### Ideas from 'System of Logic' by John Stuart Mill [1843], by Theme Structure

#### [found in 'System of Logic (9th ed, 2 vols)' by Mill,John Stuart [Longmans, Green etc 1875,-]].

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###### 4. Formal Logic / F. Set Theory ST / 7. Natural Sets
 8625 What physical facts could underlie 0 or 1, or very large numbers? [Frege]
###### 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
 17895 Combining two distinct assertions does not necessarily lead to a single 'complex proposition'
###### 5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
 10427 All names are names of something, real or imaginary
###### 5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
 4944 Mill says names have denotation but not connotation [Kripke]
 7762 Proper names are just labels for persons or objects, and the meaning is the object [Lycan]
###### 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
 9801 Numbers must be assumed to have identical units, as horses are equalised in 'horse-power'
###### 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
 8742 The only axioms needed are for equality, addition, and successive numbers [Shapiro]
###### 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
 9800 Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal
###### 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
 5201 Mill says logic and maths is induction based on a very large number of instances [Ayer]
 9360 If two black and two white objects in practice produced five, what colour is the fifth one? [Lewis,CI]
 9888 Mill mistakes particular applications as integral to arithmetic, instead of general patterns [Dummett]
 9796 Things possess the properties of numbers, as quantity, and as countable parts
 9795 Numbers have generalised application to entities (such as bodies or sounds)
 9794 There are no such things as numbers in the abstract
 9799 3=2+1 presupposes collections of objects ('Threes'), which may be divided thus
 9803 We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious
 9802 Numbers denote physical properties of physical phenomena
 9804 Arithmetical results give a mode of formation of a given number
 9805 12 is the cube of 1728 means pebbles can be aggregated a certain way
 8741 Numbers must be of something; they don't exist as abstractions
 9797 '2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts
 9798 Different parcels made from three pebbles produce different actual sensations
###### 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
 12411 Mill is too imprecise, and is restricted to simple arithmetic [Kitcher]
 5656 Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started [Frege]
###### 6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
 9624 Numbers are a very general property of objects [Brown,JR]
###### 9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
 9806 Whatever is made up of parts is made up of parts of those parts
###### 9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
 11156 The essence is that without which a thing can neither be, nor be conceived to be
###### 10. Modality / A. Necessity / 2. Nature of Necessity
 12190 Necessity is what will be, despite any alternative suppositions whatever
###### 12. Knowledge Sources / B. Perception / 6. Inference in Perception
 16859 Most perception is one-tenth observation and nine-tenths inference
###### 12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
 9082 Clear concepts result from good observation, extensive experience, and accurate memory
###### 14. Science / A. Basis of Science / 5. Anomalies
 16860 Inductive generalisation is more reliable than one of its instances; they can't all be wrong
###### 14. Science / C. Induction / 1. Induction
 16843 Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Lipton]
 16845 The whole theory of induction rests on causes
###### 14. Science / D. Explanation / 1. Explanation / a. Explanation
 17086 Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience [Ruben]
###### 14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
 17091 Explanation is fitting of facts into ever more general patterns of regularity [Ruben]
###### 14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
 16805 Causal inference is by spotting either Agreements or Differences [Lipton]
###### 14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
 16835 The Methods of Difference and of Agreement are forms of inference to the best explanation [Lipton]
###### 15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
 9079 We can focus our minds on what is common to a whole class, neglecting other aspects
###### 15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
 9081 We don't recognise comparisons by something in our minds; the concepts result from the comparisons
###### 18. Thought / E. Abstraction / 1. Abstract Thought
 9080 General conceptions are a necessary preliminary to Induction
 9078 The study of the nature of Abstract Ideas does not belong to logic, but to a different science
###### 26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
 8345 A cause is the total of all the conditions which inevitably produce the result
###### 26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
 10391 Causes and conditions are not distinct, because we select capriciously from among them
 14547 The strict cause is the total positive and negative conditions which ensure the consequent
###### 26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
 8377 Causation is just invariability of succession between every natural fact and a preceding fact
###### 26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
 14545 A cause is an antecedent which invariably and unconditionally leads to a phenomenon
###### 26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
 4773 Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes [Psillos]
 4775 In Mill's 'Method of Agreement' cause is the common factor in a range of different cases [Psillos]
 4776 In Mill's 'Method of Difference' the cause is what stops the effect when it is removed [Psillos]
###### 26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
 9417 What are the fewest propositions from which all natural uniformities could be inferred?