1. Philosophers tend to talk of belief as a ‘propositional attitude.’ As Fodor says:" The standard story about believing is that it's a two place relation, viz., a relation between a person and a proposition. My story is that believing is never an unmediated relation between a person and a proposition. In particular nobody grasps a proposition except insofar as he is appropriately related to some vehicle that expresses the proposition. " Fodor's story – that belief is a three-place relation (...) between a person, a proposition and a vehicle – is hardly non-standard; by assigning to propositions an essential place in acts of belief, he too is a ‘propositionalist’. My own view is that believing is primarily a relation between a believer and the world . While a great many human beliefs are propositional, many, perhaps most, are mondial and propositionless. As for animals who lack language, it may be that all their beliefs are mondial. In the present article, I show that distinguishing these two very different kinds of belief – de mundo as well as de dicto – enables one to explain phenomena of doxastic dissonance that standard propositionalist accounts cannot adequately explain .The next two sections, §1.1 and §1.2, are about ‘the world’ that is the doxastic object in the primary belief relation, providing needed background for the thesis that mondial belief is more primitive and basic than propositional belief.1.1. The world does not contain itself. Things in the world are …. (shrink)

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. (shrink)

Modern thinkers regard logic as a purely formal discipline like number theory, and not to be confused with any empirical discipline such as cognitive psychology, which may seek to characterize how people actually reason. Opposed to this is the traditional view that even a formal logic can be cognitively veridical – descriptive of procedures people actually follow in arriving at their deductive judgments (logic as Laws of Thought). In a cognitively veridical logic, any formal proof that a deductive judgment, intuitively (...) arrived at, is valid should ideally conform to the method the reasoning subject has used to arrive at that judgment. More specifically, it should reveal the actual reckoning process that the reasoning subject more or less consciously carries out when they make a deductive inference. That the common logical words used in everyday reasoning – words such as 'and', 'if,''some', 'is''not,' and 'all'– have fixed positive and negative charges has escaped the notice of modern logic. The present paper shows how, by unconsciously recognizing 'not' and 'all' as 'minus-words', while recognizing 'and', 'some', and 'is' as 'plus words', a child can intuitively reckon, for example, 'not (−) all (−) dogs are (+) friendly' as equivalent to 'some (+) dogs aren't (−) friendly': −(−D+F) = +D−F. (shrink)