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Ideas for
'Frege's Concept of Numbers as Objects', 'Ideas: intro to pure phenomenology' and 'Physics'
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28 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
9790
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Geometry studies naturally occurring lines, but not as they occur in nature [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
13861
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Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13892
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One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
22962
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Two is the least number, but there is no least magnitude, because it is always divisible [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
13867
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Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
18090
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Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
22929
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Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
22930
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Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin]
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18833
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A continuous line cannot be composed of indivisible points [Aristotle]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17441
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Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck]
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13862
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There are five Peano axioms, which can be expressed informally [Wright,C]
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17853
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Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C]
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17854
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What facts underpin the truths of the Peano axioms? [Wright,C]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
13894
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Sameness of number is fundamental, not counting, despite children learning that first [Wright,C]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10140
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We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K]
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8692
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Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend]
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17440
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Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck]
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13893
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It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
13888
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If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
13869
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Number platonism says that natural number is a sortal concept [Wright,C]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
13870
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We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C]
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9974
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Ten sheep and ten dogs are the same numerically, but it is not the same ten [Aristotle]
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6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
13873
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Treating numbers adjectivally is treating them as quantifiers [Wright,C]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
13899
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The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C]
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13896
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The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C]
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7804
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Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
13863
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Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C]
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13895
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The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C]
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