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Single Idea 16881

[filed under theme 5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic ]

Full Idea

Since in view of the boundless multitude of laws that can be enunciated we cannot list them all, we cannot achieve completeness except by searching out those that, by their power, contain all of them.

Gist of Idea

The laws of logic are boundless, so we want the few whose power contains the others

Source

Gottlob Frege (Begriffsschrift [1879], §13)

Book Ref

'From Frege to Gödel 1879-1931', ed/tr. Heijenoort,Jean van [Harvard 1967], p.29

A Reaction

He refers to these laws in the previous sentence as the 'core'. His talk of 'power' is music to my ears, since it implies a direction of explanation. Burge says the power is that of defining other concepts.

The 34 ideas with the same theme [broad views about different systems of logic]:

18794 Logic has precise boundaries, and is the formal rules for all thinking [Kant]
7728 Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner]
16881 The laws of logic are boundless, so we want the few whose power contains the others [Frege]
6110 Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell]
9358 There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI]
18724 In logic nothing is hidden [Wittgenstein]
16908 We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein]
23502 Logic fills the world, to its limits [Wittgenstein]
23504 Logic concerns everything that is subject to law; the rest is accident [Wittgenstein]
13979 Logic studies consequence, compatibility, contradiction, corroboration, necessitation, grounding.... [Ryle]
13010 In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine]
9020 My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine]
12666 We can base logic on acceptability, and abandon the Fregean account by truth-preservation [Ellis]
11066 Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna]
9722 Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton]
3809 If complex logic requires rules, then so does basic logic [Searle]
12595 We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman]
3093 Any two states are logically linked, by being entailed by their conjunction [Harman]
10766 Logic is either for demonstration, or for characterizing structures [Tharp]
12342 Topos theory explains the plurality of possible logics [Badiou]
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
13831 Logic is based on transitions between sentences [Prawitz]
9457 The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette]
7681 Logic describes inferences between sentences expressing possible properties of objects [Jacquette]
8091 Situation theory is logic that takes account of context [Devlin]
13627 There is no 'correct' logic for natural languages [Shapiro]
13642 Logic is the ideal for learning new propositions on the basis of others [Shapiro]
14980 There is a real issue over what is the 'correct' logic [Sider]
15000 'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or ¬p' [Sider]
13235 Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall]
13238 Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall]
17741 To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
18815 Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt]