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Single Idea 17638

[filed under theme 2. Reason / A. Nature of Reason / 6. Coherence ]

Full Idea

Two obvious propositions of which one can be deduced from the other both become more certain than either in isolation; thus in a complicated deductive system, many parts of which are obvious, the total probability may become all but absolute certainty.

Gist of Idea

If one proposition is deduced from another, they are more certain together than alone

Source

Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279)

Book Ref

Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.279

A Reaction

Thagard picked this remark out, in support of his work on coherence.

The 24 ideas with the same theme [principles of mutual support between propositions]:

2082 A rational account is essentially a weaving together of things with names [Plato]
1672 Maybe everything could be demonstrated, if demonstration can be reciprocal or circular [Aristotle]
17638 If one proposition is deduced from another, they are more certain together than alone [Russell]
2764 Full coherence might involve consistency and mutual entailment of all propositions [Blanshard, by Dancy,J]
17070 Coherence is consilience, simplicity, analogy, and fitting into a web of belief [Smart]
17072 We need comprehensiveness, as well as self-coherence [Smart]
12596 Reasoning aims at increasing explanatory coherence [Harman]
12599 Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman]
6954 A coherent conceptual scheme contains best explanations of most of your beliefs [Harman]
9784 A false proposition isn't truer because it is part of a coherent system [Cartwright,R]
4262 If the only aim was consistent beliefs then new evidence and experiments would be irrelevant [Goldman]
12770 We may end up with a huge theory of carefully constructed falsehoods [Fraassen]
8877 We can't attain a coherent system by lopping off any beliefs that won't fit [Sosa]
8833 Why should we prefer coherent beliefs? [Klein,P]
8797 The negation of all my beliefs about my current headache would be fully coherent [Sosa]
3700 Coherence can't be validated by appeal to coherence [Bonjour]
8893 For any given area, there seem to be a huge number of possible coherent systems of beliefs [Bonjour]
10237 Coherence is a primitive, intuitive notion, not reduced to something formal [Shapiro]
17596 Coherence problems have positive and negative restraints; solutions maximise constraint satisfaction [Thagard]
17597 Coherence is explanatory, deductive, conceptual, analogical, perceptual, and deliberative [Thagard]
17598 Explanatory coherence needs symmetry,explanation,analogy,data priority, contradiction,competition,acceptance [Thagard]
12801 Coherentists seek relations among beliefs that are simple, conservative and explanatory [Foley]
8616 How can multiple statements, none of which is tenable, conjoin to yield a tenable conclusion? [Elgin]
8617 Statements that are consistent, cotenable and supportive are roughly true [Elgin]