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
What physical facts could underlie 0 or 1, or very large numbers?
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'
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
All names are names of something, real or imaginary
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Mill says names have denotation but not connotation
Proper names are just labels for persons or objects, and the meaning is the object
6. Mathematics / A. Nature of Mathematics / 3. Numbers / o. Units
Numbers must be assumed to have identical units, as horses are equalised in 'horse-power'
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / a. Axioms for numbers
The only axioms needed are for equality, addition, and successive numbers
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / b. Greek arithmetic
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
Mill says logic and maths is induction based on a very large number of instances
If two black and two white objects in practice produced five, what colour is the fifth one?
Mill mistakes particular applications as integral to arithmetic, instead of general patterns
Numbers have generalised application to entities (such as bodies or sounds)
Things possess the properties of numbers, as quantity, and as countable parts
There are no such things as numbers in the abstract
'2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts
Different parcels made from three pebbles produce different actual sensations
3=2+1 presupposes collections of objects ('Threes'), which may be divided thus
Numbers denote physical properties of physical phenomena
We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious
Arithmetical results give a mode of formation of a given number
12 is the cube of 1728 means pebbles can be aggregated a certain way
Numbers must be of something; they don't exist as abstractions
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Mill is too imprecise, and is restricted to simple arithmetic
Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Numbers are a very general property of objects
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
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
10. Modality / A. Necessity / 2. Nature of Necessity
Necessity is what will be, despite any alternative suppositions whatever
12. Knowledge Sources / B. Perception / 6. Inference in Perception
Most perception is one-tenth observation and nine-tenths inference
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
Clear concepts result from good observation, extensive experience, and accurate memory
14. Science / A. Basis of Science / 5. Anomalies
Inductive generalisation is more reliable than one of its instances; they can't all be wrong
14. Science / C. Induction / 1. Induction
Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction
The whole theory of induction rests on causes
14. Science / D. Explanation / 1. Explanation / a. Explanation
Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience
14. Science / D. Explanation / 2. Types of Explanation / d. Lawlike explanations
Explanation is fitting of facts into ever more general patterns of regularity
14. Science / D. Explanation / 2. Types of Explanation / f. Causal explanations
Causal inference is by spotting either Agreements or Differences
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
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
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
18. Thought / E. Abstraction / 1. Abstract Thought
The study of the nature of Abstract Ideas does not belong to logic, but to a different science
General conceptions are a necessary preliminary to Induction
26. Natural Theory / C. Causation / 2. Particular Causation / c. Conditions of causation
A cause is the total of all the conditions which inevitably produce the result
26. Natural Theory / C. Causation / 2. Particular Causation / d. Selecting the cause
Causes and conditions are not distinct, because we select capriciously from among them
The strict cause is the total positive and negative conditions which ensure the consequent
26. Natural Theory / C. Causation / 3. General Causation / a. Constant conjunction
Causation is just invariability of succession between every natural fact and a preceding fact
26. Natural Theory / C. Causation / 3. General Causation / d. Causal necessity
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
Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes
In Mill's 'Method of Agreement' cause is the common factor in a range of different cases
In Mill's 'Method of Difference' the cause is what stops the effect when it is removed
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?