confidence is normally modelled by rich sets of probability
functions. Those sets are literally built from point-valued probability functions. Their
behaviour is thus fixed by that of those probability functions. In turn this suggests that
probabilistic norms are explanatorily fundamental in epistemology. But that's not quite
right; for thick confidence is not built from credence, and its norms do not derive from
those for credence. It’s the other way around. Explanatorily basic norms for confidence
are those for thick confidence. The truth in Probabilism is but a limit case of more
general truth. And that more general truth overlaps, in part, with the epistemology of
everyday life. After all, the full-dress epistemology of confidence overlaps, in part, with
the epistemology of coarse belief.
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