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
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8625
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What physical facts could underlie 0 or 1, or very large numbers? [Frege]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
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17895
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Combining two distinct assertions does not necessarily lead to a single 'complex proposition'
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5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
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10427
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All names are names of something, real or imaginary
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5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
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4944
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Mill says names have denotation but not connotation [Kripke]
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7762
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Proper names are just labels for persons or objects, and the meaning is the object [Lycan]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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9801
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Numbers must be assumed to have identical units, as horses are equalised in 'horse-power'
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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8742
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The only axioms needed are for equality, addition, and successive numbers [Shapiro]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
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9800
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Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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5201
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Mill says logic and maths is induction based on a very large number of instances [Ayer]
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9360
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If two black and two white objects in practice produced five, what colour is the fifth one? [Lewis,CI]
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9888
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Mill mistakes particular applications as integral to arithmetic, instead of general patterns [Dummett]
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9796
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Things possess the properties of numbers, as quantity, and as countable parts
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9794
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There are no such things as numbers in the abstract
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9795
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Numbers have generalised application to entities (such as bodies or sounds)
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9798
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Different parcels made from three pebbles produce different actual sensations
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9797
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'2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts
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9799
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3=2+1 presupposes collections of objects ('Threes'), which may be divided thus
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9803
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We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious
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9802
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Numbers denote physical properties of physical phenomena
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9804
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Arithmetical results give a mode of formation of a given number
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9805
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12 is the cube of 1728 means pebbles can be aggregated a certain way
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8741
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Numbers must be of something; they don't exist as abstractions
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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12411
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Mill is too imprecise, and is restricted to simple arithmetic [Kitcher]
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5656
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Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started [Frege]
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6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
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9624
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Numbers are a very general property of objects [Brown,JR]
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9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
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9806
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Whatever is made up of parts is made up of parts of those parts
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9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
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11156
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The essence is that without which a thing can neither be, nor be conceived to be
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10. Modality / A. Necessity / 2. Nature of Necessity
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12190
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Necessity is what will be, despite any alternative suppositions whatever
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22623
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Necessity can only mean what must be, without conditions of any kind
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12. Knowledge Sources / B. Perception / 6. Inference in Perception
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16859
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Most perception is one-tenth observation and nine-tenths inference
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12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
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9082
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Clear concepts result from good observation, extensive experience, and accurate memory
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14. Science / A. Basis of Science / 5. Anomalies
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16860
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Inductive generalisation is more reliable than one of its instances; they can't all be wrong
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14. Science / C. Induction / 1. Induction
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16843
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Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Lipton]
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16845
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The whole theory of induction rests on causes
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14. Science / D. Explanation / 1. Explanation / a. Explanation
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17086
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Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience [Ruben]
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14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
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17091
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Explanation is fitting of facts into ever more general patterns of regularity [Ruben]
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14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
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16805
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Causal inference is by spotting either Agreements or Differences [Lipton]
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14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
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16835
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The Methods of Difference and of Agreement are forms of inference to the best explanation [Lipton]
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15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
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9079
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We can focus our minds on what is common to a whole class, neglecting other aspects
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15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
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9081
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We don't recognise comparisons by something in our minds; the concepts result from the comparisons
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18. Thought / E. Abstraction / 1. Abstract Thought
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9078
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The study of the nature of Abstract Ideas does not belong to logic, but to a different science
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9080
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General conceptions are a necessary preliminary to Induction
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26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
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8345
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A cause is the total of all the conditions which inevitably produce the result
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26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
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10391
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Causes and conditions are not distinct, because we select capriciously from among them
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14547
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The strict cause is the total positive and negative conditions which ensure the consequent
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26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
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8377
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Causation is just invariability of succession between every natural fact and a preceding fact
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26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
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14545
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A cause is an antecedent which invariably and unconditionally leads to a phenomenon
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26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
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4773
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Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes [Psillos]
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4775
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In Mill's 'Method of Agreement' cause is the common factor in a range of different cases [Psillos]
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4776
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In Mill's 'Method of Difference' the cause is what stops the effect when it is removed [Psillos]
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26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
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9417
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What are the fewest propositions from which all natural uniformities could be inferred?
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