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 'horsepower'

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 onetenth observation and ninetenths inference

12. Knowledge Sources / D. Empiricism / 4. ProEmpiricism
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?
