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Single Idea 19243

[filed under theme 14. Science / A. Basis of Science / 2. Demonstration ]

Full Idea

Were every probable inference less certain than its premises, science, which piles inference upon inference, often quite deeply, would soon be in a bad way.

Gist of Idea

If each inference slightly reduced our certainty, science would soon be in trouble

Source

Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV)

Book Ref

Peirce,Charles Sanders: 'Reasoning and the Logic of Things', ed/tr. Ketner,K.L. [Harvard 1992], p.165

A Reaction

This seems to endorse Aristotle's picture of demonstration about scientific and practical things as being a form of precise logic, rather than progressive probabilities. Our generalisations may be more certain than the particulars they rely on.

The 27 ideas with the same theme [proving physical facts by observation and reason]:

16647 Demonstration starts from a definition of essence, so we can derive (or conjecture about) the properties [Aristotle]
24048 Demonstrations move from starting-points to deduced conclusions [Aristotle]
12309 There cannot be a science of accidentals, but only of general truths [Aristotle]
11386 Demonstrations about particulars must be about everything of that type [Aristotle]
24068 Demonstration is more than entailment, as the explanatory order must match the causal order [Aristotle, by Koslicki]
17310 Aristotle gets asymmetric consequence from demonstration, which reflects real causal priority [Aristotle, by Koslicki]
21359 Aristotle doesn't actually apply his theory of demonstration to his practical science [Leroi on Aristotle]
12365 We can know by demonstration, which is a scientific deduction leading to understanding [Aristotle]
1667 Premises must be true, primitive and immediate, and prior to and explanatory of conclusions [Aristotle]
12371 A demonstration is a deduction which proceeds from necessities [Aristotle]
10918 Demonstrative understanding rests on necessary features of the thing in itself [Aristotle]
12374 Demonstrations must be necessary, and that depends on the middle term [Aristotle]
1674 All demonstration is concerned with existence, axioms and properties [Aristotle]
12148 Demonstrations are syllogisms which give explanations [Aristotle]
1679 Universal demonstrations are about thought; particular demonstrations lead to perceptions [Aristotle]
1680 Demonstration is better with fewer presuppositions, and it is quicker if these are familiar [Aristotle]
12147 The principles of demonstrations are definitions [Aristotle]
12383 There must be definitions before demonstration is possible [Aristotle]
1691 Aim to get definitions of the primitive components, thus establishing the kind, and work towards the attributes [Aristotle]
20779 Demonstration derives what is less clear from what is clear [Stoic school, by Diog. Laertius]
16577 Induction is not demonstration, because not all of the instances can be observed [Buridan]
19243 If each inference slightly reduced our certainty, science would soon be in trouble [Peirce]
16799 Inductive inference is not proof, but weighing evidence and probability [Lipton]
16798 We infer from evidence by working out what would explain that evidence [Lipton]
22110 Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump]
15111 In demonstration, the explanatory order must mirror the causal order of the phenomena [Koslicki]
15115 In a demonstration the middle term explains, by being part of the definition [Koslicki]