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9358
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There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI]
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Full Idea:
The fact is that there are several logics, markedly different, each self-consistent in its own terms and such that whoever, using it, avoids false premises, will never reach a false conclusion.
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From:
C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.366)
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A reaction:
As the man who invented modal logic in five different versions, he speaks with some authority. Logicians now debate which version is the best, so how could that be decided? You could avoid false conclusions by never reasoning at all.
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9357
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Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI]
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Full Idea:
The law of excluded middle formulates our decision that whatever is not designated by a certain term shall be designated by its negative. It declares our purpose to make a complete dichotomy of experience, ..which is only our penchant for simplicity.
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From:
C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.365)
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A reaction:
I find this view quite appealing. 'Look, it's either F or it isn't!' is a dogmatic attitude which irritates a lot of people, and appears to be dispensible. Intuitionists in mathematics dispense with the principle, and vagueness threatens it.
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14234
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If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
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Full Idea:
A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives').
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro)
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A reaction:
A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology.
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14237
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We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
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Full Idea:
Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects.
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro)
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A reaction:
[Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it.
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14246
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If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
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Full Idea:
If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics.
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1)
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A reaction:
Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application.
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14247
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Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
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Full Idea:
Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers.
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From:
Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2)
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A reaction:
Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated.
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9365
|
We can maintain a priori principles come what may, but we can also change them [Lewis,CI]
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Full Idea:
The a priori contains principles which can be maintained in the face of all experience, representing the initiative of the mind. But they are subject to alteration on pragmatic grounds, if expanding experience shows their intellectual infelicity.
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From:
C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.373)
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A reaction:
[compressed] This simply IS Quine's famous 'web of belief' picture, showing how firmly Quine is in the pragmatist tradition. Lewis treats a priori principles as a pragmatic toolkit, which can be refined to be more effective. Not implausible...
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21500
|
We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI]
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Full Idea:
When the whole range of empirical beliefs is taken into account, all of them more or less dependent on memorial knowledge, we find that those which are most credible can be assured by their mutual support, or 'congruence'.
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From:
C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 334), quoted by Erik J. Olsson - Against Coherence 3.1
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A reaction:
Lewis may be over-confident about this, and is duly attacked by Olson, but it seems to me roughly correct. How do you assess whether some unusual element in your memory was a dream or a real experience?
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6556
|
If anything is to be probable, then something must be certain [Lewis,CI]
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Full Idea:
If anything is to be probable, then something must be certain.
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From:
C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 186), quoted by Robert Fogelin - Walking the Tightrope of Reason Intro
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A reaction:
Lewis makes this comment when facing infinite regress problems. It is a very nice slogan for foundationalism, which embodies the slippery slope view. Personally I feel the emotional pull of foundations, but acknowledge the very strong doubts about them.
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21498
|
Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI]
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Full Idea:
A set of statements, or a set of supposed facts asserted, will be said to be congruent if and only if they are so related that the antecedent probability of any one of them will be increased if the remainder of the set can be assumed as given premises.
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From:
C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 338), quoted by Erik J. Olsson - Against Coherence 2.2
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A reaction:
This thesis is vigorously attacked by Erik Olson, who works through the probability calculations. There seems an obvious problem without that. How else do you assess 'congruence', other than by evidence of mutual strengthening?
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5828
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Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI]
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Full Idea:
"The denotation or extension of a term is the class of all actual or existent things which the term correctly applies to or names; the connotation or intension of a term is delimited by any correct definition of it." ..And intension determines extension.
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From:
C.I. Lewis (An Analysis of Knowledge and Valuation [1946]), quoted by Stephen P. Schwartz - Intro to Naming,Necessity and Natural Kinds §II
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A reaction:
The last part is one of the big ideas in philosophy of language, which was rejected by Putnam and co. If you were to reverse the slogan, though, (to extension determines intension) how would you identify the members of the extension?
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9363
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Science seeks classification which will discover laws, essences, and predictions [Lewis,CI]
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Full Idea:
The scientific search is for such classification as will make it possible to correlate appearance and behaviour, to discover law, to penetrate to the "essential nature" of things in order that behaviour may become predictable.
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From:
C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.368)
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A reaction:
Modern scientific essentialists no longer invoke scare quotes, and I think we should talk of the search for the 'mechanisms' which explain behaviour, but Lewis seems to have been sixty years ahead of his time.
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