Proposition

About: Proposition is a research topic. Over the lifetime, 1591 publications have been published within this topic receiving 29722 citations.

Calibration of probabilities: the state of the art to 1980

Abstract: From the subjectivist point of view (de Finetti, 1937/1964), a probability is a degree of belief in a proposition. It expresses a purely internal state; there is no “right,” “correct,” or “objective” probability residing somewhere “in reality” against which one's degree of belief can be compared. In many circumstances, however, it may become possible to verify the truth or falsity of the proposition to which a probability was attached. Today, one assesses the probability of the proposition “it will rain tomorrow.” Tomorrow, one looks at the rain gauge to see whether or not it has rained. When possible, such verification can be used to determine the adequacy of probability assessments. Winkler and Murphy (1968b) have identified two kinds of “goodness” in probability assessments: normative goodness, which reflects the degree to which assessments express the assessor's true beliefs and conform to the axioms of probability theory, and substantive goodness, which reflects the amount of knowledge of the topic area contained in the assessments. This chapter reviews the literature concerning yet another aspect of goodness, called calibration. If a person assesses the probability of a proposition being true as .7 and later finds that the proposition is false, that in itself does not invalidate the assessment. However, if a judge assigns .7 to 10,000 independent propositions, only 25 of which subsequently are found to be true, there is something wrong with these assessments.

A Theory of Conditionals

Abstract: A conditional sentence expresses a proposition which is a function of two other propositions, yet not one which is a truth function of those propositions I may know the truth values of “Willie Mays played in the American League” and “Willie Mays hit four hundred” without knowing whether or not Mays, would have hit four hundred if he had played in the American League This fact has tended to puzzle, displease, or delight philosophers, and many have felt that it is a fact that calls for some comment or explanation It has given rise to a number of philosophical problems; I shall discuss three of these

Attitudes de dicto and de se

Abstract: If I hear the patter of little feet around the house, I expect Bruce. What I expect is a cat, a particular cat. If I heard such a patter in another house, I might expect a cat but no particular cat. What I expect then seems to be a Meinongian incomplete cat. I expect winter, expect stormy weather, expect to shovel snow, expect fatigue-a season, a phenomenon, an activity, a state. I expect that someday mankind will inhabit at least five planets. This time what I expect is a state of affairs. If we let surface grammar be our guide, the objects of expectation seem quite a miscellany. The same goes for belief, since expectation is one kind of belief. The same goes for desire: I could want Bruce, want a cat but no particular cat, want winter, want stormy weather, want to shovel snow, want fatigue, or want that someday mankind will inhabit at least five planets. The same goes for other attitudes to the extent that they consist partly of beliefs or desires or lacks thereof. But the seeming diversity of objects might be an illusion. Perhaps the objects of attitudes are uniform in category, and it is our ways of speaking elliptically about these uniform objects that are diverse. That indeed is our consensus. We mostly think that the attitudes uniformly have propositions as their objects. That is why we speak habitually of "propositional attitudes." When I hear a patter and expect Bruce, for instance, there may or may not be some legitimate sense in which Bruce the cat is an object of my attitude. But, be that as it may, according to received opinion my expectation has a propositional object. It is directed upon a proposition to the effect that Bruce is about to turn up. If instead I expect a cat but no particular cat, then the object of my expectation is a different proposition to the effect that some cat or other is about to turn up. Likewise for our other examples. The case of expecting a cat shows one advantage of our policy of uniformly assigning propositional objects. If we do not need a Meinongian incomplete cat as object of this attitude, then

Notes on formalizing context

Abstract: These notes discuss formalizing contexts as first class objects. The basic relation is ist(c,p). It asserts that the proposition p is true in the context c. The most important formulas relate the propositions true in different contexts. Introducing contexts as formal objects will permit axiomatizations in limited contexts to be expanded to transcend the original limitations. This seems necessary to provide AI programs using logic with certain capabilities that human fact representation and human reasoning possess. Fully implementing transcendence seems to require further extensions to mathematical logic, i.e. beyond the nonmonotonic inference methods first invented in AI and now studied as a new domain of logic. Various notations are considered, but. these notes are tentative in not, proposing a single language with all the desired capabilities.