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All the ideas for 'Symposium', 'System of Logic' and 'Philosophical Logic'

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80 ideas

4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The temporal Barcan formulas fix what exists, which seems absurd [Burgess]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Is classical logic a part of intuitionist logic, or vice versa? [Burgess]
It is still unsettled whether standard intuitionist logic is complete [Burgess]
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
What physical facts could underlie 0 or 1, or very large numbers? [Frege on Mill]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Classical logic neglects the non-mathematical, such as temporality or modality [Burgess]
The Cut Rule expresses the classical idea that entailment is transitive [Burgess]
Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess]
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Philosophical logic is a branch of logic, and is now centred in computer science [Burgess]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Formalising arguments favours lots of connectives; proving things favours having very few [Burgess]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
Combining two distinct assertions does not necessarily lead to a single 'complex proposition' [Mill]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
All occurrences of variables in atomic formulas are free [Burgess]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
All names are names of something, real or imaginary [Mill]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Mill says names have denotation but not connotation [Mill, by Kripke]
Proper names are just labels for persons or objects, and the meaning is the object [Mill, by Lycan]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
The denotation of a definite description is flexible, rather than rigid [Burgess]
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess]
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess]
We can build one expanding sequence, instead of a chain of deductions [Burgess]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models leave out meaning, and just focus on truth values [Burgess]
We only need to study mathematical models, since all other models are isomorphic to these [Burgess]
We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
The only axioms needed are for equality, addition, and successive numbers [Mill, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [Mill]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Mill says logic and maths is induction based on a very large number of instances [Mill, by Ayer]
If two black and two white objects in practice produced five, what colour is the fifth one? [Lewis,CI on Mill]
Mill mistakes particular applications as integral to arithmetic, instead of general patterns [Dummett on Mill]
There are no such things as numbers in the abstract [Mill]
Things possess the properties of numbers, as quantity, and as countable parts [Mill]
Numbers have generalised application to entities (such as bodies or sounds) [Mill]
Different parcels made from three pebbles produce different actual sensations [Mill]
'2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts [Mill]
3=2+1 presupposes collections of objects ('Threes'), which may be divided thus [Mill]
Numbers denote physical properties of physical phenomena [Mill]
We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious [Mill]
Arithmetical results give a mode of formation of a given number [Mill]
12 is the cube of 1728 means pebbles can be aggregated a certain way [Mill]
Numbers must be of something; they don't exist as abstractions [Mill]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Mill is too imprecise, and is restricted to simple arithmetic [Kitcher on Mill]
Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started [Frege on Mill]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Numbers are a very general property of objects [Mill, by Brown,JR]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
Whatever is made up of parts is made up of parts of those parts [Mill]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
The essence is that without which a thing can neither be, nor be conceived to be [Mill]
10. Modality / A. Necessity / 2. Nature of Necessity
Necessity is what will be, despite any alternative suppositions whatever [Mill]
Necessity can only mean what must be, without conditions of any kind [Mill]
10. Modality / A. Necessity / 4. De re / De dicto modality
De re modality seems to apply to objects a concept intended for sentences [Burgess]
10. Modality / A. Necessity / 6. Logical Necessity
General consensus is S5 for logical modality of validity, and S4 for proof [Burgess]
Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess]
It is doubtful whether the negation of a conditional has any clear meaning [Burgess]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
Most perception is one-tenth observation and nine-tenths inference [Mill]
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
Clear concepts result from good observation, extensive experience, and accurate memory [Mill]
14. Science / A. Basis of Science / 5. Anomalies
Inductive generalisation is more reliable than one of its instances; they can't all be wrong [Mill]
14. Science / C. Induction / 1. Induction
The whole theory of induction rests on causes [Mill]
Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Mill, by Lipton]
14. Science / D. Explanation / 1. Explanation / a. Explanation
Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience [Mill, by Ruben]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Explanation is fitting of facts into ever more general patterns of regularity [Mill, by Ruben]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Causal inference is by spotting either Agreements or Differences [Mill, by Lipton]
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
The Methods of Difference and of Agreement are forms of inference to the best explanation [Mill, by Lipton]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
We can focus our minds on what is common to a whole class, neglecting other aspects [Mill]
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
We don't recognise comparisons by something in our minds; the concepts result from the comparisons [Mill]
18. Thought / E. Abstraction / 1. Abstract Thought
General conceptions are a necessary preliminary to Induction [Mill]
The study of the nature of Abstract Ideas does not belong to logic, but to a different science [Mill]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
A cause is the total of all the conditions which inevitably produce the result [Mill]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
Causes and conditions are not distinct, because we select capriciously from among them [Mill]
The strict cause is the total positive and negative conditions which ensure the consequent [Mill]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
Causation is just invariability of succession between every natural fact and a preceding fact [Mill]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
A cause is an antecedent which invariably and unconditionally leads to a phenomenon [Mill]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes [Mill, by Psillos]
In Mill's 'Method of Agreement' cause is the common factor in a range of different cases [Mill, by Psillos]
In Mill's 'Method of Difference' the cause is what stops the effect when it is removed [Mill, by Psillos]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
What are the fewest propositions from which all natural uniformities could be inferred? [Mill]