Combining Texts

All the ideas for 'The Advancement of Learning', 'Carnap and Logical Truth' and 'Mathematical logic and theory of types'

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28 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics is the best knowledge, because it is the simplest [Bacon]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon]
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon]
Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes can be reduced to propositional functions [Russell, by Hanna]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine]
10. Modality / A. Necessity / 6. Logical Necessity
Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine]
12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention
Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
We don't assume there is no land, because we can only see sea [Bacon]
14. Science / A. Basis of Science / 3. Experiment
Science moves up and down between inventions of causes, and experiments [Bacon]
14. Science / B. Scientific Theories / 5. Commensurability
Many different theories will fit the observed facts [Bacon]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
People love (unfortunately) extreme generality, rather than particular knowledge [Bacon]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Essences are part of first philosophy, but as part of nature, not part of logic [Bacon]