intensions

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If a language is to serve human needs at all, it must contain what are in English at least (all other I-E languages, I think – I leave it to specialists to say what is the case in other language families). In these contexts, intensions, which usually are tools for finding the right extensions, the means to getting to the referents, become the referents themselves.

Languages have two pure strategies for expressing these situations (apparently – I’d love to hear of another). Plan One is to set aside certain places in the deep structure of various predicates to be taken in an intensional way. The terms that go into these places are the normal expressions for extensions but they are taken in semantic analysis as referring to the intensions behind those extensions. This generates the problems of intensional/opaque contexts: failure of exchange of equivalences and of Generalization and Instantiation, and issues associated with talking about nonexistent things. Plan Two is to have in the language predicates that permit or require that certain of their places be filled references to intensional objects: properties, propositions, events and the like (there is not language-independent final list here). The difference between the two is just that in the first “a P b,” where the second place is intensional, “a bears the relation P to the concept that characterizes b,” while the second plan has it say simply “a bears the relation P to the concept b.”

The benefit of the pure opaque strategy is that you do not have to acknowledge intensional entities in your overt metaphysics and are thereby saved (at least until philosophers come along) from getting into the problems which intensional objects create (what does it mean to say such things exist? If they do, where are they? And so on through the bulk of philosophy). The disadvantage is that sentences that look very much the same behave very differently (even look identical, I fear: there seems to be for me a sense of “see” in which, when I see George Bush I see the President of the United States and another in which this only happens if I know that George Bush is the President of the United States and am conscious of it at the time). The other plan has the advantage that all places behave the same with respect to their terms. But you are stuck from the get-go with “things” like properties and propositions, with all that entails even in non-philosophical usage.

As far as I can tell, languages all use a mixed strategy: some predicates take only extensional terms in their intensional places, other permit either type, but with appropriately different meanings – each of the type of the term used. And, of course, most have no truck with intensions at all. (I would hope that no predicate that uses extensional terms for intensional meanings also has a second meaning that takes extensional terms extensionally, but I am far from sure that this is the case. See “see” just above.) The different approaches seem to sort them out by type (as perceived within the language, say); in English, verbs of knowledge and communication tend to be intensional (the communication ones also extensional but with an extensional meaning) while verbs of volition and creation seem to tend toward the extensional. Thus, Charlie may say that he loves his mother (a proposition – but he also say “I love my mother” – a sentence) but he still wants a car (not carness, though that is what “a car” refers to in this case). Other languages may tend more heavily in one direction than another, but all are mixed; even an Indian logician, after a hard day of arguing whether fierinessness pervades smokienessness, just wants a bowl of lentil curry.

Lojban seems to tend strongly toward the intensional side – when it notices that an intensional matter is at hand. Thus, the predicates that correspond to those that take propositions in English

Take propositions in Lojban as well (and more clearly so, since propositions and the like are much more clearly marked in Lojban). The clearly volitional predicates also take events in the tricky place, rather than occurrences or occurrence components. And, triumphantly for the cause of intensional usage, {sisku} “seek” (but not – a falling away – {kalte} “hunt”) takes a property in the troubling place. But many other predicates take extensional terms when intensional ones are called for – and, often, I think – also when the extensional is meant. And there are in Lojban (as in every language I expect) contexts that are intensional but unmarked even lexically and thus are distinguishable from extensional contexts only when the fertilizer gets in the air conditioning. (the ever popular {lo pavyseljirna cu blabi} leaps to mind).

Lojban also fudges (I suppose other languages do too): it allows extensional expressions in situations that strictly require intensional one, provided that the extensional one is flagged as being a part of an intensional expressions whose other parts are either unimportant or too obvious to need repeating. The classic here is {mi nitcu tu’a lo mikce}, where {tu’a} stands for a {lo nu … co’e} and {co’e} involves at least that the doctor is available for appropriate activities (to treat a problem, to buy the stock, whatever). This has led some to think that this place can – and should be, indeed – filled by an extensional term. And this tendency has been aided by the fact that that place can indeed be filled by terms which bear on their faces the evidence that their referents exist in this world: indexical expressions first and foremost, but not most description or names (we can fudge a little by bringing in outside knowledge, but we run risks in doing so: the fact that Chucky exists does not mean that exchange of identities will work for him, though generalization and instantiation will. Some call these semi-opaque cases – or translucent.). Thus, “I need that ladder” presents no problems (or far fewer), but “I need a ladder” does.

So, I propose to legislate a three-fold approach: every place of the appropriate takes officially (1) the right sort of abstraction, including (2) the reduced form with {tu’a}, and by extension when existence is guarantee one way or another (overt form or covert knowledge) (3) ordinary unmarked sumti. The third case is not transparent but only translucent, so perhaps it should be marked also but that seems overly fastidious. Notice, however, {lo} terms will never be appropriate for a type 3 case (there may be some referents but not the ones called for in the intension). Generally, type 3s are most dangerous when the property involved depends upon how a reference is made (“Giorgione was so called because of his size” for a famous example or the ever popular “I need Superman” which definitely does not imply “I need Clark Kent” – or perhaps better and certainly more traditional “The Evening Star (or Hesperus) appears near the sun shortly after sunset” which certainly does not imply the same claim about the Morning Star (or Phosphorus]. Use type 3 with care and only when generalization, not interchange, is likely to be a factor.

Note that type 3 situations are different from those where the basic predicate takes extensions as well as intensions {cusku} for example. If we quote the sentence rather than cite the proposition, none of the intensional factors come into play. It may be that these kinds of double roles need to be done away with, though the results seem like duplications. Xorxes once proposed a system of duplicating all predicates with one with intensional place – or without where there was one. That plan failed, as I recall, because of technical problems with the particular proposal and even a successful plan would be overworking, but perhaps some flags – other than in this case quotes is needed (we could say “the first line on this page” rather than actually quoting and still be extensional.)

The permission (2) to allow shortened versions of abstractions, favors those abstraction in which sumti play a major role: event descriptions over almost any other sort except propositions (and indeed these two are not always easy to tell apart – compare property functions and propositional functions for properties). When it is the sumti that is determinative, then, we need to have a general fallback position to permit abbreviating. For properties, we have {le/lo se ckaji be ---} to be reduced to {tu’a ---} and in general we can talk about {le/lo si’o srana ---} where {si’o} is to be the relevant abstraction (we really need to sort out {le} and {lo} with abstractions – is there more than one of each type, for starters). And, when names are the determinative factor, we need a general device for saying that the abstraction – whatever it is – is important here because of the name, not the referent (actual or possible) of the name, i.e., that the intension involved is the individual-concept (haeceity, thusness) associated with the name, not the mere biographical recapitulation that characterizes the individual (but note that, for fictional characters, these come to the same thing: the sense of “Sherlock Holmes” is just that the individual does what the Canon says he does; anything more is speculation). Perhaps the mere fact that the name is used is sufficient, except that it often is the biographical stuff we want, and it is not clear which is the more common. And even in particular cases it may not be clear which is intended, though, with real objects it is likely to be the concept of the thing itself and with fictional ones the name-concept (all they have, after all).

This proposal involves reworking the definitions of many predicates (and related cmavo). Although the changes need not be great in reality, they may seem large in works. If {zasti1}, for example, is intensional then the definition has to become something like “x1 is realized (instantiated, exemplified, has a locus…. for x2 in metaphysics x3” and {xanri} becomes “x1 is not realized for x2, who imagines its realization.”

A significant number amount of usage would have to be modified, mainly by inserting {tu’a} in front of terms in the newly discovered intensional places (and some of the known ones as well, alas).

The advantage is consistency: every place filled with a simple term, all the laws of logic applying to all terms. The disadvantage – for English (etc.) speakers -- is that the terms are often not the ones that we expect. The generalization on {mi nitcu tu’a lo mikce} is not either kind of generalization on {lo mikce} but only on {le/lo nu lo mikce co’e}: {mi nitcu su’o da}. And similarly for the interchanges (and identity between abstracta is much less common then between concreta). But the differences are borne on their faces, rather than being concealed: we don’t have to wonder whether an exchange or a generalization applies or not (except, perhaps, in type 3 situations, which may need more thinking about).