Thursday, May 14, 2009

Propositional Functions

I do not claim to be a Frege Scholar, but I am interested in this distinction between propositions and propositional functions that Drew and Mark Textor talked about last night. My interest is of course epistemological and probabilistic. Take the assertion that:
Fido smokes.
Lets stipulate that there is a particular dog named Fido. Let's also disambiguate "smokes" so that it means inhales tobacco with the nicotine delivery mechanism known as "fags", not some wierdly tensed expression for the early signs of catching fire.
Now I gather that according to Frege there is a fundamental difference between "Fido" and "smokes", and we can pretty easily get a grip on what this difference is. One way of saying what the difference is is that Fido names an object, whereas "smokes" doesn't name anything but predicates of something. Therefore, in a sense, "Fido" stands alone, whereas "smokes" doesn't. Fido is complete, whereas smokes is incomplete. We can use the ontology of propositions to make this difference clearer. "Fido" names a dog, "Fido smokes" names a proposition (or a truth value) but "smokes" names nothing.
Drew made an interesting distinction between a variable and a gap. We can complete "smokes" with a variable easily. Someone smokes. Who smokes? Who smokes dies. If you smoke please do so outside. Smoking causes cancer. We can also names those who smoke "smokers". The thought begins to emmerge that "smokes" is little different from a collective name for all those who smoke. We can think of smokes as a set or class, constituted by its members. The only difference between "Fido" and "smokes" is that Fido names one thing, whereas "smokes" names many things.
Now we enter into epistemology. We have a grammatical trick for converting predicates into collective names. "Ravens are black", is no different in structure from "black things are ravens".
The switch involves a difference in meaning, but this is just because "are" is directional. Since there are more than one Raven and more than one black thing, we can see that these two statements fail to satisfy the law of excluded middle until we quantify the first term with "all" "some" "no" or any proportion or range. So "75% of Ravens are black" is true or false and this has a clear empirical meaning. The meaning is very different from "75% of black things are Ravens". A probabilistic account presents itself. "Ravens are black" is the probability X is black given x is a raven. We then can complete it by a number or a range. P(B R) = 0.75. for 75% of ravens are black. P(B R) = 1, for all ravens are black. P(B R) > 0 for some ravens are black, and P(B R) = 0 for no ravens are black.
Now I don't believe that "Ravens" or "black things" name sets, or are constituted by their extension. The reason I don't believe this is because we can understand and act upon P(B R) = 0.75 without being acquainted with all the ravens that every have been or will be, and without being acquainted with all the black things. All we need are two independent criteria, one for verifying that x is a raven, and one for verifying that x is black. Our belief P(B R) = 0.75 is justified by its success, without the need to be true or false. 0.75 is the success rate of inferences from x is a raven to x is black.
So we still have "x", we still have these objects that underlie everything. This is because Fido smokes does not work like this at all. Fido smokes is a stand alone proposition that automatically obeys the law of excluded middle. We might be able to wonder what P(smokes Fido). But it would be a mistake to think there is any objective answer to this other than 0 or 1. If we were forced to bet, we might consider the classes to which Fido belongs and derive a probability this way. P(smokes dog) is probably very low, I don't know the exact figure. But if we knew that Fido was a circus dog, then we might be better off using P(smokes circus dog) which could be a lot higher. However, both these probabilities would be informed by our coming to know propositions of the form Fido smokes. Finding out that Fido is a circus dog and that Fido smokes would inform our P(smokes circus dog). If our prior belief was 0, we could not thereby reject the testimony of our own eyes when we see Fido lighting up. Our experience of particulars are the foundations on which the whole edifice rests. It is through dogs like Fido that we learn about dogs, and philosophers like Socrates that we learn about Philosophers. But it is not through "smokes" that we learn about Fido, or through "is mortal" that we learn about Socrates.

49 Comments:

Anonymous Anonymous said...

Seems to me smokes could easily be an object and Fido giving more information about the onject: there is some action called
smokes--and this smokes is done by
something named FIdo.

5:32 PM  
Anonymous Anonymous said...

VS Bandaneer here,
If I see Fido with a lit cigarette
in his mouth --but he does not inhale-- I can say he "sort of" smoke or his action resembles smoking. it is smoking to a degree== I don't have to say he is not smoking.
You could also hold that "smokes"
names an action----a particular
action---and that action is an event and an event is an object--
a stand alone object--that does not need Fido. Fido could be a modifier of the object smokes.
Where is the necessity for being inflexible about objects? Why would I need to subscribe to your
implied limitations concerning those things?
Fundamental difference between smokes and Fido? I have the option in my view, of considering a smoking Fido--one object. A vase has shape and color--are those separate objects?

5:51 PM  
Anonymous Anonymous said...

Yes, its difficult to say what the subject predicate distinction is, and I am all for collapsing it. Fido is just a property of smoking. Although I can easily imagine a dog not smoking, I find it difficult to imagine a smoking without anything doing the smoking. (the best I can do is an invisible man smoking) Still, I don't know whether this is just how my particular imagination works. When I first found out about Plato's forms, I kind of imagined them like this. What is this object smoking? Where is it? In heaven? In our minds? I don't want to try imagining smoking too hard since it just gives me useless cravings.

12:24 AM  
Anonymous Anonymous said...

RG Torrington

I'm not sure if this is hopelessly naive, but I thought I'd sick my, or rather Plato's, oar in. I'm doing so because I'm really tempted by what he believed language did and how it did it.

So I'm not sure if this is reiterating or wide of the mark or just plain wrong, but its my foray onto Bloggin the Question, via Plato. He came up with this distinction in the first place, so its him we should blame for the problems, but I hope that what's below somehow sheds light on how whatever we're looking at now was to a degree anticipated and included by Plato.

Plato assumed language (1) "makes a statement about that which is or is becoming or has become or is to be" and (2) that "words uttered indicate action or inaction or existence of anything that exists or does not exist" (Sophist 262c-d)

This means (1) makes claims about things that are (on the one hand) and (on the other) things that became, are becoming or will become. These things are what Plato calls "onoma", names or nouns, existent things having either being (things that are) or becoming (put into the 3 basic tenses; past, present, future)

In (2), the "words uttered" refer to "the indication which relates to action". Or, whatever the thing does, a verb. Plato uses the Greek "rhema" for this, meaning "that which is said about such-and-such". Aristotle uses it to mean predicate, and on the basis of what Plato says about "rhema", it had this broader meaning too.

So it looks like Plato is subscribing to the simple subject/predicate model. He did so because he thought that, if you listed all the onoma, "Fido", "Rex", "Rover" et al, you fail to make "logos". Similarly, if you listed all the rhema, "smokes", "sits", "rules" et al, you fail to make "logos". Only when a proper coherence or continuity, "sunecheia", between onoma and rhema occurs do we have meaning.

But the problem seems to me to be this; we learn nothing about Fido from "smokes", that is "smokes" by itself, we only learn about Fido when we learn "Fido smokes", because Fido smokes tells us something about Fido, and about dogs more generally. But "smokes" cannot do this on its own, unless we say that smokes is a subject to which "and Fido does it" is predicated.

This confused me a little, and I hope I'm getting it right with my own example. Let's say, a la Animal Farm, Fido moves on from smoking to Tyranny. If Fido became our ruler, we would say of him "Fido rules", where "rules" is predicated of Fido. But in generations hence, when we look back at the great canine leaders we have had, we can talk of "rulers" and predicate of "rulers" "that Fido was one", or more simply "Fido". And we could also predicate of those rulers "Rex" and "Rover", much like we tell people about "American Presidents" by listing "Obama, Bush, Clinton, Bush" etc.

So the subject/predicate distinction, inaugurated by Plato, comes unstuck because it looks like one man's subject is another man's predicate.

RGT - continued below

11:34 AM  
Anonymous Anonymous said...

Then there is VS Bandaneer's "one-object" model, where a "smoking Fido" represents a single object, the "smoking" as inseparable from "smoking Fido" as "Fido". But I can't understand something about the vase's shape and colour. They cannot be separated into two distinct objects. They are, along with all its other 'properties' part of the same one object, the vase. But the problem arises, to me at least, about changing the colour of the vase and thus making a new object. Or taking Fido's cigarette away, and changing him into a new object. If this does occur, then there are lots of objects, or lots of event/objects, all particular. In fact there's slightly more than lots, probably regressively many objects. This makes epistemology and reference very difficult ("smoking Fido at t" vs. "smoking Fido at t`"? "smoking Fido at location a" vs. "smoking Fido location b"? etc), to my mind at least, so I'd appreciate clarification.

But if this is not the case (that stopping Fido smoking changes the "smoking Fido"), then what is Fido? It seems that he's just a Fido and smokes, and if changing the smoking does not change the "Fido", then we haven't moved away from subject/predicate at all.

But the problem still seems to be that subjects and objects swap around, or can be made to seem to swap around, in a way that makes the distinction pointless.

Plato's answer would be this. Onoma and rhema are "two kinds of vocal indications of being" (261e). Now, Plato thought that onoma and rhema were the different ways we can indicate different ways of being. Being, par excellence, would be Formal reality. Here, onoma and rhema may collapse into one another - The Form of Beauty is beautiful, inseparably like the vase and its colour and shape. But lesser kinds of beings, such as Fido, do not have the luxury of being such (like the vase). This is because they are in a process of becoming. So the rhema and onoma are separate to indicate (on the one hand) the becoming thing and (on the other) what it is becoming. So "Fido smokes" tells us that something has become (Fido exists) and that of this thing an action can be said (that it smokes). Why can't we swap the predicate over for the subject, for instance when thinking about the set of smoking things? For Plato, only Forms have the luxury of inseparability that we saw with the vase. And in this sense, interchangeability between subject/predicate - Beauty is beautiful, beautiful-ness is Beauty. However, "smokes" is not a becoming onoma. This is because, as was quite rightly pointed out, we cannot imagine "smokes" on its own (except perhaps with an invisible man, but it is obvious what's wrong here). We can imagine it as an event, or as contributing to the formation of the set "smokers" (to get this I needed the presidents analogy, so I hope its not disanalogous) and hence predicate to this the "Fido". But again, events and sets are not onoma, they are not becomings in and of themselves, they are "that which is said of such-and-such". Put another way, they cannot be forced into onoma, because they describe they way in which a becoming thing becomes.

RGT - continued below

11:35 AM  
Anonymous Anonymous said...

This is what is meant by the "two vocal indications of being". There are two to pick out the ways in which things become (this is obvious a metaphysical, not linguistic, point). And indeed, we always think of there being this distinction in play, we just swap who's in which role. But Plato won't allow the slip, because existing things (onoma) become, and we need to explain how they do so in such-and-such a way (rhema).

Forms though don't need the distinction for Plato. In fact, misunderstanding this, and thinking that they do, leads to the 3rd Man argument and other confusions about self-predication. So Plato implicitly grasps the notion that Bandaneer puts forward, but does not ascribe it to existent things. Perhaps this is because of my confusion about what happens during change. Forms do not have this problem, not even the Form of Change.

So, the difference between "Fido" and "smokes" is not the difference between a subject and predicate, noun and verb, but rather the difference between a thing, a metaphysical entity, and how it becomes this entity as such. Fido can smoke, or not smoke, be a dog or not a dog, it doesn't matter for Plato. But he will say that we learn about Socrates through Socrates, and not "is mortal", not because Socrates is a subject of predication, determining the predicates predicated thereof, but because Socrates became, and his becoming can be indicated in two ways - onoma and rhema. Rhema is just that which is said about such-and-such, where such and such is an entity. So you cannot learn about that which such-and-such is said, without a such-and-such to say it about.

Now the whole shabang arises from understanding this problem of language linguistically. This is a problem derived from metaphysics. So the switch that happens with the presidents is blocked, because while grammatically we have a subject/predicate reverse, ontologically we do not. Ontologically, each individual president is an entity that became, whereas "rules" is that way in which that entity did.

?

RG Torrington

Sorry for the multipost - silly character limit ...

11:36 AM  
Anonymous Anonymous said...

Could we say that there are agents and actions? Onoma being agents and rhema being actions? Fido rules, the vase is red, the river flows, change is beautiful, red is loud.
If we look at it this way, we can recognise that we can be agents or actions ourselves and the metaphysical difference can be accessed first personally. "agent" and "action" carry with them an implication of intentionality, but so what? (It is raining, to what does "it" refer?) (Walter Relegh introduced smoking to the English)
We are all born. I was born. This is an event that happened to me. My parents, especially my Mother, were essentially involved. I was an action of theirs. But in some strange way, I was an agent of this action.
Every day nearly we fall asleep. I slept. I woke up. These are actions of mine, and to an extent, sometimes intentional. In being asleep I am my own action.
One might, in a physicalist frame of mind, think it absurd to talk about actions and agents since only beings with minds can act, and us mental beings are rare. But lets give idealism a fair chance. We can cause inanimate objects to act in particular ways. I can cause ice to melt, wounds to sting, my computer to shut down.

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Anonymous Anonymous said...

but is a dog can smoke? I'm not agree. I was once see a monkey that was smoke on the tv. Was funy but the monkey was die.

9:28 AM  

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