[analytic] Davidson, Grice and akrasia
Jlspe...@aol.com
'patterns' for the generation of a reasoned practical and alethic judgement:
> Boulomaic Version:
> 1. pf (A, !p)
> 2. pf (A & B,!p)
> 3. pf (A & B & C, !p)
> 4. pf (all things before me, !p)
> 5. pf (ATC, !p)
> 6. !p
> 7. R wills !p
> Doxastic Version
> 1. pr (A, p)
> 2. pr (A & B, p)
> 3. pr (A & B & C, p)
> 4. pr (all things before me, p)
> 5. pr (ATC,p)
> 6. |- p
> 7. R judges p
Tapper asks:
> (What are pf and pr here, preference functions?
>
Sort of. I would think 'pf' abbreviates 'prima facie' and that 'pr'
abbreviates 'probability', or more accurately, the adverb, 'probably' (with 'pf'
adverbially readable as 'prima-faciably'). Grice & Baker -- like Davidson? -- are
concerned with the generation of a 'reasoned' propositional content --
associated with either the imperative or the indicative mode. Grice expands on this in
_Aspects of Reason_:
We should compare such sentences as
1. Given that the barometer falls, it will probably
rain tomorrow.
2. Given that action A would be a lie, and that
action B would not, B is better than A.
These may be regarded as exemplifying, respectively,
the forms:
1b. Prob (m1; p)
2b. Pf (m1; B better than A)
["'Pf is to be read as 'prima facie'].
_Aspects of Reason_, p. 46
Grice notes some signs of discomforts in trying the analogy between 'pf' and
'pb' too far.:
in practical arguments, unlike probabilistic arguments,
the special connective ... will not disappear in the
conclusion. p.47
and there are other discomforts, too -- but none too great for Grice to
_disfavour_ the central analogy, I would think.
More later, I hope.
JL
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Larry Tapper
Thanks to Speranza for explaining Grice's notation: "pf" is "prima-
faciably", "pr" is "probably".
JLS writes:
"Grice notes some signs of discomforts in trying the analogy
between 'pf' and 'pr' too far.
> in practical arguments, unlike probabilistic arguments,
> the special connective ... will not disappear in the
> conclusion. p.47
>
and there are other discomforts, too -- but none too great for Grice
to _disfavour_ the central analogy, I would think."
I see. Another possible discomfort occurs to me. If probability is
conceived as something that falls short of certainty (that is p < 1)
then you can't safely conjoin strings of pr-type judgments.
That is, if E is your total evidence, and "pr" means "more probable
than not", and
pr (E, p)
and
pr (E, q)
and
pr (E, r)
then (if we're thinking of these pr's as the sorts of things that
correspond to numerical values) it does *not* follow that
pr (E, p & q & r).
The principle involved is that if you believe a thousand things, each
with degree of confidence .99, it is nevertheless *improbable* that
the grand conjunction of all of these thousand things is true.
It's not clear that pf should work the same way. Perhaps if pf (q)
and pf (q) and pf (r) then we'd want to say that pf (p & q & r).
Yrs, LM
Jlspe...@aol.com
'primafaciably' and 'probably'
Primafaciably, it is wrong to lie.
Probably, the sun will shine tomorrow.
Tapper writes:
> Another possible discomfort occurs to me. If probability is
> conceived as something that falls short of certainty (that is p < 1)
> then you can't safely conjoin strings of pr-type judgments.
> That is, if E is your total evidence, and "pr" means "more probable
> than not", and
> pr (E, p) and pr (E, q) and pr (E, r)
> then (if we're thinking of these pr's as the sorts of things that
> correspond to numerical values) it does *not* follow that
> pr (E, p & q & r).
> The principle involved is that if you believe a thousand things, each
> with degree of confidence .99, it is nevertheless *improbable* that
> the grand conjunction of all of these thousand things is true.
Then perhaps there is something wrong with the principle of total evidence?
Grice expands on a problem having to do with the COMPOUNDING of antecedent
clauses in probability-judgement on p. 80ff: "[Mr. Thornton] owns a firm which
makes and sells ornaments constructed from seashells, and [Mr. Thornton] is
concerned, at time t-1, to estimate whether his firm's business will improve during
the coming year. Mr. Thornton reflects:
"These days, every beachcomber is collecting
seashells like mad so as to sell them to firms
such as mine; so I can get seashells more
cheaply: so it is likely, given that I shall get
seashells more chepaly, that the business
will improve."
Mr. Thornton _also_ reflects:
"My not easily replaceable craftsmen are getting
restive for higher pay and I may hae to give in."
So, he accepts:
"Given that the craftsmen are restive, the business
will NOT improve."
He further reflects:
"Ornaments from seashells are all the rage at the
moment, so I may be able to put
my prices UP and make more money"
Mr. Thornton now CONSOLIDATES his reflections and judges:
"It is pretty LIKELY, given that I will get
seashells more cheaply, AND that my
employees are restive, AND that
everyone is eager to buy seashell ornaments,
that my business will improve.
Grice adds in connection with Davidson's "principle of total evidence":
"[Mr. Thornton] now searches further to see if he
can fnd ANY CONSIDERATION which, when
added to the antecedent of his last judgement,
would result in an acceptable conditional
favouring the supposition that his business will
NOT improve."
"After due search, he FAILS to find any such distiburbing consideration; so
he 'detaches' and judges that it IS PRETTY LIKELY that his business WILL
improve".
Grice has a caveat here: "I have said here nothing about the INITIAL
ESTABLISHMENT of weighted acceptability-generalisations (from which singular
acceptability-conditionals may be derived by instantiation) nor about HOW TO COMPOUND
THEM." Grice acknowledges 'these are important and difficult questions" (p.
82). --- I'm not sure this relates to Tapper's point, but it concerns
_probability_, hey. -- Cheers,