Typos in Objective Becoming


1. page 16, proposition (9) should read: "Let T be any time and S any sentence that is true at T. Then necessarily, if all the sentences in D are true, and all the sentences in C are true, S is true at T." (This has been corrected in the paperback edition. Thanks: Cody Gilmore)


Addenda to Objective Becoming


1. In section 2.5, page 20, I say that it is a mistake to formulate reductionism about tense so that it gives truth-conditions for tensed sentence tokens; instead it should give truth-conditions for tensed sentence types. I am no longer sure why I wrote that. The most natural way of doing these things makes them more or less equivalent: saying that the sentence-type "X was F" is true at T iff X is F at a time earlier than T is pretty much the same as saying that a token of "X was F" is true iff X is F at a time earlier than the time at which that sentence token exists. Of course, if you are after a compositional semantic theory it is better to focus on sentence types; but this is a consideration that goes beyond those raised in the book.


2. In chapter 5 I argue that the branching time theory cannot give a reductive analysis of future indeterminacy. I consider one attempt in the theory to do this in a sentence numbered (6):

(6) "It is indeterminate whether there will be condominiums on Mars" is true at T if and only if there are condominiums on Mars later than T in some but not all branches.

Sentence (6) offers a tenseless truth-condition for an ordinary tensed sentence. I went on to say that the branching time theory, as I formulated it, rejects reductionism about tense, and so cannot give tenseless truth-conditions. That is, (6) does not even make sense in the theory, since the language in which the theory is formulated does not contain tenseless verbs.

So what truth-conditions for sentences claiming future indeterminacy can the theory give? In the book I consider one possibility:

I argue that this is, intuitively, the wrong truth-condition. But aren't there other possibilities? I don't consider any others in the book.

Sentence (7) purports to give supertensed truth-conditions for an ordinary tensed sentence. The reader may have noticed that (7) does not correspond to either the weak or the strong supertensed truth-conditions for tensed sentences that I discuss, in the context of the moving spotlight theory, in chapter 4. But truth-conditions that do correspond are not any better. Let's consider them. Here is a weak truth-condition:

This is bad for the same reason that (7) is. The right-hand side could be true even if it super-will be the case that there are Martian condos in every future branch.

What about a strong truth-condition? Here it is:

This is even worse; the condition on the right-hand side cannot be satisfied.

My question has been, what reductive analysis of future indeterminacy could the branching time theory give? So far I have been reading the tensed verbs in sentences about future indeterminacy as ordinary tensed verbs. Would it help to read them as supertensed? No, it wouldn't. We would have to try something like this:

But it just cannot be that whether it is indeterminate whether something super-will be the case is completely settled by how things super-are.


3. Ted Sider wrote this about the Moving Spotlight Theory:

Nonpresentist defenders of passage face the question of why they accept primitive tense operators, given that they accept past and future objects....[The Moving Spotlight Theorist] accepts that there exist dinosaurs located before 2011; but this is the spatializer's [The Block Universe Theorist's] proposed truth-condition for an utterance in 2011 of 'There were dinosaurs.' More generally, the spotlight theorist can accept the spatializer's reduction of tense for all tensed statements except those concerning presentness. For the latter, there can be no reduction. (Writing the Book of the World, p. 260).

This observation about the Moving Spotlight Theory is connected to the complaint that the theory is just the Block Universe Theory with facts about the motion of presentness "added on." I should have emphasized more in the book that this complaint does not apply (not in this form anyway) to the versions of the moving spotlight theory I describe, especially not to MST-Supertense. The truth-conditions I give in section 4.2 for tensed language, including the sentence "There were dinosaurs," are not the same as the "spatializer's" truth-conditions. (For one thing, the truth-conditions are given in a (super-)tensed language, while the spatializer's truth-conditions are given in a tenseless language.)


4. In section 5.2 I worried about versions of the moving spotlight theory that pick some non-frame foliation of spacetime by instants, and said that those were the instants that are successively present. I said that only versions that pick a foliation of spacetime by instants for which that is a "natural way to define the temporal distance between two instants" were legitimate (p. 155). The idea was that only with this restriction can the theory make sense of the rate of time's passage. I now think this restriction unnecessary. It is in the spirit of the theory of relativity to reject the questions "How fast is time passing? How many seconds later is the instant that super-will be present in 1 supersecond?" One could say that the only meaningful questions about the rate of time's passage are place-relative. The meaning questions are: how fast is time passing here? How fast is it passing there? In more detail, though still speaking roughly (that is, ignoring the need to pass to a limit), given a congruence of timelike curves (a collection of non-intersecting timelike curves that fill spacetime), the rate at which time is passing at a point of spacetime P that is located on the instant that is present is gotten by (i) finding the instant I that will be present in 1 supersecond, (ii) finding the timelike curve L in the congruence that passes through P, and (iii) finding the spacetime length N (interval) in seconds-squared of the segment of L that starts at P and ends on I; then the rate at which time is passing at P is equal to √N seconds per supersecond. This definition makes use only of the notion of the spacetime length of a timelike segment, which the geometry of spacetime guarantees is always well-defined; it does not require there to be a natural way (or even an unnatural way) to define the temporal distance between any two instants (in the foliation).