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All the ideas for 'Phenomenalism', 'On the Algebra of Logic' and 'works'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
18086 Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher]
     Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors.
     From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18092 Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock]
     Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits.
     From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4
     A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts.
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
14303 Truth-functional conditionals have a simple falsification, when A is true and B is false [Peirce]
     Full Idea: The utility of [truth-functional conditionals] is that it puts us in possession of a rule...[namely] The hypothetical proposition may be ...falsified by a single state of things, but only by one in which A [antecedent] is true and B [consequent] is false.
     From: Charles Sanders Peirce (On the Algebra of Logic [1895], p.218), quoted by Stephen Mumford - Dispositions
     A reaction: Personally I am rather more interested in verifying conditionals than in falsifying them. I certainly don't accept them until they are falsified, unless they have massive support from surrounding facts.
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
2614 Modern phenomenalism holds that objects are logical constructions out of sense-data [Ayer]
     Full Idea: Nowadays phenomenalism is held to be a theory of perception which says that physical objects are logical constructions out of sense-data.
     From: A.J. Ayer (Phenomenalism [1947], §1)
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
2615 The concept of sense-data allows us to discuss appearances without worrying about reality [Ayer]
     Full Idea: The introduction of the term 'sense-datum' is a means of referring to appearances without prejudging the question of what it is, if anything, that they are appearances of.
     From: A.J. Ayer (Phenomenalism [1947], §1)