Ideas of Ian Hacking, by Theme

[Canadian, b.1936, At theUniversity of Toronto, and at Stanford University.]

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1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
Gassendi is the first great empiricist philosopher
2. Reason / D. Definition / 3. Types of Definition
A decent modern definition should always imply a semantics
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction
Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C'
Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
The various logics are abstractions made from terms like 'if...then' in English
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic is the strongest complete compact theory with L÷wenheim-Skolem
A limitation of first-order logic is that it cannot handle branching quantifiers
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order completeness seems to need intensional entities and possible worlds
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
If logical truths essentially depend on logical constants, we had better define the latter
With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers
5. Theory of Logic / J. Model Theory in Logic / 3. L÷wenheim-Skolem Theorems
If it is a logic, the L÷wenheim-Skolem theorem holds for it
10. Modality / B. Possibility / 6. Probability
Probability was fully explained between 1654 and 1812
Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence)
Epistemological probability based either on logical implications or coherent judgments
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
In the medieval view, only deduction counted as true evidence
Formerly evidence came from people; the new idea was that things provided evidence
14. Science / A. Basis of Science / 3. Experiment
An experiment is a test, or an adventure, or a diagnosis, or a dissection
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Follow maths for necessary truths, and jurisprudence for contingent truths