[lit-ideas] Re: Berkeleyiana

  • From: "" <dmarc-noreply@xxxxxxxxxxxxx> (Redacted sender "Jlsperanza" for DMARC)
  • To: lit-ideas@xxxxxxxxxxxxx
  • Date: Thu, 24 Sep 2015 12:29:47 -0400

In a message dated 9/24/2015 10:22:29 A.M. Eastern Daylight Time,
_lawrencehelm@roadrunner.com_ (mailto:lawrencehelm@xxxxxxxxxxxxxx) refers to
Geary's "seeming Berkeleyism" ... and that "having read Berkeley in the past
and
rejected him [I] don't like the association." ... "My association with
Berkeley is even less than that."

Well, for the record I see that the OTHER (so far) quote of the 'esse est
percipi' in the Stanford Encyclopedia is in Bell's entry:

Bell, John L., "Continuity and Infinitesimals", The Stanford Encyclopedia
of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), URL =
<http://plato.stanford.edu/archives/win2014/entries/continuity/>.

and it may be worth quoting it:

Bell is concerned about ONE item, but oddly, Grice compares 'stars' with
the 'infinity', when he writes, "As far as I know, there are infinite stars"
(He is considering this a rather 'otiose' thing to say, in WoW -- because
Grice feels there is a clash betweeen the use of 'know' and the concept of
'infinity': as an intuitionist, you cannot KNOW anything about 'infinity'.

Bell writes:

"The philosopher George Berkeley (1685–1753), noted both for his subjective
idealist doctrine of esse est percipi and his denial of general ideas, was
a persistent critic of the presuppositions underlying the mathematical
practice of his day (see Jesseph [1993])."

"His most celebrated broadsides were directed at the calculus, but in fact
his conflict with the mathematicians went deeper."

"For Berkeley's denial of the existence of abstract ideas of any kind went
in direct opposition with the abstractionist account of mathematical
concepts held by the majority of mathematicians and philosophers of the day."

"The central tenet of this doctrine, which goes back to Aristotle, is that
the mind creates mathematical concepts by abstraction, that is, by the
mental suppression of extraneous features of perceived objects so as to focus
on properties singled out for attention."

"Berkeley rejected this,"

-- as he rejected many other things. It wouldn't be unfair to call him the
greatest rejectionist of all time.

Bell goes on:

"asserting that mathematics as a science is ultimately concerned with
objects of sense, its admitted generality stemming from the capacity of
percepts to serve as signs for all percepts of a similar form. At first
Berkeley
poured scorn on those who adhere to the concept of infinitesimal.
maintaining that the use of infinitesimals in deriving mathematical results is
illusory, and is in fact eliminable. But later he came to adopt a more tolerant

attitude towards infinitesimals, regarding them as useful fictions in
somewhat the same way as did Leibniz. In The Analyst of 1734 Berkeley launched
his
most sustained and sophisticated critique of infinitesimals and the whole
metaphysics of the calculus. Addressed To an Infidel Mathematician [25],
the tract was written with the avowed purpose of defending theology against
the scepticism shared by many of the mathematicians and scientists of the
day. Berkeley's defense of religion amounts to the claim that the reasoning
of mathematicians in respect of the calculus is no less flawed than that of
theologians in respect of the mysteries of the divine. Berkeley's arguments
are directed chiefly against the Newtonian fluxional calculus. Typical of
his objections is that in attempting to avoid infinitesimals by the
employment of such devices as evanescent quantities and prime and ultimate
ratios
Newton has in fact violated the law of noncontradiction by first subjecting
a quantity to an increment and then setting the increment to 0, that is,
denying that an increment had ever been present. As for fluxions and
evanescent increments themselves, Berkeley has this to say.

It is a good thing Bell quotes direct from Berkeley whose prose is so
powerful:

Berkeley writes:

"[As for fluxions and evanescent increments themselves], And what are these
fluxions? The velocities of evanescent increments? And what are these same
evanescent increments? They are neither finite quantities nor quantities
infinitely small, nor yet nothing. May we not call them the ghosts of
departed quantities?"

Poetic, almost.

Bell concludes the segment on Berkeley:

"Nor did the Leibnizian method of differentials escape Berkeley's
strictures."

Ah, well, as long as they did not escape Leibniz's own strictures!

Cheers,

Speranza
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