In celebration of my one year in the blogosphere I have decided to start a new (randomly published) series of posts highlighting a post from exactly one year ago that did not recieve much attention. Here is the third installment.
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As I sit here and type this in late 2007, in my living room, it seems to me that all of me is in the room that I am in right now. From a common sense perspective I am entirely in this room; we can put this by saying that I am wholly present in this room. The four-dimensionalist denies this common sense claim. They think that I have some parts, temporal parts, which are not in this room right now. For instance, I have a temporal part that is at work yesterday, or is my child-hood self back in Los Angeles. This is a very odd view indeed! 4-dimensionalism is closely related to eternalism, which Jason has recently defended in an audio post over at Philosophical Pontifications. Kripke has a well known argument which is supposed to show that four-dimensionalism is false. It is a very simple argument which claims that the four-dimensionalist cannot capture certain basic facts about the world. In particular it is not able to capture certain facts about whether a certain disk was spinning in its lifetime or not. Let us look at his very simply argument.
Kripke has argued (in unpublished lectures) that the, as he calls it, Holographic Theory (so-called because the temporal slices are presumed to be three-D, like holograms) has serious problems by suggesting that it is unable to model certain facts about the history of the world. His argument relies on two thought experiments. First, consider a disk made from uniform material. It is a single color and is made from entirely continuous matter. Now, a disk modeled in three dimensions (which turns into a cylinder as it ‘progresses’ through the third dimension) is akin to modeling a three dimensional object in time. Any problems that our three-D model of the disk will have will be simplified versions of problems for the view that objects are four-dimensional. So, now what if we are looking at the resulting cylinder, which represents the disk’s ‘life’, and we wonder ‘was the disk spinning during its life?’
The temporal stage theory is unable to answer this question. We cannot answer the question because the model of the disk’s ‘life’ is incapable of representing this kind of fact. What we need in order to answer the question is an answer to the question ‘is some specific part of the disk now in another place?’ The same thing being at a different place later is what motion is. Since we have no criterion to determine if we have the same substance in the same place we cannot, in principle, answer the question about the disk’s motion. Presumably the disk was either spinning or not and since there is no way to account for this, one way or the other, the temporal slice theory is in trouble. The second thought experiment is quite similar and involves an infinite river. He introduces this variation only so that he may avoid the objection that a disk made from uniform matter is impossible. The water in the river takes care of this. We need not rehearse it here, as it is basically a reiteration of the previous argument applied to the river. Kripke concludes that the temporal slice theory is wrong and suggests we that need a primitive notion of the identity of substance.
This really should not come as much of a surprise as it is clear that Kripke had this idea in mind when he delivered the lectures now known as Naming and Necessity. He argues that we can stipulate that we are talking about certain substances and ask what would happen to them in a possible world. This is only possible because there are substances out there with which we have interacted. It is because I have interacted with Kripke that I can ask what would happen to him, Saul Kripke, had he not been interested in philosophy. Similarly I can stipulate that I am talking about this table right here and ask about what happened to it yesterday, or what might happen to it three days from now. The argument that Kripke advanced against 4-d-ism is merely making explicit something that has been implicitly accepted by anyone who finds Kripke’s arguments compelling; Namely that we must take the logical relation of the identity of substance (A=A) as a primitive notion.
To illustrate Kripke talks about possible states of two six-sided die. The fundamental question is what we are to say in the cases where we get a four and a three, say. Is there just one state or are there two? Kripke argues that each possible state of the dice is distinct. These states will be distinct because the two die are enduring substances that we can rigidly designate. So each die will have a unique state that it can be in or not. Let us call the two die Alice and George. Then there is one possible state where Alice is four and George is three and another possible state where George is four and Alice is three. These two states are distinct even though the two dice, and so the two states, are qualitatively identical. Kripke’s basic admonishment is that we cannot count possible states of an object simply by qualitative similarity, as that collapse the number of possibilities.
In the next post I want to address Ted Sider’s temporal counter-part theory as a response to Kripke’s argument.
Richard Brown 