Thus axiomatic and semantic approaches to truth are intertwined.
Woodger has done in The Axiomatic Method in Biology (1937) and Clark Hull (for psychology) in Principles of Behaviour (1943).
The basic logical tool is essentially axiomatic formal analysis.
Mathematical theories such as set theory and category theory are axiomatic theories.
In fact, this is what you would expect if the proposed axiomatic solution is at all plausible.
The Burgess-Xu axiomatic system and some of its extensions are presented in the supplementary document:
It is commonplace to explore alternatives to an axiomatic system and expected utility theory is no exception.
The main ideas are discussed in the entry on axiomatic theories of truth, to which we will leave the details.
See Pauly 2008 and Endriss 2011 for interesting discussions of axiomatic characterization results from a logician’s point-of-view.
In this way, logic, the axiomatic method (such as that employed in geometry), and semiotic (the general science of signs) converged toward metalogic.
Within this approach, Arrow's axiomatic method is perhaps even more influential than his impossibility theorem (on the axiomatic method, see Thomson 2000).
Some authors have also looked into axiomatic theories of truth based on non-classical logic (see, for example, Field 2008, Halbach and Horsten 2006, Leigh and Rathjen 2012).
This reduction shows that, if the premises of the reducible mood are true, then it follows, by rules of conversion and one of the axiomatic moods, that the conclusion is true.
Since Zermelo was working within the axiomatic tradition of Hilbert, he and his followers were interested in the kinds of questions that concern any axiomatic theory, such as: Is ZF consistent?
The contributions of Gottlob Frege (1848–1925) to logic from the period 1879–1903, based on an axiomatic approach to logic, had very little influence at the time (and the same can be said of the diagrammatic systems of C.S.
Curry’s paradox | dialetheism | Gödel, Kurt | Gödel, Kurt: incompleteness theorems | logic: many-valued | logic: provability | self-reference | Tarski, Alfred | Tarski, Alfred: truth definitions | truth | truth: axiomatic theories of | truth: revision theory of | vagueness
compositionality | logic: and games | logic: dependence | logic: independence friendly | logic: infinitary | logic: intuitionistic | logic: temporal | meaning, theories of | model theory | model theory: first-order | Tarski, Alfred | truth | truth: axiomatic theories of | truth: deflationary theory of | truth: revision theory of
dialetheism | Gödel, Kurt: incompleteness theorems | lambda calculus, the | liar paradox | logic: algebraic propositional | logic: combinatory | logic: linear | logic: paraconsistent | logic: substructural | negation | paradoxes: and contemporary logic | Russell’s paradox | self-reference | set theory: alternative axiomatic theories
In one of his last papers, Axiomatic Versus Constructive Procedures in Mathematics, written sometime after 1953, he saw the battle between Hilbertian formalism and Brouwerian intuitionism in which he had participated in the 1920s as having given way to a “dextrous blending” of the axiomatic approach to mathematics championed by Bourbaki and the algebraists (themselves mathematical descendants of Hilbert) with constructive procedures associated with geometry and topology.
Curry’s paradox | epistemic paradoxes | Fitch’s paradox of knowability | Frege, Gottlob | Frege, Gottlob: theorem and foundations for arithmetic | liar paradox | logic: linear | logic: paraconsistent | logic: substructural | Quine, Willard van Orman: New Foundations | recursive functions | Russell, Bertrand | Russell’s paradox | set theory | set theory: alternative axiomatic theories | set theory: constructive and intuitionistic ZF | set theory: early development | set theory: non-wellfounded | set theory: Zermelo’s axiomatization of | Sorites paradox | Tarski, Alfred: truth definitions | truth | truth: axiomatic theories of | type theory | vagueness | Zeno of Elea | Zeno of Elea: Zeno’s paradoxes
- containing aphorisms or maxims
Example: axiomatic wisdom
- evident without proof or argument
Example: an axiomatic truth
- of or relating to or derived from axioms
Example: axiomatic physics
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Currys paradox | epistemic paradoxes | Fitchs paradox of knowability | Frege Gottlob | Frege Gottlob theorem and foundations for arithmetic | liar paradox | logic linear | logic paraconsistent | logic substructural | Quine Willard van Orman New Foundations | recursive functions | Russell Bertrand | Russells paradox | set theory | set theory alternative axiomatic theories | set theory constructive and intuitionistic ZF | set theory early development | set theory non-wellfounded | set theory Zermelos axiomatization of | Sorites paradox | Tarski Alfred truth definitions | truth | truth axiomatic theories of | type theory | vagueness | Zeno of Elea | Zeno of Elea Zenos paradoxes