Consider the following philosophical rule of etiquette:
(E) If a paradox is bad for everybody, don't use it to refute your opponents unless you personally have a solution.
I believe Deustch has violated (E). That's bad not only because it's rude, but because it's begging for a tu qoque response. I'll give that here.
Deustch thinks that any structured proposition theory is inconsistent because of the following argument:
Consider a set of propositions w, such that a proposition p is in w just in case the following obtains:
a) for some set of propositions m, p is the proposition that everything in m is true
b) p is not in m
He then asks that you consider the following proposition:
(P) everything in w is true
The argument goes as follows
1) Propositions have constituents
2) (1) -> (3)
3) Those constituents must exist if the proposition exists
4) (P) exists
5) w exists (3&4)
I'll divide the argument up for clarity. Here's to establish that if P is in w, then p is not in w, therefore p cannot be in w:
6) P is in w (assume for reductio)
7) The set of propositions such that P is the proposition that everything in it is true is w
8) P is not in w (6&7, by the conditions under which a proposition is in w)
To establish that P is in w:
9) P is not in w
10) there's a set of propositions such that (a) and (b) hold of (P) (9, w satisfies a and b for P)
11) P is in w (10, conditions under which a proposition is in w)
main argument:
12) P is in w and P is not in w (8, 11)
13) ~(1) (closed reductio)
Deustch contrasts this with the main objection against unstructure proposition theory, which is Soames' objection we saw earlier this term. Soames' objection applies directly to unstructured proposition theorists and nobody else. Deustch can only frame this as the main objection to structure proposition theory if it only applies to them. If it applies to unstructured proposition theory as well, his game is over.
This argument, of course, is a version of russel's paradox. This paradox springs up pretty much any place in which there's some principle of unrestricted composition (things can always combine to make bigger/more complex things). We see this in set theory, mereology, when formulating what properties are, possible worlds, everywhere. As for this particular formulation, the unstructured proposition theorists would deny (1) (of course). However we don't need a premise as strong as (1) to get the paradox going. Consider the same argument except replace premises (1), (2) and (3) with the following:
(1') Propositions are about things
(2') (1') -> (3')
(3') The things propositions are about exist
The argument goes through exactly as before. So the unstructured proposition theorist can't simply deny one. In fact, Deustch takes a different route when resisting the paradox. Here's what Deustch says about this:
"The essential assumption is that if a and b are distinct objects, then the propositions having them as constituents differ.[15] This is not true of possible worlds semantics, since e.g. the propositions expressed by "Jones wears a hat or he doesn't" and "Smith wears a hat or he doesn't" will express the same proposition whether or not Smith and Jones are identical.[16]"
This can be seen as a rather convoluted rejection of (7). Just because (P) is 'about' w over here, doesn't mean it's 'about' w over there. However, if one is going to be wishy-washy with aboutness facts, then plausibly propositions aren't (intrinsically) about anything (perhaps they're about something relative to a mode of presentation or something). This leads to a denial of (1'). This is already biting the bullet big time, but I can make things worse. Consider just talking about sentences, not propositions. Let (P) just be the sentence, not the proposition expressed. Let w be a set of sentences, m be a set of sentences etc. Replaces (1'), (2'), (3') and (4) with:
(1'') Proper names have referents
(2'') (1') -> (3')
(3'') If S is a well-formed sentence of non-fiction, the referents of all the proper names in S exist.
(4) (P) is well-formed sentence of non-fiction
With the proper modifications in the rest of the argument (just chanings 'proposition' to 'sentence' in each case) the argument goes through. Again, the denial of modified (7) would pretty quickly lead to the denial of (1''). Alternately the unstructured proposition theorist could deny (4), or (2''). However, the denial of these is a hefty cost.
A proponent of structured proposition theory may deny (2) (meinongianism, gappy proposition theory), or they could deny (4). For dealing with the modified arguments, they have similar options as the unstructured proposition theorist. These would also be costs, but the costs would be comparable to the costs of unstructured proposition theory.
Friday, December 5, 2008
Tuesday, November 25, 2008
King on propositions and changing truth values
King kind of confuses me right at the start of chapter 6 when he talks about how propositions "must and must not change truth value across time and location". He makes this claim before he even starts laying out his position, but I am still trying to see the problem that he is so adamant about.
My understanding of where King starts from:
1) If the truth value of propositions is determined by the semantic value (relative to context) of sentences, then (2) & (3).
2) Propositions, according to his 'in Carnelian Bay' example, change truth value over different worlds, locations, and times.
3) Propositions, according to his 'Santa Monica based belief' example, do not change truth value over time or location.
4) ~ [(1) & (2)]
5) Therefore, further inquiry into the relation between propositional truth value and the semantic value of sentences is required.
I am having trouble with the examples that King is using in (2) and (3). In (2), he says (referring to the sentence "In Carnelian Bay there is a boat launching ramp") that "If 'there is a boat launching ramp' expressed a proposition (relative to that context) that didn't vary its truth value over locations, the locational operator 'In Carnelian Bay' would be vacuous, and the sentence would "feel" like 'In Carnelian Bay arithmetic is incomplete.' But it doesn't!" (pg 166).
I have no idea what King means when he says that the two sentences would "feel" the same. Furthermore, from what I understand, I think King has the example backwards. If propositions did not change their truth value over location, then wouldn't changing "In Carnelian Bay" with any other location (operator) result in "the same feeling" as the original sentence (instead of changing the proposition and keeping the location the same)?
For example, what King should have said is that if propositions do not change their truth value over location, then "In Carnelian Bay there is a boat launching ramp" (where the truth determining context lies in 'there is a boat launching ramp') would "feel" the same as "In the Sahara Desert there is a boat launching ramp". This poses much more of a problem because here the vacuous operator should not affect the truth of the proposition (being that the context of 'there is a boat launching ramp' stays with 'there is a boat launching ramp') but the truth value has obviously changed. I don't think, however, that in King's example the two sentences necessarily "feel" different.
If this line of thought is true, then it is an objection to (2) and the argument is no longer valid.
Now to address (3).
Again, King confuses me with the example that he uses. He says that he is in Santa Monica right now and when he says "I believe the sun is shining" it is about Santa Monica right now. From this he claims that if he were to change location or time, the proposition would still be about "Santa Monica at this time" and so would not change in truth value. I think King is either confusing two different propositions or is being lazy in his speaking. Technically speaking, when King asserts "The sun is shining", he is not asserting anything about Santa Monica; or at the very least that he is implying that the context he is in at the time he says that sentence is to be taken as part of the proposition itself (some kind of non-spoken magically attaching part). Basically, I think King is just trying to get away with being lazy when it comes to saying when you really meant when you expressed a proposition.
The proposition King actually said was: "The sun is shining".
The proposition King intended the listener to understand was: "The sun is shining where I am right now", or "The sun is shining in Santa Monica right now", or "The sun is shining in Santa Monica at 3:05pm", etc. etc. etc.
When you blur this distinction, but then claim that people are wrong to say that your belief is not about Santa Monica when you say "The sun is shining", you are just confused by your own vagueness (and laziness - which is not a bad thing because speaking would become lengthy, tedious, and robotic if we were to speak as precisely as is needed in order to avoid these shortcuts in meaning).
If this line of argument is true, then it is an objection to (3) and King's starting argument is invalid.
My understanding of where King starts from:
1) If the truth value of propositions is determined by the semantic value (relative to context) of sentences, then (2) & (3).
2) Propositions, according to his 'in Carnelian Bay' example, change truth value over different worlds, locations, and times.
3) Propositions, according to his 'Santa Monica based belief' example, do not change truth value over time or location.
4) ~ [(1) & (2)]
5) Therefore, further inquiry into the relation between propositional truth value and the semantic value of sentences is required.
I am having trouble with the examples that King is using in (2) and (3). In (2), he says (referring to the sentence "In Carnelian Bay there is a boat launching ramp") that "If 'there is a boat launching ramp' expressed a proposition (relative to that context) that didn't vary its truth value over locations, the locational operator 'In Carnelian Bay' would be vacuous, and the sentence would "feel" like 'In Carnelian Bay arithmetic is incomplete.' But it doesn't!" (pg 166).
I have no idea what King means when he says that the two sentences would "feel" the same. Furthermore, from what I understand, I think King has the example backwards. If propositions did not change their truth value over location, then wouldn't changing "In Carnelian Bay" with any other location (operator) result in "the same feeling" as the original sentence (instead of changing the proposition and keeping the location the same)?
For example, what King should have said is that if propositions do not change their truth value over location, then "In Carnelian Bay there is a boat launching ramp" (where the truth determining context lies in 'there is a boat launching ramp') would "feel" the same as "In the Sahara Desert there is a boat launching ramp". This poses much more of a problem because here the vacuous operator should not affect the truth of the proposition (being that the context of 'there is a boat launching ramp' stays with 'there is a boat launching ramp') but the truth value has obviously changed. I don't think, however, that in King's example the two sentences necessarily "feel" different.
If this line of thought is true, then it is an objection to (2) and the argument is no longer valid.
Now to address (3).
Again, King confuses me with the example that he uses. He says that he is in Santa Monica right now and when he says "I believe the sun is shining" it is about Santa Monica right now. From this he claims that if he were to change location or time, the proposition would still be about "Santa Monica at this time" and so would not change in truth value. I think King is either confusing two different propositions or is being lazy in his speaking. Technically speaking, when King asserts "The sun is shining", he is not asserting anything about Santa Monica; or at the very least that he is implying that the context he is in at the time he says that sentence is to be taken as part of the proposition itself (some kind of non-spoken magically attaching part). Basically, I think King is just trying to get away with being lazy when it comes to saying when you really meant when you expressed a proposition.
The proposition King actually said was: "The sun is shining".
The proposition King intended the listener to understand was: "The sun is shining where I am right now", or "The sun is shining in Santa Monica right now", or "The sun is shining in Santa Monica at 3:05pm", etc. etc. etc.
When you blur this distinction, but then claim that people are wrong to say that your belief is not about Santa Monica when you say "The sun is shining", you are just confused by your own vagueness (and laziness - which is not a bad thing because speaking would become lengthy, tedious, and robotic if we were to speak as precisely as is needed in order to avoid these shortcuts in meaning).
If this line of argument is true, then it is an objection to (3) and King's starting argument is invalid.
Sunday, November 23, 2008
Harry D.
Harry D. asks some questions. He isn't sure King can answer them. I will try to, though I may do a poor job because I don't really understand the questions in question.
(Q1) King's use of models.
(1) King says that propositions are not mathematical objects.
(2) King's motivation for (1) is Benacerrafian reasons which entail (3).
(3) King doesn't think there are any mathematical objects.
(4) But he uses diagrams for propositions.
(5) And these diagrams have to be mathematic objects. They are a certain kind of graph.
(6) But we cannot identify propositions with the graphs.
(7) So King has not answered: What are propositions?
(A1) I don't think (7) follows.
I'm not so bothered by (6). I don't think that it entails (7) I'm not bothered by introducing things via models. I might say that atoms are like little marbles that dance when heated. I don't mean to identify atoms with marbles or heating with dancing.
But maybe we still have to ask, nice model aside, what the atoms are. And so too with propositions. But if atoms and propositions are non-observables, I'm not sure how we can talk about them with the use of models and diagrams unless we give some attempt at representation. My scientific commitments are that the observables are all eliminable and reducible to the unobservable. So I'm not bothered by being able to talk about the essence of something, but not being able to pictorially show it. (6) seems to be taken to show King can only hint at what propositions are. (7) takes this to be invalid. I don't think it is invalid.
I'm not sure about (3). I don't think King denies that there are 'mathematical objects'. He certainly thinks that there are objects with which mathematics is concerned. I don't see how a structuralist / functionalist about numbers is a number-hater. I don't think that being non-platonistic about something makes you deny that it exists.
About (4): It seems like the model King uses is a representation of the proposition. A proposition seems to be a representation + semantic contents. And it seems that agents have to add the semantic contents. So we can never fully map what a proposition is in a diagram or model. But I don't see this to be a big deal.
(Q2) What is language?
(1) King never tells us what a language or a sentence of a language is ontologically.
(2) Whatever else English is, we know it is productive. One can produce novel sentences.
(3) On King's view, the propositions don't exist until the words get said.
(4) (3) should strike us as odd. The Chisholm style theory doesn't have this worry.
(5) King's account closes the door a priori on animals thinking propositionally.
(6) So King is vague about language, and his conclusions are counter-intuitive.
(A2) I think we can deny (6).
It seems easy to supply a King friendly account to attack (1). I think we can use some Sellars here to help King out. Language exists in the narrowly physical causal order. It is scribbles and squawks. But language is also in the broadly construed physical causal order. We don't just hear sounds, we hear words. We don't just understand sounds, we understand words.
I think the same problem could be posed for maps. Maps are in a sense just designs, blips, dots or scribbles. But when one knows how to read a map, the map is much richer. We don't just see the representation. We see what is represented.
About (2) - (4): Productivity doesn't seem to be an issue. Given the atomic bits of English, one can construe novel combinations. Given the rules of English, one can construe novel acceptable combinations. We don't need the propositions to have existed prior, we only needed the constituents to have. I don't need all the numbers to exist in order to do any math. I only need '1', '2', etc., '9', '0'. I can just reuse these numbers to get '12' or '124'. I don't see any problem with this.
I think (5) is a silly concern. I don't think it is bad that King closes the door a priori on animals thinking propositionally. It is still an open question, in a sense, even if we so close the door. But I think there are pre-theoretical reasons to doubt this anyways. Some people don't. There is reason, even if King is right, for one to argue that animals have an animal language or a private language, so they could think propositionally even if King were right.
(Q3) Vagueness on properties and relations.
(1) King assumes that there are properties and relations.
(2) He doesn't say what they are.
(3) He should.
(4) So it's not clear how propositions can exist in his sense, since he doesn't tell us what properties and relations are.
(5) Why cannot we think of propositions as being properties of the actual world?
(A3) I think one could deny (4), since even if he doesn't tell us what properties and relations are, it seems easy to figure out.
I guess I don't have a lot to say here. About (2): I think that the ideas of properties and relations is common enough. A property is a feature or character of a thing. A thing is hot or cold, small or large. I relation is a feature or character between things. A thing is next to another, distant from another.
One could be process ontology oriented. A 'property' like 'being tall' is a way for a thing to be intrinsically. So Wes is tall because there is a tallness going on. A 'relation' like 'being a brother' is a way for a thing to be extrinsically. So Wes is a brother because there is a thing he is related to via brotherness. These things are in space and time and enduring things so they seem non-spooky and physical.
I hope that isn't poorly stated. But it doesn't seem to be contrary to King's view.
About (5): Since propositions are representational, it seems the cannot be properties of the world in the way Harry D. wants. But maybe we can say that since they exist, like the CN Tower and my breakfast, they are properties of the world.
(Q1) King's use of models.
(1) King says that propositions are not mathematical objects.
(2) King's motivation for (1) is Benacerrafian reasons which entail (3).
(3) King doesn't think there are any mathematical objects.
(4) But he uses diagrams for propositions.
(5) And these diagrams have to be mathematic objects. They are a certain kind of graph.
(6) But we cannot identify propositions with the graphs.
(7) So King has not answered: What are propositions?
(A1) I don't think (7) follows.
I'm not so bothered by (6). I don't think that it entails (7) I'm not bothered by introducing things via models. I might say that atoms are like little marbles that dance when heated. I don't mean to identify atoms with marbles or heating with dancing.
But maybe we still have to ask, nice model aside, what the atoms are. And so too with propositions. But if atoms and propositions are non-observables, I'm not sure how we can talk about them with the use of models and diagrams unless we give some attempt at representation. My scientific commitments are that the observables are all eliminable and reducible to the unobservable. So I'm not bothered by being able to talk about the essence of something, but not being able to pictorially show it. (6) seems to be taken to show King can only hint at what propositions are. (7) takes this to be invalid. I don't think it is invalid.
I'm not sure about (3). I don't think King denies that there are 'mathematical objects'. He certainly thinks that there are objects with which mathematics is concerned. I don't see how a structuralist / functionalist about numbers is a number-hater. I don't think that being non-platonistic about something makes you deny that it exists.
About (4): It seems like the model King uses is a representation of the proposition. A proposition seems to be a representation + semantic contents. And it seems that agents have to add the semantic contents. So we can never fully map what a proposition is in a diagram or model. But I don't see this to be a big deal.
(Q2) What is language?
(1) King never tells us what a language or a sentence of a language is ontologically.
(2) Whatever else English is, we know it is productive. One can produce novel sentences.
(3) On King's view, the propositions don't exist until the words get said.
(4) (3) should strike us as odd. The Chisholm style theory doesn't have this worry.
(5) King's account closes the door a priori on animals thinking propositionally.
(6) So King is vague about language, and his conclusions are counter-intuitive.
(A2) I think we can deny (6).
It seems easy to supply a King friendly account to attack (1). I think we can use some Sellars here to help King out. Language exists in the narrowly physical causal order. It is scribbles and squawks. But language is also in the broadly construed physical causal order. We don't just hear sounds, we hear words. We don't just understand sounds, we understand words.
I think the same problem could be posed for maps. Maps are in a sense just designs, blips, dots or scribbles. But when one knows how to read a map, the map is much richer. We don't just see the representation. We see what is represented.
About (2) - (4): Productivity doesn't seem to be an issue. Given the atomic bits of English, one can construe novel combinations. Given the rules of English, one can construe novel acceptable combinations. We don't need the propositions to have existed prior, we only needed the constituents to have. I don't need all the numbers to exist in order to do any math. I only need '1', '2', etc., '9', '0'. I can just reuse these numbers to get '12' or '124'. I don't see any problem with this.
I think (5) is a silly concern. I don't think it is bad that King closes the door a priori on animals thinking propositionally. It is still an open question, in a sense, even if we so close the door. But I think there are pre-theoretical reasons to doubt this anyways. Some people don't. There is reason, even if King is right, for one to argue that animals have an animal language or a private language, so they could think propositionally even if King were right.
(Q3) Vagueness on properties and relations.
(1) King assumes that there are properties and relations.
(2) He doesn't say what they are.
(3) He should.
(4) So it's not clear how propositions can exist in his sense, since he doesn't tell us what properties and relations are.
(5) Why cannot we think of propositions as being properties of the actual world?
(A3) I think one could deny (4), since even if he doesn't tell us what properties and relations are, it seems easy to figure out.
I guess I don't have a lot to say here. About (2): I think that the ideas of properties and relations is common enough. A property is a feature or character of a thing. A thing is hot or cold, small or large. I relation is a feature or character between things. A thing is next to another, distant from another.
One could be process ontology oriented. A 'property' like 'being tall' is a way for a thing to be intrinsically. So Wes is tall because there is a tallness going on. A 'relation' like 'being a brother' is a way for a thing to be extrinsically. So Wes is a brother because there is a thing he is related to via brotherness. These things are in space and time and enduring things so they seem non-spooky and physical.
I hope that isn't poorly stated. But it doesn't seem to be contrary to King's view.
About (5): Since propositions are representational, it seems the cannot be properties of the world in the way Harry D. wants. But maybe we can say that since they exist, like the CN Tower and my breakfast, they are properties of the world.
Saturday, November 22, 2008
C1 and C2 wonder
I think King's motivation for his C1 and C2 distinction is good. I'm motivated to accept something like what he wants, though I would want to avoid his problems. I think the classical empirical-foundationalists also want something like what he has.
The motivation behind C1, rationally reconstructed, seems to be one's being able to get into the space of reasons, make material inferences, paraphrase, justify, etc. one's use of language.
The motivation behind C2, rationally reconstructed, seems to be one's being able to reliably report, assert, identify, etc. One has to be able to use the words correctly.
Someone like CI Lewis is going to say that C1 is basically being able to know what is logically implied by a term; and, it seems, what is analytically implied. Lewis thinks these are distinct, but King could be said to just conjoin a term's 'connotation' and 'signification' as Lewis uses the words (roughly).
Lewis would say that C2 is one's being able to recognize instances. One has to know what the term picks out, and all consistently thinkable cases where the term would pick out those things. Again, King could be said to just have conjoined the ideas of 'denotation' and 'comprehension' as Lewis uses the words (roughly).
Maybe Russell-Mill would take C1 to be one's knowing connotations, C2 knowing denotations.
These people all want to cash out 'word-meaning' and 'sense-meanings'. It seems that something like this distinction between 'inter-linguistic transitions' and 'language-entry transitions' is good to have. Even for Quine we need stimulus-meanings 'in presence' and 'in absence'. HH Price likes this notion of 'in presence' and 'in absence' so he would want C1 to be something like 'thinking of a term in absence' and 'thinking of a term in presence'.
So even if we don't like King's formulation, shouldn't we look to keep a sort of C1 and C2 distinction for linguistic competency?
The motivation behind C1, rationally reconstructed, seems to be one's being able to get into the space of reasons, make material inferences, paraphrase, justify, etc. one's use of language.
The motivation behind C2, rationally reconstructed, seems to be one's being able to reliably report, assert, identify, etc. One has to be able to use the words correctly.
Someone like CI Lewis is going to say that C1 is basically being able to know what is logically implied by a term; and, it seems, what is analytically implied. Lewis thinks these are distinct, but King could be said to just conjoin a term's 'connotation' and 'signification' as Lewis uses the words (roughly).
Lewis would say that C2 is one's being able to recognize instances. One has to know what the term picks out, and all consistently thinkable cases where the term would pick out those things. Again, King could be said to just have conjoined the ideas of 'denotation' and 'comprehension' as Lewis uses the words (roughly).
Maybe Russell-Mill would take C1 to be one's knowing connotations, C2 knowing denotations.
These people all want to cash out 'word-meaning' and 'sense-meanings'. It seems that something like this distinction between 'inter-linguistic transitions' and 'language-entry transitions' is good to have. Even for Quine we need stimulus-meanings 'in presence' and 'in absence'. HH Price likes this notion of 'in presence' and 'in absence' so he would want C1 to be something like 'thinking of a term in absence' and 'thinking of a term in presence'.
So even if we don't like King's formulation, shouldn't we look to keep a sort of C1 and C2 distinction for linguistic competency?
The Guy's Talk
I think that guy with his cut between:
1. Intentionality
2. Representationality
3. Propositionality
Is a little odd. If the him / Prof B. dudes claim that someone like me or King run together (1) and (3) I think the natural response is that for someone like me or King we cut it:
1. proto-intentionality
2. Representationality (intentionality)
3. Propositionality (intentionality)
I wanted to say something about Dan's question, but can't remember what it was. Could someone (preferably Dan himself) remind me of what that was?
1. Intentionality
2. Representationality
3. Propositionality
Is a little odd. If the him / Prof B. dudes claim that someone like me or King run together (1) and (3) I think the natural response is that for someone like me or King we cut it:
1. proto-intentionality
2. Representationality (intentionality)
3. Propositionality (intentionality)
I wanted to say something about Dan's question, but can't remember what it was. Could someone (preferably Dan himself) remind me of what that was?
Thursday, November 20, 2008
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