Monday, September 12, 2011

The Growing Argument

Hi All,

Here is the argument we discussed today:

1. If M is a material object, then M is identical to the sum S of material particles that compose M at time t.
2. If M is identical to the sum S of material particles that compose M at t, then M is always distinct from any sum S* that is distinct from S.
3. So, if M is a material object, then M is always distinct from any sum S* that is distinct from S.
4. If M is always distinct from any sum S* that is distinct from S, then M never survives the gain or loss of any parts.
5. So, if M is a material object, then M never survives the gain or loss of any parts.

Here is some support for its premises:
Support for 1. Assume M is material. Then it seems the only option for M is for it to be (identical to) some (hunk of or sum of) matter. So (1) is true.

Support for 2. Assume the antecedent. The consequent then follows provided strict identity is not temporary: if ever x = y, then always x = y (or at least whenever x or y exist). This may sound surprising, but I don’t think it should. Recall strict identity is governed by Leibniz’s Law. Now suppose x used to be distinct from y, but later on will not be. Then x has the following property: it used to be distinct from y. But y lacks that property. But LL says if x = y, then Fx iff Fy. Since they differ in their properties, it cannot be the case that they are strictly identical. So identity is not temporary. So 2 is true.

Support for 3. Subconclusion.

Support for 4. Assume antecedent. Suppose M gained or lost a part. Then we would be considering another sum S* that is distinct from S. M can’t be S* since M is identical to S. So 4 is true.

Finally, here's what we said about identity:
Identical: Strict, literal identity. Not like “identical” twins. Like 4 is identical to the sum of 2 and 2. Identity is a two-place logical relation governed by Leibniz’s Law: if x = y, then Fx iff Fy (x and y have all of the same properties).

Some good suggestions came up in class concerning where things might be going wrong. Other thoughts?


  1. We discussed how the argument could go wrong at point 1 or point 2, but I think we should also look at point 3. In class I had brought up how I thought M=S and that S could eventually come to exist such that S=S* (and thus M=S=S*). But it was pointed out that something containing 4 cells at some point in time cannot be equal to something containing 3 cells at some point in time. I agree that in science and math this argument and Leibniz’s Law makes sense. However what if we consider the case of Tillman:

    Tillman is a material object (M) who has all his body parts intact. Thus, Tillman (M) = a body containing all its parts (S). Suppose at some point Tillman loses an arm. We would argue that Tillman is no longer a body containing all its parts (S), but a body containing most of its parts (S*). This is where I see the problem with point 3: If M is a material object, then M is always distinct from any sum S* that is distinct from S. We can see that S ≠ S*, for a body containing all its parts ≠ a body containing most of its parts. But wouldn’t we argue that Tillman is still a material object? He is still Tillman, but he is no longer a body containing all its parts. It seems that now Tillman (M) = a body containing most of its parts (S*) but ≠ a body containing all of its parts (S). But the logic of this argument says that for M to be a material object it must be identical to S. I argue that Tillman is still a material object existing in space time even though he has undergone a change. We wouldn’t say that there are two Tillmans: the one that existed with all its body parts and the one that exists now with most of its body parts. Tillman is still a material object, albeit changed. Perhaps S cannot change and become S*, but couldn’t there exist a change in M such that at one point M = S but now M=S*?

    Does that mean that the argument concerning material objects is not valid? Or does it mean that we can only apply it to certain cases?

    I know there are some holes in my argument, but I cannot fathom applying this argument to people. If a person goes through some change he/she does not necessarily become a completely different person.


  2. I think the real problem here is that living things are not solely material objects - that is, 'objects' possessing some level of sentience cannot be the same as non-sentient things such as bricks, rocks and ships. If Tillman loses a body part, Tillman's body has changed but Tillman is still Tillman. A person's 'identity' seems more connected to the mind than the body, so I would argue that people are only material objects in so far as it can be thought that the mind is a material object. So maybe we can't apply the argument to living (sentient) things.

    That said, I'm not sure there really is a problem with the argument when applied to purely physical objects. While it seems strange to say that an object never survives the loss or gain of any parts, it's only strange if this is taken to mean that the object ceases to exist - it could instead be interpreted to mean only that a transformation has taken place and that the object still exists but in a different form. Maybe there's some way to set aside strict identity and come up with an explanation for the transformation of material objects.

  3. Maddy:

    (3) follows from (1) and (2). So, if we want to deny (3), we're going to have to deny one of its premises (i.e., (1) or (2)). I think your Tillman-scenario can be used to attack (2). I'll try to reformulate your objection to do this.

    Suppose that a material object exists. Let's say that the material object is a stone. Call him 'Stoney'. Stoney is identical to the sum of sand-particles (call this sum 'S') that compose Stoney at some time (call this time 't').

    Next, suppose at another time (t+1) Stoney loses a particle of sand. Now at t+1, Stoney is identical to S* (which is the sum of the particles of sand making up Stoney at t+1), and S is distinct (nonidentical) from S*.

    According to (2), if Stoney is identical to S at t, then Stoney is always distinct from S*. But Maddy's case shows that while Stoney is identical to S at t, it is not the case that Stoney is always distinct from S*. There is some time (namely, t+1) where Stoney is identical to S*. So, (2) is false.

    Is this the idea you had in mind?

  4. I think the main problem with this argument is the way it is represented. If, for example we have some mystery object (M) be identical to the sum of it's parts (S), and it loses a part, representing it as S* causes issue because nothing is stating that M is identical to S*. Instead it should be represented as S-1 if it loses a part. Therefore, M would be interchangeable with S, and it could similarly represented as M-1, thus the identity is preserved.

    Furthermore another issue I see is that there should be a distinction of what are necessary parts and what are temporary. If Tillman were to lose an arm he would still be Tillman, because his arm isn't necessary to his identity. If however he were to lose his cerebral cortex, then the argument could be made that his identity had changed, because chances are he wouldn't resemble anything like his former self.

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  6. Adam:

    If s = 4 balls at t, and s* = 3 balls at t2 and m=s, then it seems if you accept Leibniz's law, then m does not equal (don't have symbol handy) s*, for m and s* do not share all the same properties. I guess you could give a story as to how Leibniz law fails and how maybe temporary identity works.


    You could just say M=S and M-1 = S-1, but this seems do avoid the issue because M does not equal M-1 and so would be a different object (which is the problem).

    As for your second point, maybe you could say that M (Tillman) does not = S (the collection of his bits at time t), but rather M = E (the collection of bits you consider necessary to him). Then your denying premise 1. But then it seems that if these necessary bits are a composite them selves (and not just a simple) then we can run the problem on those objects. I also don't think there is any simple that is M.


    Deny premis 4 (i didn't think of this my self, chris wrote it on the board briefly).

    M = S and M does not = S*. M can lose a part though. When M does it still has the property of at some time not being identical with S*, where as S* has the the property of always being identical to its self. Thus by Leibniz law M Does not = S*.

    Ummm, my problem with this answer. If s= 4 balls and s* = 3 balls and m=s and s* is a proper part of m and m loses one ball, then these are two objects that exist in the exact same location, namely m and S*. But i think this is just another problem of material composition (i forget which one) that we all still have to deal with (except the nihilist).

    So ya, please refute :)

  7. Miriam,

    In reagrds to your second paragraph, if some object fails to survive the loss or addition of its parts at t, then it ceases to exist at t. I don't see any plausibly correct way of interpreting 'fails to survive the loss or addition of parts' that avoids this consequence.

    I think what you might be getting at is something like the following: One can deny (4) and support such a denial with an argument that makes use of the notion of transformation. This might be a fruitful way to go.

  8. Greg and Miriam:

    I think Greg is correct.

    To elaborate on his second point (and my positive argument) To deny premise four you must deny the consequent (since the antecedent is the conclusion of p3). To deny it you must show how M can gain and lose parts and still be distinct from S*. I showed how you can do this a few comments ago, but its seems to rely on the thought that objects can "move through" (transform (which seems to be your thought)) time.

    I wounder how we could argue for or against this last point? Maybe appeal to intuitions? Maybe one of them has consequences we wouldn't accept that the other doesn't have? I remember reading David Lewis "On The Plurality Of Worlds" where he briefly talks about this point. He talks about endurance and predurance. Endurance is when an object persists through time by being wholly present at different temporal stages and predurance is when something persists through time by having different temporal stages (3D and 4D respectively). He agrees with the latter case. My argument assumes the former.

    I think i am getting a bit off track though. I'm sure we will have more time to talk about these views.

    Last thing. The four dimensionalist can deny p1. M does not = S at T. M = all the temporal stages of its like which includes S at T.

    Any thought for either 4D or 3D?

  9. I have found a way to re-state what I was trying to get across in class today (the 19th).

    In rejection of (1) -

    Could we ditch S? Why do we need a specific number or set of particles?

    This version of the argument also requires dropping t. A specific time frame would, I think, mess with what I'm trying to get across.

    I think that as long as the particles are the same (such that they are a property of M or have the capacity to form M) then any quantity of said particles would still compose M.

    Therefore, we could eliminate S and restate the premise as follows:

    (1) If M is a material object, then M is identical to any sum of particle G that compose M.

    ^ This way, we are stating that as long as particle G is involved, any sum would still be equal to M.

    I feel like I still haven't developed this far enough and I'm not sure about how T's involvement or lack thereof plays out even in my own theory.

    This is just a preliminary musing.

    Also, the name is from another blog I have on this site. This is Spencer. The other blog is private so I'm hoping it can't be reached by clicking me. :) :)

  10. Mr. Unger:

    An advocate of the reformulated Maddy objection (and defender of temporary identity) could claim that she doesn't violate Leibniz' Law by relativizing LL to times. So:

    LL': For any material objects x and y, if x = y @t, then Fx @t iff Fy @t.

  11. Mr. Gingera (if that is your real name!)

    Ok so lets discuss relativising identity to times. It seems to me that if we do temporary identity then things can not be identical to themselves over a period of time?

    So if S = (temporary identity) 4 bits @t and S = 4 bits @t', then S @t does not = S @t' because there is no time to relativise S@t and S@t' to because they are different times. Sound right? Either the left hand side or the right hand side of the bi-conditional in the consequent of you definition will be false because either we are relativising to t or t' and then either S@t or S@t' will make either Fx @t or Fy@t false.

    Seems like a bad consequence. I don't know about others intuitions, but does it seems odd to say that I am not the same guy as I was a few seconds ago?


    After class me and Chris discusses my positive view and he explained two ways i could go.

    1) (My original idea) Deny premise 4 by saying even though m is always distinct from s*, it can gain and lose parts. This is because when m loses a part, it still has the property of at some time being distinct from s*, which s* does not have. But as a consequence, if s* is a proper part of s at t and m=s at t and is only one part short of sharing all its parts with all the parts of m at t, then when m loses one part at t' it does share all its parts with s* at t', yet s composes m and s* does not. One may think its odd to have a privileged time decide what m is composed of. Maybe not though. Maybe we just take that privileged time to be the "birth" of the object, but then we still have the problem of two objects occupying the exact same space yet one composes m and one doesn't.

    Second solution Deny premise one

    M does not = s, rather M coincides with s at t, and m coincides with s* at t' and so on for gaining and loosing parts with ought destroying the object. The problem with this view is that there is no thing that m is. Hmmmmm, weird. If i am m and somebody asked you, "who is m" (unless they meant, what does m coincide with) you couldn't really say M is x, for there is no x such that m is it.

  12. Mr Unger:

    I think that a temporal identity-ist could reply to you that LL' only applies to objects at one time; it doesn't make any claim about what it takes for an object at one time to be identical to an object at another time.

    Also, I do think that you're right in that temporary identity is an odd view. But I don't think that we have found a knock-down objection to it yet.

  13. The problem with posting later is that you have to make sure that you are not just repeating what the other people are saying. I skimmed over and I don't think this was said already. If it was then I apologize.

    Some thoughts on what it means to persist over time- (what does it mean for something to survive the loss or gain of its parts)

    Sider presents in his and Conee's book 'Riddles of Existence' the following ideas:
    Perhaps x can persist over time iff x is
    1. something that is qualitatively equivalent over time
    2. something that is quantitatively equivalent over time
    3. something has spatiotemporal continuity

    All these three requirements for x to persist over time present moral problems that are brought up in 'the debtor's paradox' as well as in Sider's book.

    Even if something has spatiotemporal continuity, like the debtor, that debtor is not quantitatively equivalent because he has lost and gained cells. Also, if someone has committed a crime and then has improved her character so that she will no longer commit such crimes again then it seems that she is qualitatively different although it still seems that she is punishable for the committed crime.