Help me out. I presume that either my methodology is flawed, or my methodology is sound but my analysis lacking, or everything is fine in principle but I am failing to see something apparent.
Let us imagine I have the following sample of things:
▲ ◯ ◼ █ ◣ ◒ ★ ☆ ⚡ ♻ ♫
I should be tempted to introduce a category-term for them, “shape”. So I would introduce a “shape framework” which would function as a sort of kind. Thus in my shape framework I have the following:
▲ ◯ ◼ █ ◣ ◒ ★ ☆ ⚡ ♻ ♫
I guess I’m sympathetic to a distinction between fundamental and superficial existences, since I want to talk about the things in my framework that are models and the things in my framework that are commentaries. Thus the shapes *▲*, * ◯*, *◼*, etc. are models for things in the world, in this case my original sample, and my category term “shape” is in the commentary. Also in my commentary are the names of the shapes, “isosceles triangle”, “circle”, “square”, “rectangle”, “rectangle”, “right triangle”, etc. The wordy bits are in the commentary, the thingy bits are in the model. The thingy bits are ‘fundamental’ in some sense, and the wordy bits are ‘superficial’.
And since I have names for the things, I can introduce terms for the tokens, and also construct for myself token-classes. Thus, I can construct the ‘triangle kind’ which includes:
▲ ◣
The ‘black shape kind’ which includes:
▲ ◼ █ ◣ ★ ⚡ ♻ ♫
and so on. So I have given in my commentary: 1) A name of the type in question, namely shapes. 2) Names for the tokens in question, namely isosceles triangle, circle, square, etc. 3) Names for the token-classes in question, namely black shapes, white shapes, triangles, stars, etc. In my model I have the shapes.
Now I seem to be pretty content with this. I have appealed to types and token classes, but they were pragmatically introduced into my commentary. Maybe I’m just nominalist leaning here. But I imagine a Platonist saying: but you have need of Platonic entities! Don’t you see that the symbols
★ ★ ★
are each instances of the same universal? The universal in question is ★ness, which is instantiated in three locations above!
Maybe I haven’t done a very good job of explaining the Platonist’s position, since I do think that “This is a *★*” is true of the three shapes above. But I don’t see the need for an appeal of a Platonic entity. After all, the first *★* is located to the left, the second is in the middle, the third is to the right. So isn’t there three kinds of *★* in play?
Maybe every shape below is an instantiation of a distinct universal:
▲ ◯ ◼ █ ◣ ◒ ★ ☆ ⚡ ♻ ♫ ♫ ♻ ⚡ ☆ ★ ◒ ◣ █ ◼ ◯ ▲
I presume there will be an appeal that the left-most shape and the right-most shape are of the same kind, namely the ‘▲-kind’. But one is left-most and one is right-most. Why not say that there is a ‘▲-left-most-kind’ and a ‘▲-right-most-kind’? This surely does seem silly. But I don’t see why we shouldn’t say this. We seem to need token-classes here.
I also wonder about shapes in general. If I have a square that is well drawn and a square that is poorly drawn, are each instances of the same universal? Or is there a poorly-drawn-squareness in the one case, and a well-drawn-squareness in the other?
If the universal doesn’t care how well or how poorly a square is drawn, why don’t rectangles count as squares? Why can’t a poorly drawn square that looks more like a trapezoid count as a square?
If the universal does care how well or how poorly a square is instantiated, then it seems we have an infinite degree of squareness. But then how to we stop a slide into every token of anything being an instance of a distinct universal?
I presume that we can bundle general shapes together. Thus, obtuse triangles, obscene triangles and scalene triangles are all triangles. Small squares, large squares and middle-sized squares are all squares. But are we not getting into a relativity to how things appear to me? If I had fuzzy vision, circles and square-like circle-impostors would look the same, and I might think that they instantiate the same universal because they strike me as being of a common and general shape. If I had sharp vision, I would notice that there are no straight lines or right angles, and that Euclidean geometry is false. Then do I have to give up on there ever having been universals for the Euclidean shapes in the first place?
And even if all this can be ignored, how can we ever figure out the fine cuts between instances of triangles of one sort or another and just near cases? How can we divide between when I pile instantiates pileness, and then when reduced instantiates something else?
Perhaps in the case of pileness is problematic in itself, but what of other shapes. I can clearly move pixels a micron this way or that. Does squareness come and go based on these little movement? I presume as well that there are no straight lines, no perfect circles, so wouldn’t we always be stuck with shades of grey?
I could go on and on. I may have gone on too long already. But this really bothers me. I think the modest and tidy framework I had up above avoids these problems. Am I wrong? Or am I right, and the framework is lacking as a result. Or is the notion of Platonism, or something near-to, lurking in the neighborhood?
Wednesday, October 1, 2008
Tuesday, September 30, 2008
Explaining A Process of Reasoning, an objection
Stalnaker proposes that a possible worlds analysis of propositions allows us to escape the dilemma facing reconstructions of arguments used to explain a process of reasoning. The idea is, supposing someone sees a footprint in the sand, and they immediately infer that a person has been walking in the sand within the last few hours, one may explain this inference by constructing a deductively valid argument of this process of reasoning. The restructured argument adds some suppressed premises, e.g. such impressions are made only by human feet, to the explicit premise (the perceptual belief). Now, the dilemma faced by the reconstruction concerns its correctness as an explanation. The suppressed premises must be accounted for, but how exactly must they have entered into the initial inference? The reconstruction either imposes on the agent implausible unconscious processes, or it fails to be an explanation, but is rather a model of how the inference might have happened.
Stalnaker’s account constructs belief states as sets of possible worlds, and individual beliefs as negative properties of belief states. The explanation above is correct, since the belief state will be one relative to which the premise entails the conclusion, and the suppressed premises can be though of as properties of the initial belief, i.e. properties which show that that belief state is one relative to which the explicit premise entails the conclusion. An argument may be extracted for further analysis as follows:
1. if for all possible worlds compatible with the initial belief state of the agent in which the premise is true, the conclusion is also true, then initial belief state of the agent is one relative to which the premise entails the conclusion.
2. The suppressed premises are properties of the initial belief state which show that the belief state is one relative to which the explicit premise entails the conclusion.
3. (1) and (2).
4. if (3) and the initial belief state of the agent contains no possible worlds in which the premises listed are false, then the reconstructed argument is a literal description of the situation.
5. If the reconstructed argument is a literal description of the situation, then it is a correct explanation.
6. The reconstructed argument is a correct explanation.
The objection I wish to raise here concerns the bloated premise (4). Essentially I’ve packed the key properties which an argument must have in order to be considered a correct explanation. A great advantage of this account allows a complicated reconstruction to have many suppressed premises, while still being a literal description – as Stalnaker notes. The problem, however, lies in the multitude of reconstructed arguments that could be assessed as literal descriptions of the situation. The problem, then, is not that it can’t explain the situation, but rather that it has too many explanations.
A weakened Benacerraf dilemma seems to face Stalnaker’s explanations. The suppressed premises may be few in number or many; depending on how complicated we wish to make our explanation. But which explanation is the correct one based on the explicit premise, inferred conclusion, and stipulated suppressed premises? They are all correct, it seems, according to Stalnaker’s account. But that doesn’t seem right. We weren’t hoping to just create an imaginative model of how the inference might have been made, but rather to correctly explain it. But an imaginative model is what we appear to be left with, for the suppressed premises, which show that the belief state is one relative to which the explicit premise entails the conclusion, may be near infinite in number. And since these suppressed premises are what differ from one argument reconstruction to another, then we are left with near infinite possible explanations. A weakened Benacerraf dilemma would conclude that for any explanation, we should not accept it.
The conception of beliefs as negative properties of a belief state was supposed to elucidate this problem of reconstructing arguments. Instead, it has left us with no explanations which we can accept. Perhaps, then, there is something wrong with considering beliefs as negative properties of a belief state.
Maybe some active (not tacit) problems for Stalnaker
Let me start by briefly summing up my understanding of Stalnaker's position in chapter 5. Stalnaker holds that if we allow the concept of acceptance states which are more fundamental than belief or desire states, then we can explain conflicting beliefs as beliefs held in different acceptance states, and deductive reasoning as the understanding which accompanies the merger of two acceptance states. For the acceptance state hypothesis to be true means that the three conditions Stalnaker lays out on pg. 82 must always be true:
1. If P is a member of a set of accepted propositions, and P entails Q, then Q is a member of that set.
2 If P and Q are each members of a set of accepted propositions, then P & Q is a member of that set.
3. If P is a member of a set of accepted propositions, then not-P is not a member of that set.
I think one of the key claims Stalnaker makes is that acceptance can be compartmentalized. This is also the first thing I would like to question. What gives us the ability to compartmentalize our acceptance states? Is it the fact that we can suspend belief periodically to allow different sets of circumstances (different acceptance states)? For instance, in philosophy we sometimes use extraodinary hypothetical situations which could never actually happen in real life to test a hypothesis. Are we not temporarily suspending our beliefs about the world right now to entertain the beliefs of a different acceptance state? The fact that beliefs could affect acceptance states (and not the other way arround) seems to suggest that beliefs are more fundamental (I'm not sure how Kosher this is).
1. If A causes changes in B, then A is more fundamental than B.
2. Beliefs/desires cause the change in acceptance states.
3. Therefore, Beliefs/desires are more fundamental than acceptance states.
I think another problem with Stalnaker's view is that the problem of Deduction poses a bigger problem than he gives credit. I do not think that his answer of tacit beliefs and active beliefs solves the problem because both are still beliefs that you must actually hold. Hypothetically speaking, what if an acceptance state of mine entailed a belief which I could not hold because we are not sufficiently evolved enough at this point to grasp such a concept? Would that concept still count as a tacit belief?
1. I believe that P
2. P entails that afsoldifjsewoifse (my mind cannot grasp such a concept so I mashed keys)
3. I believe that afsoldifjsewoifse
I realize that the trick here is that I could never find an actual example of this to show Stalnaker because recognizing such an example would mean that I could grasp afsoldifjsewoifse to begin with. I guess you would have to add a premise 4 to the above argument where 4. There exists concepts that my mind cannot grasp which can be logically entailed by my current beliefs.
My last thought is that there seems to be something fishy about having tacit beliefs in a completely closed system of belief (like the one Stalnaker accepts in response to Kyburg's "one single fat statement" objection. Stalnaker embraces the idea that all our inductive knowledge could be represented by one fat statement because it makes for one very thin proposition. Wouldn't you also have to include your tacit beliefs into this huge conjuction? If you do not, then it seems incomplete, and if you do then you cannot avoid the problem of deduction. I think this is the biggest problem Stalnaker faces.
1. If P is a member of a set of accepted propositions, and P entails Q, then Q is a member of that set.
2 If P and Q are each members of a set of accepted propositions, then P & Q is a member of that set.
3. If P is a member of a set of accepted propositions, then not-P is not a member of that set.
I think one of the key claims Stalnaker makes is that acceptance can be compartmentalized. This is also the first thing I would like to question. What gives us the ability to compartmentalize our acceptance states? Is it the fact that we can suspend belief periodically to allow different sets of circumstances (different acceptance states)? For instance, in philosophy we sometimes use extraodinary hypothetical situations which could never actually happen in real life to test a hypothesis. Are we not temporarily suspending our beliefs about the world right now to entertain the beliefs of a different acceptance state? The fact that beliefs could affect acceptance states (and not the other way arround) seems to suggest that beliefs are more fundamental (I'm not sure how Kosher this is).
1. If A causes changes in B, then A is more fundamental than B.
2. Beliefs/desires cause the change in acceptance states.
3. Therefore, Beliefs/desires are more fundamental than acceptance states.
I think another problem with Stalnaker's view is that the problem of Deduction poses a bigger problem than he gives credit. I do not think that his answer of tacit beliefs and active beliefs solves the problem because both are still beliefs that you must actually hold. Hypothetically speaking, what if an acceptance state of mine entailed a belief which I could not hold because we are not sufficiently evolved enough at this point to grasp such a concept? Would that concept still count as a tacit belief?
1. I believe that P
2. P entails that afsoldifjsewoifse (my mind cannot grasp such a concept so I mashed keys)
3. I believe that afsoldifjsewoifse
I realize that the trick here is that I could never find an actual example of this to show Stalnaker because recognizing such an example would mean that I could grasp afsoldifjsewoifse to begin with. I guess you would have to add a premise 4 to the above argument where 4. There exists concepts that my mind cannot grasp which can be logically entailed by my current beliefs.
My last thought is that there seems to be something fishy about having tacit beliefs in a completely closed system of belief (like the one Stalnaker accepts in response to Kyburg's "one single fat statement" objection. Stalnaker embraces the idea that all our inductive knowledge could be represented by one fat statement because it makes for one very thin proposition. Wouldn't you also have to include your tacit beliefs into this huge conjuction? If you do not, then it seems incomplete, and if you do then you cannot avoid the problem of deduction. I think this is the biggest problem Stalnaker faces.
Monday, September 29, 2008
A futile defense of Stalnaker
Stalnaker seems to have one hell of a time defending his view. I think this is partly due to his view being false (and vague), but let's see if we can help him out anyhow.
Mark Richard has a pretty clever argument against him. He considers an argument, and evaluates Stalnaker's methods of avoiding the deduction problem with respect to it. The argument is as follows (p.14)
(C) Barbers shave only those who do not shave themselves,
(D) The barber Jones shaved all those who attacked Lionel,
(E) Anderson shaves himself
(C&D&E) -> (A)&(C&D&E)
(A) Anderson did not attack Lionel
But also (C&D&E) -> (J)&(C&D&E)
(J) Jones did not attack Lionel.
Richard's argument runs roughly as follows:
(1) Stalnaker's view
(2) (1) -> (3)
(3) deductive inference is acheived when one considers two or more belief states, and integrates them by having as his/her new belief state the intersection of the states considered
(4) (3)->(5)
(5) There is only one deductive consequence of considering (C&D&E)
(6) (A) is distinct from (J)
(7) (A) and (J) are deductive consequences of considering (C&D&E)
(8) ~(6) (5, 7)
(9) (6)&~(6)
(10) ~(1)
I'd like to apologize to Chelsey for my rampant use of reductio.
(2) is supported in Stalnaker, I'll throw in a couple of quotes
"A person may be disposed, in one kind of context, or with respect to one kind of action, to behave in ways that are correctly explained by one belief state, and at the same time be disposed in another kind of context or with respect to another kind of action to behave in ways that would be explained by a different belief state."(p.83)
And Richard quoting Stalnaker:
"There may be propositions whose truth might be discovered by a purely deductive inquiry... The thesis [is] that acquiring deductive knowledge is putting one's seperate belief states together"
(4) is derived by presuming that the only (or best) way of integrating one's beliefs is to take the intersection of them (the possible worlds). This is the natural way of looking at belief integration under this model, and moreover it's not clear how else one could integrate beliefs.
(6) is supposed to be obvious. Intuitively there are two distinct propositions under question. (7) is assumed by hypothesis). The rest follows.
I believe Stalnaker already has a response to this up his sleeve. Recall Stalnaker chapter (4), in which he discusses the sentence 'Jim is a doctor' as said in the mouth of a child and an adult. I left that paper at school, so I won't quote. However, Stalnaker seems to have the view that the child does not understand the propositions that Jim is a doctor as well as an adult because there are many situations under which the adult could determine the truth value of the proposition, but the child could not. For instance, if the child is unaware that philosophers are Doctors (or has some dim notion of it) then the child wouldn't know the truth value of the proposition if Jim had been a philosopher.
This is all kind of rough and ready, and I think it conflicts with other things Stalnaker says, but let's run with it. On this picture the child and the adult are actually grasping (understanding, whatever) a different set of worlds when considering the proposition that Jim is a doctor. This seems a lot like some sort of descriptivism about that-clauses. There's a set of worlds that a speaker associates with a that-clause. If this is true, there can be multiple associations. This could tell against (4). It may be true that one performs deductive inference by taking the intersection of belief states. However, these belief-states don't match up directly to propostions in the ways that (4) requires. When one considers the consequences of (C&D&E), one takes the intersection of the sets of worlds one currently associates with (C&D&E). This set of worlds is not, however, the set of worlds determined by (C&D&E). So for (4) to be false one merely has to make the deduction twice, each time associating (C&D&E) with different sets of worlds.
This sort of approach can also account for deductive error, and various hooded-man type situations. However, the drawback is that it is descriptivism, and falls prey to the 100,000,000 lethal objections to descriptivism. It also makes it nearly impossible for propositions to be shareable.
On a side note, I can't decide whether or not this is actually Stalnaker's view.
Mark Richard has a pretty clever argument against him. He considers an argument, and evaluates Stalnaker's methods of avoiding the deduction problem with respect to it. The argument is as follows (p.14)
(C) Barbers shave only those who do not shave themselves,
(D) The barber Jones shaved all those who attacked Lionel,
(E) Anderson shaves himself
(C&D&E) -> (A)&(C&D&E)
(A) Anderson did not attack Lionel
But also (C&D&E) -> (J)&(C&D&E)
(J) Jones did not attack Lionel.
Richard's argument runs roughly as follows:
(1) Stalnaker's view
(2) (1) -> (3)
(3) deductive inference is acheived when one considers two or more belief states, and integrates them by having as his/her new belief state the intersection of the states considered
(4) (3)->(5)
(5) There is only one deductive consequence of considering (C&D&E)
(6) (A) is distinct from (J)
(7) (A) and (J) are deductive consequences of considering (C&D&E)
(8) ~(6) (5, 7)
(9) (6)&~(6)
(10) ~(1)
I'd like to apologize to Chelsey for my rampant use of reductio.
(2) is supported in Stalnaker, I'll throw in a couple of quotes
"A person may be disposed, in one kind of context, or with respect to one kind of action, to behave in ways that are correctly explained by one belief state, and at the same time be disposed in another kind of context or with respect to another kind of action to behave in ways that would be explained by a different belief state."(p.83)
And Richard quoting Stalnaker:
"There may be propositions whose truth might be discovered by a purely deductive inquiry... The thesis [is] that acquiring deductive knowledge is putting one's seperate belief states together"
(4) is derived by presuming that the only (or best) way of integrating one's beliefs is to take the intersection of them (the possible worlds). This is the natural way of looking at belief integration under this model, and moreover it's not clear how else one could integrate beliefs.
(6) is supposed to be obvious. Intuitively there are two distinct propositions under question. (7) is assumed by hypothesis). The rest follows.
I believe Stalnaker already has a response to this up his sleeve. Recall Stalnaker chapter (4), in which he discusses the sentence 'Jim is a doctor' as said in the mouth of a child and an adult. I left that paper at school, so I won't quote. However, Stalnaker seems to have the view that the child does not understand the propositions that Jim is a doctor as well as an adult because there are many situations under which the adult could determine the truth value of the proposition, but the child could not. For instance, if the child is unaware that philosophers are Doctors (or has some dim notion of it) then the child wouldn't know the truth value of the proposition if Jim had been a philosopher.
This is all kind of rough and ready, and I think it conflicts with other things Stalnaker says, but let's run with it. On this picture the child and the adult are actually grasping (understanding, whatever) a different set of worlds when considering the proposition that Jim is a doctor. This seems a lot like some sort of descriptivism about that-clauses. There's a set of worlds that a speaker associates with a that-clause. If this is true, there can be multiple associations. This could tell against (4). It may be true that one performs deductive inference by taking the intersection of belief states. However, these belief-states don't match up directly to propostions in the ways that (4) requires. When one considers the consequences of (C&D&E), one takes the intersection of the sets of worlds one currently associates with (C&D&E). This set of worlds is not, however, the set of worlds determined by (C&D&E). So for (4) to be false one merely has to make the deduction twice, each time associating (C&D&E) with different sets of worlds.
This sort of approach can also account for deductive error, and various hooded-man type situations. However, the drawback is that it is descriptivism, and falls prey to the 100,000,000 lethal objections to descriptivism. It also makes it nearly impossible for propositions to be shareable.
On a side note, I can't decide whether or not this is actually Stalnaker's view.
An extraction of an argument from Richards and some words about it
I doubt this will count as a comment paper, but I did the work and thought I may as well share it!
Richards runs an argument of this sort against a possible-worlds semantics, which seems to be the more popular flavor of the 'unstructured proposition theory':
1. According to a possible-worlds semantics, the truth of a valid arguments premises ensures that of its conclusions, and the worlds in which all its premises are true are exactly the world in which all the premises and the conclusion are true.
2. Therefore valid arguments are logical truths. (from 1)
3. Valid arguments are not logical truths.
4. Therefore possible-worlds semantics is false. (from 1 - 3)
I hope that that is structured OK. I really cannot tell!
Richard gives an example with the argument:
Barbers shave only those who do not shave themselves; the barber Jones shaved all the men who attacked Lionel; hence, Jones didn't attack Lionel
which is clearly valid. This of course means that the truth of the premise ensures the truth of the conclusion. This means that the worlds where the premises are true are the worlds where the premises are true and the conclusion is true.
This also means that the intension of:
Barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel
is the intension of:
Barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel, and Jones didn't attack Lionel.
But then that means that it is a truth of logic that:
Whoever believes that (barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel), believes that (barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel, and Jones didn't attack Lionel).
And as Richard points out, this doesn't seem to be a truth, let alone a logical one.
It seems that the unstructured proposition theorist casts too wide a net. They may go on to offer a more restricted interpretation, but it fails as well. It seems that generally unstructured proposition theories have a heck of a time with deduction.
Richards runs an argument of this sort against a possible-worlds semantics, which seems to be the more popular flavor of the 'unstructured proposition theory':
1. According to a possible-worlds semantics, the truth of a valid arguments premises ensures that of its conclusions, and the worlds in which all its premises are true are exactly the world in which all the premises and the conclusion are true.
2. Therefore valid arguments are logical truths. (from 1)
3. Valid arguments are not logical truths.
4. Therefore possible-worlds semantics is false. (from 1 - 3)
I hope that that is structured OK. I really cannot tell!
Richard gives an example with the argument:
Barbers shave only those who do not shave themselves; the barber Jones shaved all the men who attacked Lionel; hence, Jones didn't attack Lionel
which is clearly valid. This of course means that the truth of the premise ensures the truth of the conclusion. This means that the worlds where the premises are true are the worlds where the premises are true and the conclusion is true.
This also means that the intension of:
Barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel
is the intension of:
Barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel, and Jones didn't attack Lionel.
But then that means that it is a truth of logic that:
Whoever believes that (barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel), believes that (barbers shave only those who do not shave themselves, and the barber Jones shaved all the men who attacked Lionel, and Jones didn't attack Lionel).
And as Richard points out, this doesn't seem to be a truth, let alone a logical one.
It seems that the unstructured proposition theorist casts too wide a net. They may go on to offer a more restricted interpretation, but it fails as well. It seems that generally unstructured proposition theories have a heck of a time with deduction.
Saturday, September 27, 2008
Concern Post #2
Maybe I can state my concern over AEs and propositions to a general concern over Types and Tokens.
I seems that Mr. Realist would want to hold that:
red rot rouge
all are instances of the same word-type. The 'redness' type. I'm not totally sure how they would go about expressing this, probably just with saying: these words all express redness. Likewise:
△ ▽ ▷ ► ▼ ◬ ▿ ◿ ▲
all are instances of ▲ity, or triangularity.
Now it seems that Mr. Realist is going to have some problems. Maybe they are just small and bred by my personal confusion. But 'redness' seems to be an English word. If there is an English and a German red-type, this seems to be really the talk of a English and German red-token-class. (Same for the triangle case, with the variety of shapes and designs.) Thus, the Sellarsean move to introduce honest-to-God types: 'red' in English, 'rot' in German, 'rouge' in French all play the same role. Each are •red•s.
Mr. Realist cannot be happy with this, I don't think. Triangularity is supposed to be an abstract entity, not some sort of functional class! Likewise, the sign-designs *△*, *▽*, *▷*, etc. are all of the triangular-kind. Mr. Nominalist wants to say that each shape is called triangular, where Mr. Realist wants to say that each shape is an instance of a three-sided closed-plain figure, i.e. instances of triangularity.
To claim that each shape plays the triangular role, that each is a •triangle• cannot make Mr. Realist very happy at all. We might say that the German 'dreieck' and English 'triangle' each play the same linguistic role: each are •triangle•s. Likewise,
△ ▽ ▷ ► ▼ ◬ ▿ ◿ ▲
are each distinct token-classes of the triangle type. Each shape stands for triangularity, in that: "This is a triangle" is true of each shape.
Mr. Realist cannot seem to be happy about this at all.
It seems that Mr. Realist wants the type to be an entity in the full-blooded sense, distinct from its tokens. The type should be able to be real (or on some accounts, exist) even if its tokens do not exist (or are not real, on those same accounts). To claim that types are only functions seems be incompatible with Mr. Realist's general philosophy. Mr. Realist wants us to have to compare things in the world against things in Platonic heaven to see what they really are. We have to compare instances and exemplifications with the damn Universal! Not with a function!
Certainly we can claim that types or numbers are real, even if they are just functions or structures, but I don't think we are being full-blooded, honest-to-God realists any more. What need have we of Universals when we outsource their explanatory role to functions?
Also, I see a problem in that presumably "the universal blah" and "an instance of the universal blah" seem to be rigid designators, where "the structure that plays the role blah" does not seem to be. Consider:
The killer of Jones is Smith.
It seems that there could be possible worlds where Smith didn't kill Jones. So the killer of Jones isn't a single entity which we can necessarily identify with Smith. Other people could play the killer role. Or no one could. Doesn't the same problem crop up if we want Universals and their instances? It seems that if we appeal to a structuralist account, then in any world, we can literally identify a different entity with the structure! This cannot make Mr. Realist happy at all. That
◣
is an instance of ◣ity seems to be necessary, not just a matter of the shape fitting a role! But this seems to be false, doesn't it.
I seems that Mr. Realist would want to hold that:
red rot rouge
all are instances of the same word-type. The 'redness' type. I'm not totally sure how they would go about expressing this, probably just with saying: these words all express redness. Likewise:
△ ▽ ▷ ► ▼ ◬ ▿ ◿ ▲
all are instances of ▲ity, or triangularity.
Now it seems that Mr. Realist is going to have some problems. Maybe they are just small and bred by my personal confusion. But 'redness' seems to be an English word. If there is an English and a German red-type, this seems to be really the talk of a English and German red-token-class. (Same for the triangle case, with the variety of shapes and designs.) Thus, the Sellarsean move to introduce honest-to-God types: 'red' in English, 'rot' in German, 'rouge' in French all play the same role. Each are •red•s.
Mr. Realist cannot be happy with this, I don't think. Triangularity is supposed to be an abstract entity, not some sort of functional class! Likewise, the sign-designs *△*, *▽*, *▷*, etc. are all of the triangular-kind. Mr. Nominalist wants to say that each shape is called triangular, where Mr. Realist wants to say that each shape is an instance of a three-sided closed-plain figure, i.e. instances of triangularity.
To claim that each shape plays the triangular role, that each is a •triangle• cannot make Mr. Realist very happy at all. We might say that the German 'dreieck' and English 'triangle' each play the same linguistic role: each are •triangle•s. Likewise,
△ ▽ ▷ ► ▼ ◬ ▿ ◿ ▲
are each distinct token-classes of the triangle type. Each shape stands for triangularity, in that: "This is a triangle" is true of each shape.
Mr. Realist cannot seem to be happy about this at all.
It seems that Mr. Realist wants the type to be an entity in the full-blooded sense, distinct from its tokens. The type should be able to be real (or on some accounts, exist) even if its tokens do not exist (or are not real, on those same accounts). To claim that types are only functions seems be incompatible with Mr. Realist's general philosophy. Mr. Realist wants us to have to compare things in the world against things in Platonic heaven to see what they really are. We have to compare instances and exemplifications with the damn Universal! Not with a function!
Certainly we can claim that types or numbers are real, even if they are just functions or structures, but I don't think we are being full-blooded, honest-to-God realists any more. What need have we of Universals when we outsource their explanatory role to functions?
Also, I see a problem in that presumably "the universal blah" and "an instance of the universal blah" seem to be rigid designators, where "the structure that plays the role blah" does not seem to be. Consider:
The killer of Jones is Smith.
It seems that there could be possible worlds where Smith didn't kill Jones. So the killer of Jones isn't a single entity which we can necessarily identify with Smith. Other people could play the killer role. Or no one could. Doesn't the same problem crop up if we want Universals and their instances? It seems that if we appeal to a structuralist account, then in any world, we can literally identify a different entity with the structure! This cannot make Mr. Realist happy at all. That
◣
is an instance of ◣ity seems to be necessary, not just a matter of the shape fitting a role! But this seems to be false, doesn't it.
Thursday, September 25, 2008
Help Quell My Concern
I still am concerned about the Benacerraf Dilemma; that it works.
If we say that there is an entity or a class of entities which are abstract entities or propositions, it seems to me that there has to be a sort of closed criteria to differentiate that single or that single kind of entity. Imagine if we thought that there was such thing as a cat or a kind of thing as cats, but that all sorts of other animals could be identified as cats.
It seems to me like having ten photographs of alleged Sasquatches. Now some true believer wants to say that in any given photo there is a Sasquatch, and in the totality of photos a kind of thing that is a Sasquatch. If the skeptic says: That could be anything in the photo!, can the true believer really get away with saying: Oh well, I guess there is a Sasquatch structure or function which many different things and kinds of things can fill! This seems absurd.
Or imagine finding a dead body. This seems like compelling proof of a murder to the conspiracy theorist. He can construct a theory based on evidence to identify the murderers as Smith or Jones. But the skeptic can point out that the theory is so loose that anyone can fit this role. There are alternative explanation for the dead body for the skeptic. There is no single killer here, nor even a single kind of killer for this body.
If "The dude who wrote Naming and Necessity", "One half of Kripkenstein, the half who isn't Wittgenstein", and "Saul Kripke" are all equally good linguistic representations of Saul Kripke, don't we have to abandon the notion that there is a single linguistic representation of Kripke, or a single kind of linguistic representation of Kripke? I'm not even sure that there is a single type or class of linguistic expressions that pick out Kripke. There are many equally good linguistic representations, many equally good kinds of linguistic representations.
This all seems like a Wittgensteinean move against Universals, with the example of what makes all games games. It seems there is just a family resemblance, a messy cross-section of related but distinct criteria. If we can say that there are cat entities and a kind of entities that are cats, we surely avoid the B.D. If we cannot say that there are proposition entities and a kind of entities that are propositions in the same manner, we should probably drop the notion that they are entities like cats are entities. I don't see this as overly devastating except to Platonism, which is false anyhow.
Thoughts?
If we say that there is an entity or a class of entities which are abstract entities or propositions, it seems to me that there has to be a sort of closed criteria to differentiate that single or that single kind of entity. Imagine if we thought that there was such thing as a cat or a kind of thing as cats, but that all sorts of other animals could be identified as cats.
It seems to me like having ten photographs of alleged Sasquatches. Now some true believer wants to say that in any given photo there is a Sasquatch, and in the totality of photos a kind of thing that is a Sasquatch. If the skeptic says: That could be anything in the photo!, can the true believer really get away with saying: Oh well, I guess there is a Sasquatch structure or function which many different things and kinds of things can fill! This seems absurd.
Or imagine finding a dead body. This seems like compelling proof of a murder to the conspiracy theorist. He can construct a theory based on evidence to identify the murderers as Smith or Jones. But the skeptic can point out that the theory is so loose that anyone can fit this role. There are alternative explanation for the dead body for the skeptic. There is no single killer here, nor even a single kind of killer for this body.
If "The dude who wrote Naming and Necessity", "One half of Kripkenstein, the half who isn't Wittgenstein", and "Saul Kripke" are all equally good linguistic representations of Saul Kripke, don't we have to abandon the notion that there is a single linguistic representation of Kripke, or a single kind of linguistic representation of Kripke? I'm not even sure that there is a single type or class of linguistic expressions that pick out Kripke. There are many equally good linguistic representations, many equally good kinds of linguistic representations.
This all seems like a Wittgensteinean move against Universals, with the example of what makes all games games. It seems there is just a family resemblance, a messy cross-section of related but distinct criteria. If we can say that there are cat entities and a kind of entities that are cats, we surely avoid the B.D. If we cannot say that there are proposition entities and a kind of entities that are propositions in the same manner, we should probably drop the notion that they are entities like cats are entities. I don't see this as overly devastating except to Platonism, which is false anyhow.
Thoughts?
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