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Full Idea
'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference.
Gist of Idea
'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction
Source
Ian Hacking (What is Logic? [1979], §06.2)
Book Ref
'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.233
A Reaction
That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic.
Related Idea
Idea 13351 'Thinning' allows that if premisses entail a conclusion, then adding further premisses makes no difference [Bostock]
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |