Above, three theoretical positions were sketched. Each attempts to resolve the dilemma faced by an austere ontology. There is a certain sense in which an utterance of 'the table in front of me exists' reflects how the world is. Regularly, one could explain this by appealing to a type of object that is meant by use of the word 'table', a material object that is referenced by the definite description 'the table in front of me', etc. But one who denies that many such objects exist, as we do, cannot avail himself of these tools. One therefore is in need of an explanation.
The Indirect Correspondence theory of truth, presented by Horgan, appeals to two different types of truth. Direct Correspondence is a relatively rare semantic standard, only applying when one is serious about his metaphyiscs, i.e. when discussing ontology. According to DC standards, a sentence is true iff the ontic claims made in the sentence reflect existing ontology. For example, 'the sky is blue' is DC true iff the single object referenced by 'the sky' has the property referenced by 'blue'.
Usually, though, an individual is not all that concerned with directly referencing actually existing objects. In these contexts one evaluate sentences under IC standards. These standards are not systematic, however, and vary across contexts. More will be said on IC standards later.
The Paraphrase Strategy works by converting everyday discourse into "literal" claims about the world. As noted above, an utterance of 'the sun moved behind the trees' is true because it can be unpacked into a complex series of claims about optics, the movement of celestial bodies, etc.
But such an analysis is problematic because it creates a disconnect between the intentions of an utterance by the speaker and an utterance itself. Consider two separate utterances of 'the sun moved behind the trees'. Utterance A is made by a 10th-century English peasant on his 20th birthday. Utterance B is made by a 21st-century physics student on his 20th birthday. What the English peasant intended to say is that, quite literally, the yellow object in the sky moved until it was behind the trees. The physics student, however, did not literally mean the sun moved while the trees remained stationary; he utilized the Paraphrase Strategy to cite a complex physical fact in six words. No such intention existed for the peasant. Indeed, if one were to ask him if he, in actuality, meant to say that the earth rotated until light emanating from the sun was obscured by trees he would say no.
This puts the Paraphrase strategy before another dilemma. Utterance A is either true or false. If it is false, then an explanation is required. Under what conditions does a paraphrase strategy succeed? Is it just in case the speaker is aware of the relevant facts and intends to use a particular utterance as a paraphrase for them? If this were the case then an enormous, perhaps insurmountable, epistemic burden is placed before any individual who hopes to say something true about the world. But if we maintain that what the peasant said is true, then there is reason to conclude that intention need not have any bearing on the truth of an utterance. If one maintains that speaker intentions play a vital role in the correct semantic theory (whatever it may be), one should seek an alternative to the Paraphrase Strategy.
Friday, August 6, 2010
Wednesday, August 4, 2010
Options for an Austere Ontologist
Once we accept (N), or any other species of austere ontology, we are in need of an explanation. Everyday discourse seemingly makes use of a variety of objects, simple and composite alike. According to nihilism, though, these objects do not exist. What, then, is one saying with an utterance of 'The sun moved behind the trees'? There is no such thing as a sun, and no such things as trees. What is going on semantically?
There are three options available. First, one can say that such sentences are false. After all, 'sun' and 'trees' fail to refer to any object existing in the world. According to this position, the Error Theory on Everyday Discourse, much of what is said in ordinary conversation is simply false.
One would like to differentiate between sentences like 'The grass is green', in which something prima facie true is conveyed, and sentences like 'The grass is blue'. It would be a blow to the view if utterances of the above sentences always had identical semantic worth. A well-fleshed theory, then, will have to accommodate this with some "pseudo-truth" condition.
Another semantic position is to claim that utterances made in everyday discourse, while true, are not as immediately true as ones that make ontic claims reflecting the correct ontology. This is done through the Paraphrase Strategy. An utterance like 'The sun moved behind the trees' is true because it is shorthand for a claim about a complex collection of astronomical facts.
The last option is the Indirect Correspondence theory of truth, presented by Horgan and Potrc. According to this theory, 'The sun moved behind the trees' is true simpliciter. Unlike Paraphrase Theory, everyday discourse need not be reduced to claims about ontology. Truth holds even though there is no object to which 'the sun' refers; furthermore, there is no way to reduce such utterances to ones that do refer to ontologically pure objects.
There are three options available. First, one can say that such sentences are false. After all, 'sun' and 'trees' fail to refer to any object existing in the world. According to this position, the Error Theory on Everyday Discourse, much of what is said in ordinary conversation is simply false.
One would like to differentiate between sentences like 'The grass is green', in which something prima facie true is conveyed, and sentences like 'The grass is blue'. It would be a blow to the view if utterances of the above sentences always had identical semantic worth. A well-fleshed theory, then, will have to accommodate this with some "pseudo-truth" condition.
Another semantic position is to claim that utterances made in everyday discourse, while true, are not as immediately true as ones that make ontic claims reflecting the correct ontology. This is done through the Paraphrase Strategy. An utterance like 'The sun moved behind the trees' is true because it is shorthand for a claim about a complex collection of astronomical facts.
The last option is the Indirect Correspondence theory of truth, presented by Horgan and Potrc. According to this theory, 'The sun moved behind the trees' is true simpliciter. Unlike Paraphrase Theory, everyday discourse need not be reduced to claims about ontology. Truth holds even though there is no object to which 'the sun' refers; furthermore, there is no way to reduce such utterances to ones that do refer to ontologically pure objects.
Tuesday, August 3, 2010
Re: Austere Realism
So I think I have a substantially clearer picture of H&P's theory in Austere realism. But I've run into another bit of confusion that is even more out of my comfort zone than the previous. I haven't read Dan Korman's review yet, so I'm not sure if he says anything about what I'm confused about. At any rate.
Before, I was confused about the semantic standards under which Indirect Correspondence was governed. Claims made in a Direct Correspondence context are true when the ontic claims match the ontology of the world. IC claims are true in virtue of the way the world is, but are not made true in any thoroughly systematic way. That is, there are no exceptionless rules that a sentence must follow.
This is best understood by contrasting it to two competing views. The first is that claims like 'the sun moved behind the trees' and 'Israel invaded the Gaza strip' are, strictly speaking, false. The view would then have to offer an explanation as to why such sentences are different than absolutely false sentences like 'the grass is blue'. Call this the Error Theory on Everyday Correspondence. Much of what is said day-to-day is simply false.
The second view is the paraphrase strategy. True sentences that don't directly reflect ontology (ontic claims do not mirror ontology) are true in virtue of some paraphrase strategy. 'The sun moved behind the trees' is true because it is a paraphrase of some complex conjunction of astronomic facts.
H&P's Indirect Correspondence theory is NOT either of these views. They say that IC sentences are true in virtue of the world and that such sentences might not be paraphrase-able to something following DC standards. The problem now is that we're left with a non-systematic way of evaluating sentences. Our semantics cannot be given in "rule" form, and that's weird.
(As an upshot of this, though, is that IC seems to provide a clean answer to problems of reference re: fiction. Claims about Sherlock Holmes reflect something about the world even if 'Sherlock Holmes' does not refer to any actual thing.)
They defend this by arguing that the mind also does not operate under systematic, exceptionless rules. That is, (if I'm getting the terminology right) they deny computational cognitive science. The reasoning is absolutely beyond me, running on mathematical models that map possible thought processes(?).
Now, it seems to me that there are two serious objections to this view that are independent of arguments in cognitive science. The first is that, presumably, other organisms do operate under some form of computational, "rule governed" cognition. Worms, or a similarly neurologically simple organism, might be an example. Given that humans evolved from some version of such an organism, how did it come about that we switched from computational cognition to non-computational cognition?
Second, if H&P are going to hold themselves to the claim that human cognition really is noncomputational, then it must be evolutionarily so. That is, humans (or an ancestor of humans) evolved into such a cognitive state. This means that noncomputational cognition is either (1) evolutionarily neutral, or (2) evolutionarily beneficial. [The actual picture is more complicated, but the simplified version should get the point across.]
If (1), then noncomputational cognition developed through some sort of genetic drift. This would imply that there should be the possibility of computationally-thinking humans. This seems odd, and I suspect a formal argument can be made out of it.
If (2), then H&P and similar noncomputationalists stand in need of an explanation. Why is it evolutionarily beneficial? And why is it (presumably) not beneficial for other organisms?
Before, I was confused about the semantic standards under which Indirect Correspondence was governed. Claims made in a Direct Correspondence context are true when the ontic claims match the ontology of the world. IC claims are true in virtue of the way the world is, but are not made true in any thoroughly systematic way. That is, there are no exceptionless rules that a sentence must follow.
This is best understood by contrasting it to two competing views. The first is that claims like 'the sun moved behind the trees' and 'Israel invaded the Gaza strip' are, strictly speaking, false. The view would then have to offer an explanation as to why such sentences are different than absolutely false sentences like 'the grass is blue'. Call this the Error Theory on Everyday Correspondence. Much of what is said day-to-day is simply false.
The second view is the paraphrase strategy. True sentences that don't directly reflect ontology (ontic claims do not mirror ontology) are true in virtue of some paraphrase strategy. 'The sun moved behind the trees' is true because it is a paraphrase of some complex conjunction of astronomic facts.
H&P's Indirect Correspondence theory is NOT either of these views. They say that IC sentences are true in virtue of the world and that such sentences might not be paraphrase-able to something following DC standards. The problem now is that we're left with a non-systematic way of evaluating sentences. Our semantics cannot be given in "rule" form, and that's weird.
(As an upshot of this, though, is that IC seems to provide a clean answer to problems of reference re: fiction. Claims about Sherlock Holmes reflect something about the world even if 'Sherlock Holmes' does not refer to any actual thing.)
They defend this by arguing that the mind also does not operate under systematic, exceptionless rules. That is, (if I'm getting the terminology right) they deny computational cognitive science. The reasoning is absolutely beyond me, running on mathematical models that map possible thought processes(?).
Now, it seems to me that there are two serious objections to this view that are independent of arguments in cognitive science. The first is that, presumably, other organisms do operate under some form of computational, "rule governed" cognition. Worms, or a similarly neurologically simple organism, might be an example. Given that humans evolved from some version of such an organism, how did it come about that we switched from computational cognition to non-computational cognition?
Second, if H&P are going to hold themselves to the claim that human cognition really is noncomputational, then it must be evolutionarily so. That is, humans (or an ancestor of humans) evolved into such a cognitive state. This means that noncomputational cognition is either (1) evolutionarily neutral, or (2) evolutionarily beneficial. [The actual picture is more complicated, but the simplified version should get the point across.]
If (1), then noncomputational cognition developed through some sort of genetic drift. This would imply that there should be the possibility of computationally-thinking humans. This seems odd, and I suspect a formal argument can be made out of it.
If (2), then H&P and similar noncomputationalists stand in need of an explanation. Why is it evolutionarily beneficial? And why is it (presumably) not beneficial for other organisms?
Friday, July 30, 2010
Sorites Applied to Composition
The sorites paradox arises frequently when the property in question appeals to some
manner of degree. Above, it was demonstrated that properties that fall under the sorites paradox cannot be natural. This is because such a property, if it is to be coherent at all, is vague. Since there is no vagueness in the world, such a property does not, in the final metaphysical picture, exist.
(1) If a property falls under the sorites paradox, then it is not a natural property.
There are, of course, a plethora of answers to the Special Composition Question. The aim of this section is only to eliminate one type of answer. Under compatibilst answers to SCQ, there are those that appeal to some degree of contact between parts. Prima facie, this type of answer is promising. Consider again our ham sandwich. Isn't it just when we take the ham and cheese and place them between the bread that a ham sandwich is formed?
This, certaintly, is a case in which the distance between the parts is relevent. There is no sandwich when the parts are scattered across the kitchen counter. But what about the parts getting closer allows for a sandwich to form? Perhaps they need to be touching. But if that were the answer to SCQ, then every time two people shake hands, they form a new object. Surely this is not the case.
1) If CONTACT is true, then every time two people shake hands, an object is formed.
2) It is not the case that every time two people shake hands, an object is formed.
3) CONTACT is not true.
A similar line of reasoning denies all answers that appeal to some connectedness between the parts (call these fusion-type answers).
Now what of an appeal direct to distance of parts? Our ham sandwich does not come into existence until all the parts are some distance away from each other. But recall the argument given against baldness. Where would one mark the distinction between ham sandwich and no ham sandwich? One meter? One centimeter? One micrometer? Surely my sandwich is allowed some measure of shifting without falling out of existence.
(1) If two parts n units apart form an object, then two parts n+1 units apart form an object.
Unfortunetly, this is sufficient to run a sorites paradox.
(1) If two parts n units apart form an object, then two parts n+1 units apart form an object.
(2) Two parts 0 units apart form an object. (If there is any distance that permits composition, it is this)
(3) Two parts 1 unit apart form an object. (From 1 and 2)
(4) Two parts 2 units apart form an object. (From 1 and 3)
...
(100,001) Two parts 99,999 units apart form an object. (From 1 and 100,000)
(100,002) Two parts 99,999 units apart do not form an object. (From common sense)
(100,003) Contradiction!
Thus, any answer to the Special Composition question cannot appeal only to the spacial relations that hold between objects. The argument can be run analogously to time, and likely any other quantitative relation. Note, however, that this argument is vulnerable if space is discrete. More on this will be said later.
manner of degree. Above, it was demonstrated that properties that fall under the sorites paradox cannot be natural. This is because such a property, if it is to be coherent at all, is vague. Since there is no vagueness in the world, such a property does not, in the final metaphysical picture, exist.
(1) If a property falls under the sorites paradox, then it is not a natural property.
There are, of course, a plethora of answers to the Special Composition Question. The aim of this section is only to eliminate one type of answer. Under compatibilst answers to SCQ, there are those that appeal to some degree of contact between parts. Prima facie, this type of answer is promising. Consider again our ham sandwich. Isn't it just when we take the ham and cheese and place them between the bread that a ham sandwich is formed?
This, certaintly, is a case in which the distance between the parts is relevent. There is no sandwich when the parts are scattered across the kitchen counter. But what about the parts getting closer allows for a sandwich to form? Perhaps they need to be touching. But if that were the answer to SCQ, then every time two people shake hands, they form a new object. Surely this is not the case.
1) If CONTACT is true, then every time two people shake hands, an object is formed.
2) It is not the case that every time two people shake hands, an object is formed.
3) CONTACT is not true.
A similar line of reasoning denies all answers that appeal to some connectedness between the parts (call these fusion-type answers).
Now what of an appeal direct to distance of parts? Our ham sandwich does not come into existence until all the parts are some distance away from each other. But recall the argument given against baldness. Where would one mark the distinction between ham sandwich and no ham sandwich? One meter? One centimeter? One micrometer? Surely my sandwich is allowed some measure of shifting without falling out of existence.
(1) If two parts n units apart form an object, then two parts n+1 units apart form an object.
Unfortunetly, this is sufficient to run a sorites paradox.
(1) If two parts n units apart form an object, then two parts n+1 units apart form an object.
(2) Two parts 0 units apart form an object. (If there is any distance that permits composition, it is this)
(3) Two parts 1 unit apart form an object. (From 1 and 2)
(4) Two parts 2 units apart form an object. (From 1 and 3)
...
(100,001) Two parts 99,999 units apart form an object. (From 1 and 100,000)
(100,002) Two parts 99,999 units apart do not form an object. (From common sense)
(100,003) Contradiction!
Thus, any answer to the Special Composition question cannot appeal only to the spacial relations that hold between objects. The argument can be run analogously to time, and likely any other quantitative relation. Note, however, that this argument is vulnerable if space is discrete. More on this will be said later.
Saturday, July 24, 2010
An Introduction to the Sorites Paradox
Meet Charles. Charles has graciously volunteered himself for a demonstration. Now, Charles is a middle-aged man and, unfortunately, has started to bald. Now, he isn't quite bald yet; he still has well-groomed mane. But there is a bald spot that for the past few weeks has been growing. Let n be the number of individual hairs on Charles' head. Suffice for our purposes, n is a pretty big number. For those that work better without variables, feel free to plug in 100,000.
(1) Charles has n hairs.
(2) Someone with n hairs is not bald.
(3) Therefore Charles, with n hairs is not bald.
Now comes the experiment. We sit Charles down on a comfortable chair and give him a big, juicy rib eye steak for his troubles. We then take a pair of tweezers and pluck out one of Charles' hairs. It seems obvious that we did not do much to change Charles' being bald or not. Sure, we may have put him one hair closer to complete baldness. But we did not make him bald by removing a single hair.
(4) Charles has n-1 hairs.
(5) Someone with n-1 hairs is not bald.
(6) Therefore charles, with n-1 hairs, is not bald.
What if we kept plucking out a hair of Charles, one by one, and asking ourselves at that juncture if he were bald? Surely, at some point he must become bald. After all, a man with no hair on his head is most certainly bald. But where is that point? A man with only a single hair would still, presumably, be bald. So, too, would a man with two hairs - as evidenced think Homer Simpson. Furthermore, the following principle seems to hold:
(7) If someone with n hairs is bald, then someone with n+1 hairs is bald.
This is grounded in the implausibility that a single hair makes the difference between baldness and non-baldness. Imagine two men standing next to each other, one bald and one not bald. Would you expect there to be only a single hair to separate the two? Is that even possible? Even more troublesome is that it appears we can also reason in the opposite direction.
(8) If someone with n hairs is not bald, then someone with n-1 is not bald.
This is justified in exactly the same way as (7). Losing a single hair cannot move anyone into a state of baldness. Thus, fully presented, the argument runs:
(1) If someone with n hairs is not bald, then someone with n-1 hairs is not bald.
(2) Someone with 100,000 hairs is not bald.
(3) Someone with 99,999 hairs is not bald. (From 1 and 2)
(3) Someone with 99,998 hairs is not bald. (From 1 and 3)
...
(100,001) Someone with 0 hairs is not bald. (From 1 and 100,000)
(100,002) Someone with 0 hairs is bald. (From common sense!)
(100,003) Contradiction!
As noted above, the argument could be run in reverse, with the intuition at (100,002) reading, "Someone with 100,000 hairs is not bald."
This type of puzzle is known as the sorites paradox. It is not restricted, of course, to baldness. Parallel arguments can be made for things like heaps of sand (or garbage). There are a variety of replies to the paradox. We will first, however, apply the paradox specifically to material composition.
(1) Charles has n hairs.
(2) Someone with n hairs is not bald.
(3) Therefore Charles, with n hairs is not bald.
Now comes the experiment. We sit Charles down on a comfortable chair and give him a big, juicy rib eye steak for his troubles. We then take a pair of tweezers and pluck out one of Charles' hairs. It seems obvious that we did not do much to change Charles' being bald or not. Sure, we may have put him one hair closer to complete baldness. But we did not make him bald by removing a single hair.
(4) Charles has n-1 hairs.
(5) Someone with n-1 hairs is not bald.
(6) Therefore charles, with n-1 hairs, is not bald.
What if we kept plucking out a hair of Charles, one by one, and asking ourselves at that juncture if he were bald? Surely, at some point he must become bald. After all, a man with no hair on his head is most certainly bald. But where is that point? A man with only a single hair would still, presumably, be bald. So, too, would a man with two hairs - as evidenced think Homer Simpson. Furthermore, the following principle seems to hold:
(7) If someone with n hairs is bald, then someone with n+1 hairs is bald.
This is grounded in the implausibility that a single hair makes the difference between baldness and non-baldness. Imagine two men standing next to each other, one bald and one not bald. Would you expect there to be only a single hair to separate the two? Is that even possible? Even more troublesome is that it appears we can also reason in the opposite direction.
(8) If someone with n hairs is not bald, then someone with n-1 is not bald.
This is justified in exactly the same way as (7). Losing a single hair cannot move anyone into a state of baldness. Thus, fully presented, the argument runs:
(1) If someone with n hairs is not bald, then someone with n-1 hairs is not bald.
(2) Someone with 100,000 hairs is not bald.
(3) Someone with 99,999 hairs is not bald. (From 1 and 2)
(3) Someone with 99,998 hairs is not bald. (From 1 and 3)
...
(100,001) Someone with 0 hairs is not bald. (From 1 and 100,000)
(100,002) Someone with 0 hairs is bald. (From common sense!)
(100,003) Contradiction!
As noted above, the argument could be run in reverse, with the intuition at (100,002) reading, "Someone with 100,000 hairs is not bald."
This type of puzzle is known as the sorites paradox. It is not restricted, of course, to baldness. Parallel arguments can be made for things like heaps of sand (or garbage). There are a variety of replies to the paradox. We will first, however, apply the paradox specifically to material composition.
Thursday, July 22, 2010
On the Types of Answers to the Special Composition Question
There are three broad types of answers that can be given to the Special Composition Question. They are divided by their position on the number of composite objects relative to objects in general:
(N) [∀x: x ∈ M] ~∃y(Pxy ^ x =/= y)
(U) [∀x: x ∈ M] [∀y: y ∈ M] ∃z(Pxz ^ Pyz)
(C) ~(U) ^ ~(N), or [∃x: x ∈ M] ∃y(Pxy ^ x =/= y) ^ [∃x: x ∈ M][∃y: y ∈ M] ~∃z(Pxz ^ Pyz)
(N), or nihilism, claims that there are no cases of composition. All material objects that exist have no proper parts (proper parts satisfy Pxy and x=/=y). Thus, no matter how I arrange my bread, meat, and cheese, they will never compose another object. All material objects are simple.
(U), or universalism, claims that for any two distinct objects (x =/= y), they compose an object. Thus, the two slices of bread compose an object. That object and the meat compose an object. And that object and the cheese compose another object. This theory still allows for simple objects. Note, however, that an object cannot be a part of a composite object if another of the objects parts already contains the first as a part. That is, all objects can be parts only once; there is no double dipping of parthood. Consider objects A, B, and 3. Object 3 is the composite of objects A and B. It is impossible for there to be a 4th object that is composed of object 3 and object B. This is because object B is a part of object 3.
(C), compatiblism, claims that composition sometimes occurs. This answer is logically incompatible with either (N) or (U). Nihilism and compatibilism disagree on there being at least one composite object. Universalism and compatibilism disagree on there being an instance of failed composition. All three disagree on the number of material objects (or at least the number of potential material objects).
(N) [∀x: x ∈ M] ~∃y(Pxy ^ x =/= y)
(U) [∀x: x ∈ M] [∀y: y ∈ M] ∃z(Pxz ^ Pyz)
(C) ~(U) ^ ~(N), or [∃x: x ∈ M] ∃y(Pxy ^ x =/= y) ^ [∃x: x ∈ M][∃y: y ∈ M] ~∃z(Pxz ^ Pyz)
(N), or nihilism, claims that there are no cases of composition. All material objects that exist have no proper parts (proper parts satisfy Pxy and x=/=y). Thus, no matter how I arrange my bread, meat, and cheese, they will never compose another object. All material objects are simple.
(U), or universalism, claims that for any two distinct objects (x =/= y), they compose an object. Thus, the two slices of bread compose an object. That object and the meat compose an object. And that object and the cheese compose another object. This theory still allows for simple objects. Note, however, that an object cannot be a part of a composite object if another of the objects parts already contains the first as a part. That is, all objects can be parts only once; there is no double dipping of parthood. Consider objects A, B, and 3. Object 3 is the composite of objects A and B. It is impossible for there to be a 4th object that is composed of object 3 and object B. This is because object B is a part of object 3.
(C), compatiblism, claims that composition sometimes occurs. This answer is logically incompatible with either (N) or (U). Nihilism and compatibilism disagree on there being at least one composite object. Universalism and compatibilism disagree on there being an instance of failed composition. All three disagree on the number of material objects (or at least the number of potential material objects).
Wednesday, July 21, 2010
On the Arcane Musings of Philosophers
In everyday discourse, we make reference to an abundance of objects. In fact, the previous sentence implied at least three with the words 'discourse', 'we', and 'abundance'. Many of these are things we can directly sense, like my cat Gizmo. Some objects, are of an abstract nature. The number three is not an object that one would expect to bump into on his way to work.
This paper will focus on the first category, so-called material objects. A material object is one that is located in the material world. It has extension: length, width, height, and therefore volume. (Note here that, technically, a material object will be defined as an object that has a part that has extension. Recall that all objects have themselves as a part.)
Where M is the set of all material objects, Pxy is the relation of x being a part of y and Ex is the property of extension:
(1) [∀x: x ∈ M] ∃y(Pyx ^ Ey)
The principle target of inquiry will be an answer to van Inwagen's Special Composition Question. That is, when is it the case that two or more objects compose an additional object?
SCQ: ∃y the xs compose y?
All of this probably seems quite obscure to the reader. Let me try to distill the jargon. Consider the food I've laid out on the kitchen counter. There are two pieces of bread, some ham, and a slice of cheese. The Special Composition Question amounts to this: in what circumstances do the bread, the ham, and the cheese compose some further object?
This paper will focus on the first category, so-called material objects. A material object is one that is located in the material world. It has extension: length, width, height, and therefore volume. (Note here that, technically, a material object will be defined as an object that has a part that has extension. Recall that all objects have themselves as a part.)
Where M is the set of all material objects, Pxy is the relation of x being a part of y and Ex is the property of extension:
(1) [∀x: x ∈ M] ∃y(Pyx ^ Ey)
The principle target of inquiry will be an answer to van Inwagen's Special Composition Question. That is, when is it the case that two or more objects compose an additional object?
SCQ: ∃y the xs compose y?
All of this probably seems quite obscure to the reader. Let me try to distill the jargon. Consider the food I've laid out on the kitchen counter. There are two pieces of bread, some ham, and a slice of cheese. The Special Composition Question amounts to this: in what circumstances do the bread, the ham, and the cheese compose some further object?
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