How total can evidence be?
Is "total" as used by Bernoulli the same as "total" as not used by Popper -- as
applied to 'evidence'?
What evidence do we have that there are Wittgenstein's old and new, English,
Welsh, and Irish, truth-tables?
McEvoy writes:
"Why do I think Popper never refers to a "principle of total evidence" (even
though I admit I can't prove this by going through the "total evidence")?
Because there is no such thing as "total evidence", in Popper's view."
OTOH, for H. Paul Grice, perhaps there was such a principle, or to echo Geary,
and use the historical present, there IS such a principle.
Every philosopher, after all, knows the Principle of Total Evidence, if you
allow me the hyperbole. It is usually associated with Carnap, who we associate
with the Vienna Circle that Popper knew so well.
The principle simply states that one should not ignore information.
Keynes writes in this "Treatise n Probability", as "a principle which seems
generally recognized", already back in 1921.
Keynes did some historical research and refers to "Bernoulli's maxim"
(Bernouilli, as his surname implicates, was an Italian) that in reckoning a
probability, we must take into account ALL the information which we have'.
The principle, alas, is not always obeyed (vide McEvoy's remarks on Popper
above), but says that, if we wish to apply such a theorem of the theory of
probability to a given knowledge situation, we have to take as evidence the
TOTAL evidence available to the person in question at the time in question,
that is to say, his total KNOWLEGE (or beliefs) knowledge of the results of his
observations, as Carnap noted in 1947, well after Popper had published his opus
magnum.
"Bernoulli's maxim" appears in "Ars Conjectandi".
Although an Italian, Bernoulli preferred to express in Cicero's Old Roman lingo:
"Non sufficit expendere unum alterumve argumentum
sed conquirenda sunt omnia
quae in cognitionem nostram venire possunt
atque ullo modo ad probationem rei facere videntur."
In brief, Bernoulli, who was associated by family with the Medicis, states
that, in reckoning a probability we must take into account all the information
which we have.
In Popper's more simplistic account, ONE FALSIFICATION counts, so no principle
such as Bernoulli, is needed (Indeed, if I understood McEvoy alright, it would
be anti-logical, since 'total evidence' compares to 'verification', a concept
Popper avoided "like the rats".
For the record, Cicero's likelihood principle is a version of the principle of
total evidence applicable to statistical inference.
It says (roughly) that, when one has a sample of data, one should take that
sample fully into account when making inferences about hypotheses.
Popper, and his 'disciple, Lakatos, speak profusely of hypothesis, but rarely
of Bernoulli, alas.
Because of the popularity of evaluating methods of inference on their long-run
behaviour, the likelihood principle is frequently broken, but unlike a heart,
it can be mended!
This could emphasise the role of the Likelihood Principle in categorising
theories (a favourite Popperian term) of statistical inference.
Grice (who followed Suppe's and Davidson's seminal work on this) did not think
anyone's really made a big deal about that yet. Grice thought that, "rather a
pity."
Then there are those philosophers Ilike Bayes, if a philosopher he was) who
want to push Bayesianism (Geary finds this "merely tautological.").
Other philosophers (such as Plato) want to push the use of raw likelihoods or
raw likelihood ratios -- vide Levi-Strauss, The raw and the cooked.
This all relates the 'importance, or lack thereof, of protocol' in Hutchison --
in the British Journal of the Philosophy of Science (after all Popper was a
philosopher of science*), Dowe, Korb, etc.
Cheers
Speranza
* When Grice was once characterized as a "philosopher of language," he got so
irritated that he said "Baloney: philosophy, like virtue, is entire! And surely
the implicature that I am a philosopher of language is that I'm a philosopher
of NOTHING but language -- odious!"
