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SIMILAR SITUATIONS Varol Akman Bilkent University, Ankara April 14, 2006 Seminar at Boğaziçi University
Caveat • Work-in-progress. • Almost nothing here that is original (with me). ☺ • Regard this as an attempt to review and evaluate the most promising ideas advanced so far. • Comments and suggestions are needed and appreciated.
Plan of talk • AI research on analogy [omitted]. • Psychological (cogsci) research on similarity and analogy [touched upon]. • Goodman on similarity. • Lewis on similarity. • Situation theory. • Waismann on ‘open texture’.
There is nothing more basic to thought and language than our sense of similarity; our sorting of things into kinds. -W. V. Quine
Analogical transfer • How to cure an inoperable tumor without using a strong beam of radiation that would kill the surrounding flesh? • IDEAL SOLUTION: Converge on the tumor with several weak beams of radiation. • PRIOR STORY: Soldiers converging on a fort.
Analogical transfer cont’d - 10% (originally) - 30% (x3) - 90% (x3) • A person encountering a new situation may not retrieve a prior experience that is available and may be useful.
Tverksy’s proposal • Object a is characterized by a set of features a. • s(a,b) denotes the similarity of a to b. • s(a,b) = θf(a∩b) – ξf(a\b) – λf(b\a), where θ,ξ,λ≥ 0.
Tversky’s proposal cont’d • f: reflects the salience (prominence) of the various features. • a∩b: the features shared by a and b. • a\b: the features of a that are not shared by b. • b\a: the features of b that are not shared by a.
Tversky’s proposal cont’d • This so-called contrast model expresses similarity between a and b as the weighted difference of the measures of their common and distinctive features. • Thus, we have a variety of similarity relations over the same set of objects.
Contrast set • Which country, Sweden or Hungary, most resembles Austria? (N.B. Relevant dimension of similarity not specified.) Include Poland Sweden. Include Norway Hungary.
Contrast set cont’d • Judgments of similarity appeal to features having a high classificatory significance. • Features of similarity Relevant contrast set Interests of participants.
Goodman on similarity • “a is similar to b” is a meaningless statement unless one can say in what ‘respects’. • “NN1 is similar to NN2.” They are both pathetic liars. • We must specify in what respects two things are similar.
Goodman on similarity cont’d • “is similar to” functions more like a blank to be filled. • Similarity tends under analysis either to disappear entirely or to require for its explanation just what it intends to explain.
Goodman on similarity cont’d • The meaning is conveyed by the specific respects, not the general notion of similarity. • Example:Moonbeams and melons are not very similar generallyspeaking.
Goodman on similarity cont’d • But if one is told that the Moonbeams have the property that the word begins withMelanie’s favorite letter, then one can generalize this property to melons with very highconfidence.
Similar worlds • Lewis on counterfactuals. • If it were the case that A, then it would be the case that C. A: antecedent (usually assumed false) C: consequent
Similar worlds cont’d • In certain possible worlds where A holds (call them A-worlds), C holds also. • Question: Which A-worlds should one consider? • Answer: Those most similar, overall, to our world.
Similar worlds cont’d • Can there be worlds where A holds but everything else is just as it actually is? • Not really. • Hence, consider a world that differs from ours only as much as it must to permit A to hold.
Similar worlds cont’d • Thus, we need to consider a world closer to our world in similarity, all things considered, than any other A-world. • Analysis:A □→ C is true at i if and only if C holds at the closest accessible A-world to i, if there is one.
Similar worlds cont’d • Comparative similarity is an imprecise notion but we frequently judge comparative similarity of complicated things. • To what extent are the philosophical writings of NN1 similar, overall, to those of NN2?
Similar worlds cont’d • Comparative overall similarity among possible worlds is taken as a primitive. • We balance off various similarities and dissimilarities according to the weights we attach to various respects of comparison.
Counterpart theory • The counterpart relation is a relation of similarity. • It is the resultant of similarities and dissimilarities in a multitude of respects, weighted by the significances of the various respects and by the degrees of the similarities.
Counterpart theory cont’d • Two respects of similarity and dissimilarity among counterparts of ‘persons’: • Personhood and personal traits. (ii) Bodyhood and bodily traits.
Counterpart theory cont’d • If we assign greater weight to (i), we obtain the personal counterpart relation. • If we assign greater weight to (ii), we get the bodily counterpart relation.
Situations • Parts of reality. • Not sets! Only in ‘toy worlds’ (e.g., chess) can we describe them completely. • Perceived and stand in relations to each other. • Metaphysically and epistemologically prior.
How to individuate a situation • Direct perception (my immediate environment here) • Thinking (my last visit to Bosporus University) • Individuation (picking out) does not mean that one is able to give precise description of everything that is (and is not) going on in that situation.
Vague objects • Are situations vague objects? • ‘Bosporus University Campus’: Does it pick out a sharply bounded area of Istanbul? • Consider the claim: “Bosporus University Campus has an even number of trees.”
Vague objects cont’d • This may be indeterminate (true only on some ways) if there are various different ways of drawing a spatial boundary to the Campus. • Note however that “Bosporus University Campus is in Istanbul” is true (true simpliciter).
Vague objects cont’d • QUESTION: How can we talk about the similarity of two objects if they are both vague objects? • ANSWER: We do this all the time. Basically, as long as we are not discussing matters that have to do with fuzzy spatio-temporal boundaries, there is no obvious complication.
Situations cont’d • Reality (one big situation) consists of situations—individuals having properties and standing in relation at various spatiotemporal locations. • One is always in situations. See them, cause them to come about, and have attitudes toward them.
Situations cont’d • Infons: discrete items of information. • Denoted as ‹‹ R,a_1,…,a_n,π›› • where R is an n-place relation, a_1,…,a_n are objects for the respective argument places of R, and π is the polarity (0 or 1).
A soccer game • NN1 and NN2 are having a conversation about a particular soccer game. • Usually, a confusion-free and informative discussion takes place. • And yet neither NN1 nor NN2 could list every item of information ‘supported’ (see presently) by that game situation.
A soccer game cont’d • Take a particular infon ϊ. • The game situation may supportϊ(viz. the latter is made factual by the former), may support the converse of ϊ, or may leave it unassigned a polarity. • Example: “NN4 and NN5 were playing cards during the game.”
A soccer game cont’d • NN3 interrupts NN1 and NN2 and asks: “What are you talking about?” • Answer: “Last night’s soccer game.” • Were they talking about nothing? • Were they not sure about what it was they were discussing?
‘Open texture’ • We use a term in order to apply it to situations with which we are familiar. • Situations are ‘rich’ (highly intensional); they cannot be described in their full detail. • Thus, infinitely many features remain implicit.
The iceberg analogy • Typically, 90% of an iceberg is under water, and that portion's shape can be difficult to guess from looking at what is visible above the surface. • Tip of the iceberg: the problem is only a small indication of a more serious trouble.
The iceberg analogy cont’d • When we describe an empirical situation, we make certain features explicit, but an indefinite number of other features remain implicit. • These implicit features constitute a hidden background.
The iceberg analogy cont’d • To apply a word to or in a novel situation, that situation must be similar to the source situations. • But we cannot foresee in advance all the possible dimensions of similarity between the source situations and possible target situations.