Combining Philosophers

All the ideas for Peter B. Lewis, David Hilbert and J Baggini / PS Fosl

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49 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
The Principle of Sufficient Reason does not presuppose that all explanations will be causal explanations [Baggini /Fosl]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
You cannot rationally deny the principle of non-contradiction, because all reasoning requires it [Baggini /Fosl]
2. Reason / C. Styles of Reason / 1. Dialectic
Dialectic aims at unified truth, unlike analysis, which divides into parts [Baggini /Fosl]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
'Natural' systems of deduction are based on normal rational practice, rather than on axioms [Baggini /Fosl]
In ideal circumstances, an axiom should be such that no rational agent could possibly object to its use [Baggini /Fosl]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
The principle of bivalence distorts reality, as when claiming that a person is or is not 'thin' [Baggini /Fosl]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
You would cripple mathematics if you denied Excluded Middle [Hilbert]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The facts of geometry, arithmetic or statics order themselves into theories [Hilbert]
Axioms must reveal their dependence (or not), and must be consistent [Hilbert]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend]
I aim to establish certainty for mathematical methods [Hilbert]
We believe all mathematical problems are solvable [Hilbert]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
Only the finite can bring certainty to the infinite [Hilbert]
We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
The idea of an infinite totality is an illusion [Hilbert]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
There is no continuum in reality to realise the infinitely small [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Number theory just needs calculation laws and rules for integers [Hilbert]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logic already contains some arithmetic, so the two must be developed together [Hilbert]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
The grounding of mathematics is 'in the beginning was the sign' [Hilbert]
The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman]
Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman]
9. Objects / F. Identity among Objects / 3. Relative Identity
If identity is based on 'true of X' instead of 'property of X' we get the Masked Man fallacy ('I know X but not Y') [Baggini /Fosl, by PG]
9. Objects / F. Identity among Objects / 4. Type Identity
'I have the same car as you' is fine; 'I have the same fiancée as you' is not so good [Baggini /Fosl]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
Leibniz's Law is about the properties of objects; the Identity of Indiscernibles is about perception of objects [Baggini /Fosl]
10. Modality / A. Necessity / 3. Types of Necessity
Is 'events have causes' analytic a priori, synthetic a posteriori, or synthetic a priori? [Baggini /Fosl]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB]
Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
'A priori' does not concern how you learn a proposition, but how you show whether it is true or false [Baggini /Fosl]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
Basic beliefs are self-evident, or sensual, or intuitive, or revealed, or guaranteed [Baggini /Fosl]
14. Science / A. Basis of Science / 6. Falsification
A proposition such as 'some swans are purple' cannot be falsified, only verified [Baggini /Fosl]
14. Science / C. Induction / 1. Induction
The problem of induction is how to justify our belief in the uniformity of nature [Baggini /Fosl]
14. Science / C. Induction / 4. Reason in Induction
How can an argument be good induction, but poor deduction? [Baggini /Fosl]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
Abduction aims at simplicity, testability, coherence and comprehensiveness [Baggini /Fosl]
To see if an explanation is the best, it is necessary to investigate the alternative explanations [Baggini /Fosl]
18. Thought / A. Modes of Thought / 5. Rationality
Consistency is the cornerstone of rationality [Baggini /Fosl]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert]