Combining Philosophers

Ideas for Hermarchus, Gottfried Leibniz and Ned Markosian

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7 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
12992 Logic teaches us how to order and connect our thoughts [Leibniz]
     Full Idea: Logic teaches us how to order and connect our thoughts.
     From: Gottfried Leibniz (New Essays on Human Understanding [1704], 3.10)
     A reaction: Leibniz had a higher opinion of logic than contemporaries like Locke. The question is whether logic can actually teach us better order than we could otherwise manage, or whether it just describes what most thinkers do.
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
19370 'Blind thought' is reasoning without recognition of the ingredients of the reasoning [Leibniz, by Arthur,R]
     Full Idea: Leibniz invented the concept of 'blind thought' - reasoning by a manipulation of characters without being able to recognise what each character stands for.
     From: report of Gottfried Leibniz (Towards a Universal Characteristic [1677]) by Richard T.W. Arthur - Leibniz
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10056 At bottom eternal truths are all conditional [Leibniz]
     Full Idea: At bottom eternal truths are all conditional, saying 'granted such a thing, such another thing is'.
     From: Gottfried Leibniz (New Essays on Human Understanding [1704], 4.11.14), quoted by Alan Musgrave - Logicism Revisited §4
     A reaction: Thus showing Leibniz to have sympathy with the if-thenist view. He cites geometry as his illustration.
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
2111 Falsehood involves a contradiction, and truth is contradictory of falsehood [Leibniz]
     Full Idea: We judge to be false that which involves a contradiction, and true that which is opposed or contradictory to the false.
     From: Gottfried Leibniz (Monadology [1716], §31)
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
12974 People who can't apply names usually don't understand the thing to which it applies [Leibniz]
     Full Idea: Someone who goes wrong in relating an idea to a name will usually go wrong about the thing he wants the name to stand for.
     From: Gottfried Leibniz (New Essays on Human Understanding [1704], 2.29)
     A reaction: This seems to give tentative support to a Millian account of names, whose only content is just the thing which is named. Leibniz's observation certainly seems to be right.
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
13002 It is always good to reduce the number of axioms [Leibniz]
     Full Idea: To reduce the number of axioms is always something gained.
     From: Gottfried Leibniz (New Essays on Human Understanding [1704], 4.06)
     A reaction: This is rather revealing about the nature of axioms. They don't have any huge metaphysical status - in fact one might say that their status is epistemological, or even pedagogic. They enable us to get out minds round things.
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
19391 We can assign a characteristic number to every single object [Leibniz]
     Full Idea: The true principle is that we can assign to every object its determined characteristic number.
     From: Gottfried Leibniz (Towards a Universal Characteristic [1677], p.18)
     A reaction: I add this as a predecessor of Gödel numbering. It is part of Leibniz's huge plan for a Universal Characteristic, to map reality numerically, and then calculate the truths about it. Gödel seems to allow metaphysics to be done mathematically.