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All the ideas for 'What is Logic?st1=Ian Hacking', 'The Metaphysics within Physics' and 'Logic for Philosophy'

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87 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
The metaphysics of nature should focus on physics [Maudlin]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Kant survives in seeing metaphysics as analysing our conceptual system, which is a priori [Maudlin]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
Wide metaphysical possibility may reduce metaphysics to analysis of fantasies [Maudlin]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
If the universe is profligate, the Razor leads us astray [Maudlin]
The Razor rightly prefers one cause of multiple events to coincidences of causes [Maudlin]
2. Reason / D. Definition / 3. Types of Definition
A decent modern definition should always imply a semantics [Hacking]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
'Theorems' are formulas provable from no premises at all [Sider]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth tables assume truth functionality, and are just pictures of truth functions [Sider]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider]
In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
System B introduces iterated modalities [Sider]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider]
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
We can treat modal worlds as different times [Sider]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
Converse Barcan Formula: □∀αφ→∀α□φ [Sider]
The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider]
System B is needed to prove the Barcan Formula [Sider]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
You can employ intuitionist logic without intuitionism about mathematics [Sider]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
The various logics are abstractions made from terms like 'if...then' in English [Hacking]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order completeness seems to need intensional entities and possible worlds [Hacking]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
The most popular account of logical consequence is the semantic or model-theoretic one [Sider]
Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]
Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider]
Maybe logical consequence is a primitive notion [Sider]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
A 'theorem' is an axiom, or the last line of a legitimate proof [Sider]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
A 'total' function must always produce an output for a given domain [Sider]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
λ can treat 'is cold and hungry' as a single predicate [Sider]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Good axioms should be indisputable logical truths [Sider]
No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider]
Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Natural deduction helpfully allows reasoning with assumptions [Sider]
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
We can build proofs just from conclusions, rather than from plain formulae [Sider]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Valuations in PC assign truth values to formulas relative to variable assignments [Sider]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
The semantical notion of a logical truth is validity, being true in all interpretations [Sider]
It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
5. Theory of Logic / K. Features of Logics / 4. Completeness
In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider]
7. Existence / C. Structure of Existence / 5. Supervenience / d. Humean supervenience
The Humean view is wrong; laws and direction of time are primitive, and atoms are decided by physics [Maudlin]
Lewis says it supervenes on the Mosaic, but actually thinks the Mosaic is all there is [Maudlin]
If the Humean Mosaic is ontological bedrock, there can be no explanation of its structure [Maudlin]
The 'spinning disc' is just impossible, because there cannot be 'homogeneous matter' [Maudlin]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider]
Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider]
A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider]
We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
To get an ontology from ontological commitment, just add that some theory is actually true [Maudlin]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
Naïve translation from natural to formal language can hide or multiply the ontology [Maudlin]
8. Modes of Existence / A. Relations / 1. Nature of Relations
A relation is a feature of multiple objects taken together [Sider]
8. Modes of Existence / B. Properties / 5. Natural Properties
A property is fundamental if two objects can differ in only that respect [Maudlin]
8. Modes of Existence / B. Properties / 12. Denial of Properties
Fundamental physics seems to suggest there are no such things as properties [Maudlin]
8. Modes of Existence / D. Universals / 2. Need for Universals
Existence of universals may just be decided by acceptance, or not, of second-order logic [Maudlin]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider]
10. Modality / A. Necessity / 3. Types of Necessity
'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider]
10. Modality / A. Necessity / 5. Metaphysical Necessity
Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider]
Logically impossible is metaphysically impossible, but logically possible is not metaphysically possible [Maudlin]
10. Modality / A. Necessity / 6. Logical Necessity
Logical truths must be necessary if anything is [Sider]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider]
10. Modality / B. Possibility / 9. Counterfactuals
A counterfactual antecedent commands the redescription of a selected moment [Maudlin]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider]
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider]
14. Science / C. Induction / 1. Induction
Induction leaps into the unknown, but usually lands safely [Maudlin]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Laws should help explain the things they govern, or that manifest them [Maudlin]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Evaluating counterfactuals involves context and interests [Maudlin]
We don't pick a similar world from many - we construct one possibility from the description [Maudlin]
The counterfactual is ruined if some other cause steps in when the antecedent fails [Maudlin]
If we know the cause of an event, we seem to assent to the counterfactual [Maudlin]
If the effect hadn't occurred the cause wouldn't have happened, so counterfactuals are two-way [Maudlin]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Laws are primitive, so two indiscernible worlds could have the same laws [Maudlin]
Fundamental laws say how nature will, or might, evolve from some initial state [Maudlin]
Laws of nature are ontological bedrock, and beyond analysis [Maudlin]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
'Humans with prime house numbers are mortal' is not a law, because not a natural kind [Maudlin]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
If laws are just regularities, then there have to be laws [Maudlin]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
I believe the passing of time is a fundamental fact about the world [Maudlin]
27. Natural Reality / D. Time / 2. Passage of Time / b. Rate of time
If time passes, presumably it passes at one second per second [Maudlin]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
There is one ordered B series, but an infinitude of A series, depending on when the present is [Maudlin]