Combining Texts

All the ideas for 'The Advancement of Learning', 'Which Logic is the Right Logic?' and 'On Nature Itself (De Ipsa Natura)'

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34 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 / 4. Axioms for Sets / j. Axiom of Choice IX
The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic is either for demonstration, or for characterizing structures [Tharp]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Elementary logic is complete, but cannot capture mathematics [Tharp]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order logic isn't provable, but will express set-theory and classic problems [Tharp]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
The main quantifiers extend 'and' and 'or' to infinite domains [Tharp]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
There are at least five unorthodox quantifiers that could be used [Tharp]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp]
The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
5. Theory of Logic / K. Features of Logics / 3. Soundness
Soundness would seem to be an essential requirement of a proof procedure [Tharp]
5. Theory of Logic / K. Features of Logics / 4. Completeness
Completeness and compactness together give axiomatizability [Tharp]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
If completeness fails there is no algorithm to list the valid formulas [Tharp]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Compactness is important for major theories which have infinitely many axioms [Tharp]
Compactness blocks infinite expansion, and admits non-standard models [Tharp]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A complete logic has an effective enumeration of the valid formulas [Tharp]
Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Substance is a force for acting and being acted upon [Leibniz]
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]
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
Final causes can help with explanations in physics [Leibniz]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
People love (unfortunately) extreme generality, rather than particular knowledge [Bacon]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
Something rather like souls (though not intelligent) could be found everywhere [Leibniz]
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 / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
There are atoms of substance, but no atoms of bulk or extension [Leibniz]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
Secondary matter is active and complete; primary matter is passive and incomplete [Leibniz]
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]
If there is some trace of God in things, that would explain their natural force [Leibniz]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
It is plausible to think substances contain the same immanent force seen in our free will [Leibniz]
28. God / C. Attitudes to God / 2. Pantheism
To say that nature or the one universal substance is God is a pernicious doctrine [Leibniz]