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Single Idea 9020

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

Full Idea

We chose a standard grammar in which the simple sentences are got by predication, and all further sentences are generated from these by negation, conjunction, and existential quantification.

Gist of Idea

My logical grammar has sentences by predication, then negation, conjunction, and existential quantification

Source

Willard Quine (Philosophy of Logic [1970], Ch.3)

Book Ref

Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.36


A Reaction

It is interesting that we 'choose' our logic, apparently guided by an imperative to achieve minimal ontology. Of these basic ingredients, negation and predication are the more mysterious, especially the latter. Quine is a bit of an 'ostrich' about that.


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

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