Adam Morton

Complex Individuals and Multigrade Relations

Goodman and Leonard pointed out in 1940 that by using the calculus of individuals one could give formalizations within first-order logic of many idioms involving what they called multigrade relations. These are relations such as are brothers, are compatriots, or built the bridge, which do not take any fixed number of arguments. One can say a and b are compatriots or a and b and . . . and z are compatriots. The purpose of this paper is to show that the reverse is also true; I give a formal account of multigrade relations and some related idioms, and show that there is a natural translation of the vocabulary of the calculus of individuals into the notation I provide which takes all the theorems of that calculus to valid sentences of the formalism.

Contrastivity and indistinguishability

We give a general description of a class of contrastive constructions, intended to capture what is common to contrastive knowledge, belief, hope, fear, understanding and other cases where one expresses a propositional attitude in terms of “rather than”. The crucial element is the agent’s incapacity to distinguish some possibilities from others. Contrastivity requires a course‐graining of the set of possible worlds. As a result, contrastivity will usually cut across logical consequence, so that an agent can have an attitude to p rather than q but not to r rather than q, where r is a logical consequence of p. We relate these ideas to some general issues about thought, such as the question of whether all possibilities that can be distinguished in emotion can be distinguished in belief.

Human bounds: rationality for our species

Is there such a thing as bounded rationality? I first try to make sense of the question, and then to suggest which of the disambiguated versions might have answers. We need an account of bounded rationality that takes account of detailed contingent facts about the ways in which human beings fail to perform as we might ideally want to. But we should not think in terms of rules or norms which define good responses to an individual’s limitations, but rather in terms of desiderata, situations that limited agents can hope to achieve, and corresponding virtues of achieving them. We should not take formal theories defining optimal behavior in watered-down bounded form, even though they can impose enormous computational or cognitive demands.

The possible in the actual

7The phrasing is a little foxy here, since Ive suddenly switched to talking of understanding sentences instead of talking straightforwardly of sentence truth value. This is because of difficulties with attributing truth value to ambiguous sentences-more of which will be said below. My justification turns on Davidsons claim that one sense of understanding the meaning is knowing the truth conditions. The way one would know the truth conditions using the incorrect (T 2) would not allow a proper understanding of what was being said to the child. 8 This also raises a difficulty for Davidson if the notion of the speakers changing meaning or intent involves us in irreducible notions of linguistic meaning. See below for remarks on this. 9 The qualification reasonable is here because there is a good bit of leeway in deciding what is to go into syntax. For example, some of the things Chomsky mentions in [1] as possibilities for inclusion in syntax have generally been considered part of semantics. 10 There is considerable discussion of this problem in literature in the philosophy of science. I discuss the problem and its effects on reference in On Criteria of Meaning Change, British Journal for the Philosophy of Science 22 (1971), 131-144.

Conventional Norms of Reasoning

There are conventional norms of reasoning. That is, we have conventions about which patterns of reasoning we encourage or disapprove of. RESUME: Il existe des normes conventionnelles du raisonnement. Cest-a-dire que nous avons des conventions quant aux modeles de raisonnement que nous encourageons et desapprouvons. I am going to argue that there are conventional norms of reasoning. That is, that there are conventions, with the element of arbitrariness that is essential to a convention, that we use to regulate our thinking. We could have used other conventions. I expect that, stated this way, the idea seems implausible. It sounds like the suggestion that given that one believes that it is snowing and also believes that when it is snowing gloves are a good idea, one then arbitrarily goes along with the convention that gloves are a good idea. Other conventions also are possible, so that ones conclusion might have been to go bare-handed, or to put both gloves on one hand. This seems crazy, especially in winter. Well, my suggestion is not this crazy thing. It is rather that we have conventions about which patterns of reasoning we encourage or disapprove of , about when and how we push one another into reasoning various ways, and to some extent how we react to these pushes. Some thinking works better than others for many reasons, some of which will not be changed by any amount of convention. But with which aspects of thinking we nudge one another, and how we direct our nudges, is something for which there is a large element of convention.

Abstracts of Comments: The Saturation of Dyspepsia: Comments on Wilson

OF COMMENTS The Saturation of Dyspepsia: Comments on Wilson By Adam Morton UNIVERSITY OF OITJAWA Wilson argues that, because of the way the world happens to be, a predicate like dyspeptic must have just two places, for a person and a time, and not (for example) three places, for a person, a time, and a place. The relevant fact about the world, which is never made very explicit, seems to be that people and the like are at only one place at one time (but can of course be at two times at the same place). Thus the history of the individual plus a time-index pins down the time of an event, while the same history and a place-index need not pin down its time. This explains why we can get along with only two-place predicates to express such things; it does not show that we cannot use three-place idioms to say the same things. I give some reasons for not being convinced by Wilsons arguments for the stronger conclusion-that we cannot construe our languages as referring irreducibly to times. (Essentially, the arguments seem to depend on question-begging principles about the ways propositions can be relatied to one another.) And I give some reasons why it might be useful to keep some spare argument-places in reserve. ABSTRACT OF SYMPOSIUM PAPER Knowledge and Skepticism By Robert NozickOF SYMPOSIUM PAPER Knowledge and Skepticism By Robert Nozick