David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 33 (3):245 - 290 (2012)
We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of ?sortal terms?, two theories that will feature prominently. Second, we propose that logic comprises four ?momental sectors?: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (in)valid deduction, inference or substitution. Third, we elaborate on two neglected features of logic: the various modes of negating some part(s) of a proposition R, not only its ?external? negation not-R; and the assertion of R in the pair of propositions ?it is (un)true that R? belonging to the neglected logic of asserted propositions, which is usually left unstated. We also address the overlooked task of testing the asserted truth-value of R. Fourth, we locate logic among other foundational studies: set theory and other theories of collections, metamathematics, axiomatisation, definitions, model theory, and abstract and operator algebras. Fifth, we test this characterisation in two important contexts: the formulation of some logical paradoxes, especially the propositional ones; and indirect proof-methods, especially that by contradiction. The outcomes differ for asserted propositions from those for unasserted ones. Finally, we reflect upon self-referring self-reference, and on the relationships between logical and mathematical knowledge. A subject index is appended
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Karl R. Popper (1972). Objective Knowledge. Oxford,Clarendon Press.
W. V. Quine (1986). Philosophy of Logic. Harvard University Press.
Peter M. Simons (1987). Parts: A Study in Ontology. Oxford University Press.
W. V. Quine (1953). From a Logical Point of View. Harvard University Press.
K. R. Popper (1966). Conjectures and Refutations. Les Etudes Philosophiques 21 (3):431-434.
Citations of this work BETA
No citations found.
Similar books and articles
Ernest Lepore & Kirk Ludwig (2002). What is Logical Form? In Gerhard Preyer & Georg Peter (eds.), Logical Form and Language. Clarendon Press 54--90.
Kevin C. Klement, Propositional Logic. Internet Encyclopedia of Philosophy.
Thomas Kroedel (2012). Implicit Definition and the Application of Logic. Philosophical Studies 158 (1):131-148.
Nicholas J. J. Smith (2012). Many-Valued Logics. In Gillian Russell & Delia Graff Fara (eds.), The Routledge Companion to Philosophy of Language. Routledge 636--51.
Maria van Der Schaar (2008). Locke and Arnauld on Judgment and Proposition. History and Philosophy of Logic 29 (4):327-341.
Peter Mittelstaedt (1978). The Metalogic of Quantum Logic. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:249 - 256.
Paul C. Rosenbloom (1950). The Elements of Mathematical Logic. New York]Dover Publications.
Kevin C. Klement, Russell-Myhill Paradox. Internet Encyclopedia of Philosophy.
Corine Besson (2009). Logical Knowledge and Gettier Cases. Philosophical Quarterly 59 (234):1-19.
Wesley H. Holliday (2015). Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism. Journal of Philosophical Logic 44 (1):1-62.
R. Gregory Taylor (2008). Symmetric Propositions and Logical Quantifiers. Journal of Philosophical Logic 37 (6):575 - 591.
Andrew Aberdein (2006). Managing Informal Mathematical Knowledge: Techniques From Informal Logic. Lecture Notes in Artificial Intelligence 4108:208--221.
Susanne Bobzien (1999). Logic: The Stoics (Part One). In Keimpe Algra & et al (eds.), The Cambridge History of Hellenistic Philosophy. Cambridge University Press
Alfred North Whitehead & Bertrand Russell (1962). Principia Mathematica, to *56. Cambridge University Press.
Added to index2012-06-30
Total downloads31 ( #128,514 of 1,906,922 )
Recent downloads (6 months)2 ( #345,620 of 1,906,922 )
How can I increase my downloads?