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Single Idea 4632
[filed under theme 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
]
Full Idea
A 'natural' system of deduction does not posit any axioms, but looks instead for its formulae to the practices of ordinary rationality.
Gist of Idea
'Natural' systems of deduction are based on normal rational practice, rather than on axioms
Source
J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §1.09)
Book Ref
Baggini,J and Fosl,P.S.: 'The Philosopher's Toolkit' [Blackwells 2003], p.26
A Reaction
Presumably there is some middle ground, where we attempt to infer the axioms of normal practice, and then build a strict system on them. We must be allowed to criticise 'normal' rationality, I hope.
The
17 ideas
with the same theme
[statements treated as true without question]:
2145
|
In mathematics certain things have to be accepted without further explanation
[Plato]
|
562
|
Axioms are the underlying principles of everything, and who but the philosopher can assess their truth?
[Aristotle]
|
573
|
The axioms of mathematics are part of philosophy
[Aristotle]
|
1668
|
An axiom is a principle which must be understood if one is to learn anything
[Aristotle]
|
20791
|
Chrysippus has five obvious 'indemonstrables' of reasoning
[Chrysippus, by Diog. Laertius]
|
5620
|
Philosophy has no axioms, as it is just rational cognition of concepts
[Kant]
|
9154
|
Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence
[Frege, by Burge]
|
9585
|
Since every definition is an equation, one cannot define equality itself
[Frege]
|
9542
|
The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules
[Russell/Whitehead, by Hughes/Cresswell]
|
9013
|
We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)'
[Quine]
|
13610
|
A logic with ¬ and → needs three axiom-schemas and one rule as foundation
[Bostock]
|
8086
|
Predicate logic retains the axioms of propositional logic
[Devlin]
|
6299
|
Axioms are often affirmed simply because they produce results which have been accepted
[Resnik]
|
8476
|
Axiomatization simply picks from among the true sentences a few to play a special role
[Orenstein]
|
7797
|
Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems
[Girle]
|
4631
|
In ideal circumstances, an axiom should be such that no rational agent could possibly object to its use
[Baggini /Fosl]
|
4632
|
'Natural' systems of deduction are based on normal rational practice, rather than on axioms
[Baggini /Fosl]
|