David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
In the 17th century, Hobbes stated that we reason by addition and subtraction. Historians of logic note that Hobbes thought of reasoning as “a ‘species of computation’” but point out that “his writing contains in fact no attempt to work out such a project.” Though Leibniz mentions the plus/minus character of the positive and negative copulas, neither he nor Hobbes say anything about a plus/minus character of other common logical words that drive our deductive judgments, words like ‘some’, ‘all’, ‘if’, and ‘and’, each of which actually turns out to have an oppositive, character that allows us, “in our silent reasoning,” to ignore its literal meaning and to reckon with it as one reckons with a plus or a minus operator in elementary algebra or arithmetic. These ‘logical constants’ of natural language figure crucially in our everyday reasoning. Because Hobbes and Leibniz did not identify them as the plus and minus words we reason with, their insight into what goes on in ‘ratiocination’ did not provide a guide for a research program that could develop a +/- logic that actually describes how we reason deductively. I will argue that such a +/- logic provides a way back from modern predicate logic—the logic of quantifiers and bound variables that is now ‘standard logic’—to an Aristotelian term logic of natural language that had been the millennial standard logic.
|Keywords||logic term logic predicate logic ratiotination Aristotle Frege Deductive Reasoning Cognitive Science|
|Categories||categorize this paper)|
|External links||This entry has no external links. Add one.|
|Through your library||Only published papers are available at libraries|
Similar books and articles
Fred Sommers (2008). Ratiocination: An Empirical Account. Ratio 21 (2):115–133.
Stewart Shapiro (1995). Reasoning, Logic and Computation. Philosophia Mathematica 3 (1):31-51.
Penelope Rush (2012). Logic or Reason? Logic and Logical Philosophy 21 (2):127-163.
Greg Restall (2005). Logic: An Introduction. Routledge.
D. S. Clarke (1973). Deductive Logic. Carbondale,Southern Illinois University Press.
Pascal Engel (2006). Logic, Reasoning and the Logical Constants. Croatian Journal of Philosophy 6 (2):219-235.
Kai F. Wehmeier (2008). Wittgensteinian Tableaux, Identity, and Co-Denotation. Erkenntnis 69 (3):363 - 376.
Tyler Burge (2003). Logic and Analyticity. Grazer Philosophische Studien 66 (1):199-249.
Gilbert Harman (2009). Field on the Normative Role of Logic. Proceedings of the Aristotelian Society 109 (1pt3):333 - 335.
Jim Mackenzie (1989). Reasoning and Logic. Synthese 79 (1):99 - 117.
Added to index2012-06-12
Total downloads68 ( #16,945 of 1,006,301 )
Recent downloads (6 months)20 ( #4,917 of 1,006,301 )
How can I increase my downloads?