Course Reserves

Brown changed the way course reserves are accessed and thereby broke my links to the course reserves. I think I have fixed all the links on my site. All the material is still available online. None of that has ever been changed.

Things to Think about for the Final Exam

Here are the ideas I think you should study for the exam.

1. Describe the essential elements of Aristotle's theory of time.
2. How are we to understand the creation of the universe according to Aristotle and Maimonides' view #1 (in Book 2, Ch. 13)?
3. What are the differences between the views that time is circular and that time is linear, and why do they matter?
4. What is the difference between the relationist's and absolutist's conception of time?
5. Where is the notion of simultaneity present in Newton's laws? Background assumptions? And what does this tell us about Newtonian conception of time?
6. What is the B-theory thought to be missing, that the A-theory doesn't according to McTaggart? C.D.Broad?
7. What is wrong with Taylor's argument for Fatalism?
8. What can the science of perception hope to tell us about the metaphysics of passage?
9. What is allegedly bad (if anything) about a conventional notion of simultaneity, dictated by special relativity, compared with a robust or objective simultaneity, derived from common sense?
10. What is Gödel's argument that time is ideal?
11. What are chronology protection theorems. Do we need chronology protecting physics?
12. What lesson is "apt to be lost" according to Price?
13. What are the differences between Albert's and Horwich's theories of the epistemic asymmetry? What are the successes and inadequacies of each approach?
14. Enumerate the various theories explaining the knowledge asymmetry (the 6 Horwich mentions, plus others).
15. Relate the Boltzmannian explanation for gasses expanding.
16. Explain why Boltzmann's thermodynamic fluctuation theory doesn't explain why we see an entropic asymmetry.
17. Explain Entropy-based explanations of the influence asymmetry and criticisms of them.
18. How do Entropy-based theories of influence relate to the conclusion reached by Dummet?

Third Assignment

The paper should be about 2000 words (minimum 1500, maximum 2300). The due date is Tuesday, May 1 at 4:30 PM. You can turn in the paper in my department mailbox. If there are last minute printing problems, email me your paper before the deadline and then turn in a written copy as soon as feasible.

1. Reconstruct Gödel’s argument which involves closed time curves (CTCs) for the conclusion that time is ideal (not objective).  Discuss why (or why not) we should go along with Gödel in thinking that the universe he describes containing CTCs is relevant to our universe, and why the fact that such a universe can be described tells us anything about the nature of time.  Think carefully about whether a different conclusion is better warranted by Gödel’s considerations of CTCs: does the potential existence of CTCs undermine our evidence for the claim that time is objective, or a different claim?

2. Describe the grandfather paradox and present David Lewis's and Michael Lockwood's treatment of it. Critically analyze Lockwood's attacks on Lewis in chapter 7, and come to some conclusion about the ultimate significance of the grandfather paradox.

Even More Notes Available!

I've added the the Course Reserves a short explanation of the issue in relativity that Lockwood raises at the end of chapter 2 but never answers. Also, I've added a bunch of stuff I wrote summarizing the issues we're discussing regarding thermodynamics. It's a bit of an oversimplification, but good to make sure you have the big issues right. Also, added some material on Albert's theory of knowledge asymmetry.

Assessing Other's Papers

You should turn in two copies. One copy should have all of your substantive criticism (of all three papers together), so that I can use it in my evaluation of the rough drafts. The other copy should be turned in attached to the student's paper you corrected and evaluated, so that Katia can deliver it to the writer.

I (DK) will be looking at the papers just to make sure the overall argument structure and topic are suitable, to ward off any dead end topics and to give you ideas for other stuff to look into.

You should be evaluating the quality of the paper and offering advice for improvement. You should do this by marking brief comments on the paper itself, circling writing errors but no need to explain, and then typing an additional statement covering the big issues. Approximate length should be about 1/2 page typed single-spaced, but make adjustments based on how much you can usefully say.

There is no need to give an overall grade for the paper, but you should make a statement about the overall quality at the beginning of your comments.

Discuss the following kinds of issues. Don't address each point with a separate discussion. Blend them together in whatever way communicates your evaluation and criticism most effectively.

1. Topic: Evaluate whether the topic is clear and interesting. Write about what you found interesting in the paper, and where you thought those topics could expanded or shifted. Was the topic too broad? If so, suggest which area you want to be focussed on?

2. Introduction: Does the paper introduce the topic in a way that matches what was later discussed? For example, the topic should not be introduced as a discussion of objective temporal passage and then mention only . Indicate how the introduction might be narrowed in that case. Does the paper discuss interesting issues regarding the topic? Could the introduction use more (or clearer) examples to make the introduction more concrete for the audience?

3. Content: Discuss any arguments that don't sound well-reasoned. Mark any comments or arguments which you think can be thrown out because of being mundane or repetitive or off-topic. Suggest any new ideas where the author can replace the content with something more to the point or more interesting.

4. Conclusion: Was there a clear philosophical upshot? Something that can be phrased in a single clear sentence?

Your comments will be graded on how useful they are with the best grades going to those who develop interesting angles on how the paper should be improved.

Your paper grade at this initial stage will be worth 10% of the overall grade, with 15% for the final version. I will assign the grade after I have taken into account the peer criticism, so the assesments will affect your grade filtered through me.

Second Paper Assignment

You will be assigned one of these two essay topics. Katia will send you a message telling you which one you are assigned.

The paper should be about 2000 words (minimum 1500, maximum 2300). The due date is Wednesday, March 21 at 4:30 PM. You can turn in the paper in my department mailbox. If there are last minute printing problems, email me your paper before the deadline and then turn in a written copy as soon as feasible.

1. Critically address C.D. Broad's critique of McTaggart's argument's argument for the unreality of time. Include a contrast of the A-series and B-series as McTaggart originally made the distinction, a description of McTaggart's argument for the unreality of time, and Broad's main arguments, making sure to characterize as precisely as you can what absolute becoming is supposed to be. Include in your evaluation of "Ostensible temporality", a discussion of whether the B-theory is consistent with absolute becoming.

2. Discuss whether special relativity gives us any sufficient reason (beyond the reasons one might have from classical physics) to abandon the tensed view of time. Include discussions of Lockwood's elaborations (pp. 57-60) on Hilary Putnam's argument, and Lockwood's argument on pp. 64-65 that special relativity robs the A-theory of the material necessary to describe the A-theory such that it appears to present a different notion of time from the B-theory.

Paper Topics

The long paper can be on any topic related to the course. Some ideas I find especially interesting are those based on the possibility of time travel or backwards causation, the knowledge asymmetry, the causal asymmetry, whether some robust notion of temporal flow can be motivated even given general relativity, Reichenbach's common cause principle, what bearing the specious present has on the metaphysics of time.

Posted New Notes

Here are the relativity notes.

First Paper Assignment

You will be assigned one of these three essay topics. Katia will send you a message telling you which one you are assigned.

The paper should be about 2000 words (minimum 1500, maximum 2300). The due date is Tuesday, February 27 at 4:30 PM. You can turn in the paper in class or put it in my department mailbox. If there are last minute printing problems, email me your paper before the deadline and then turn in a written copy as soon as feasible.

1. Aristotle held that "time is [a] number of motion in respect of 'before' and 'after'" (Book IV, Section 11). Explain Aristotle's view on time with regard to (a) the topology of time, (b) the universality of time (whether there can be more than one time), and (c) the continuity of time. Clarify and criticize Aristotle's rationale for having these views, being careful to relate them to his theory about how time relates to motion.

2. Consider a situation (A) where the entire universe, except for a small and remote (from us) part of it ceased to experience all changes for 10 hours (or "hours") and a situation (B) where there are no changes anywhere in the universe for 10 hours (or "hours"). Explain Aristotle's theory of the ontological relation between time and motion/change, and discuss how Aristotle should analyze these situations, given his theoretical commitments. Consider whether his philosophy of time relies essentially on his belief that the heaven spheres are in eternal motion at a constant rotational speed. Critically evaluate Aristotle's philosophy of time with respect to any issues raised by this pair of examples. (Do they show some deficiency in the theory? What philosophical commitments are uncovered by the examples? Are they devastating to the core of Aristotle's philosophy of time? etc.)

3. Constrast what Absolutism and Relationism claim about the structure of space and time. Describe Leibniz's shift argument with regard to time (not space), and discuss responses Newton could give. Describe Newton's bucket argument and clarify the conclusion of this argument. Even if Newton's bucket argument is successful, what does it imply about the nature of time?

Newton's Laws and Their Importance for the Structure of Time

• Law I: Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
• Law II: The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
• Law III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Also relevant is the inverse square law of gravity, (Book III, Proposition 7, Theorem 7): "That there is a power of gravity pertaining to all bodies, proportional to the several quantities of matter which they contain." And a few paragraphs later in Corollary II: "The force of gravity towards the several equal particles of any body is inversely as the square of the distance of places from the particles;... "

Notice that the second law (and the first law that it entails) require some kind of temporal metric. This is implicit in the understanding of acceleration as the rate at which velocity changes.

Notice also that the need for an objective simultaneity relation comes only from the dynamics (i.e., the force laws (like the law of gravity) and constraints on them (like the third law)). Since Newton himself thought the law of gravity was only an approximation of some to-be-discovered local law of gravity, one might have speculated way back in the 17th century that there was no objective simultaneity relation.

Brief Summary of Absolutist vs. Relationist Debate

Disclaimer: The following is an overly brief synopsis of the debate between Newton and Leibniz on the nature of space and time. A lot more could be said and has been said by others. Links to some recommended books are listed on the left, if you're interested in the more nuanced discussion. What follows is just a rough explanation together with my biased opinion.

Relationists (Liebniz, Mach) argue that space is an idealization that is grounded merely in the distance relations between material objects. Space doesn't really exist. Fundamentally, the universe consists of different clumps of matter with distances between them. The distances are fundamental relation facts and are not derived from facts about where objects are located. It is as if God's inventory of the universe consists of a spreadsheet with all the objects listed vertically and horizontally, with a triangular patch of numbers indicating the distances between them. The only sense in which space exists is that we imagine that these distance relations are actually imbedded in three dimensions.

Absolutists (Newton, Clarke) argue that space is an entity in its own right, that space would exist even if there were no matter in the universe. The structure (properties) of space means it makes sense to talk about quantities like absolute position and absolute velocity, even though we have no epistemological access to the absolute position or velocity of anthing in the universe. The classic justification for believing in absolute space is that a sufficient explanation of centrifugal effects in rotation requires more than just relational quantities. Toy version of Newton's bucket argument: The still bucket and rotating bucket are relationally equivalent. They are physically different. Thus, space is not relational. Thus, space is absolute (Newtonian).

Leibniz and Newton debated about the nature of space and time. Leibniz argued that space is a kind of fiction. He agreed that there are facts about how far apart objects are from one another, but disagreed that these distance-facts were the consequence of facts about where objects were located. Leibniz takes the distance facts to be primitive, and thinks that all other spatial facts are derived from these.

Leibniz offers several arguments like the following: Suppose the positions of all objects were shifted a distance away in some direction. Such a change would not be distinguishable from the actual world. By the principle of identity of indiscernibles, the actual world and the shifted world are identical, which means that the shift did nothing at all. This backs up Leibniz's theory of space in that fundamentally the only facts about space are distances between objects, and so the shift does nothing, just like the argument says should happen. If there is an independent space, however, as Newton thought, then there would exist an objective difference between the actual world and the shifted world. Thus, Newton is wrong.

This argument also comes in a theological variety, using the principle of sufficient reason, which claims that everything that happens happens for a reason. If the actual world and shifted world were distinct, God would have to choose which one to instantiate. But since they are alike in all detectible respects, God would have no reason to prefer one over the other. Therefore, there is no difference between the two.

Similar arguments can be made using velocity boosts, static rotations, and shifts in time, in place of the spatial shifts.

Newton's argued that although we cannot, even in principle, detect the true (absolute) positions of things, there are still facts about positions irrespective of other material bodies. We need the concept of absolute space, he argues, to explain rotation. Leibnizian theories of space cannot explain why the water in a rotating bucket becomes concave, because the relative distances among all the parts of the bucket and water remain constant whether the bucket is at rest or rotating.

A subtle point is that Leibniz can express the observed phenomena (the concave surface of the water) in terms acceptable to him, but what he can't do is express any facts that explain why the water would become concave. Newton can explain the bucket phenomena because he can use facts about how fast each bit of water is traveling in the direction perpendicular to the radius. Leibniz cannot use this fact because motion perpendicular to the radius does not supervene on changes in the distances between bits of water (or any other matter).

Nowadays, we see that a better solution is to reject both the Leibnizian and Newtonian spacetime structures in favor of Galilean spacetime. In all three spacetimes, there are matters of fact about what events happen at the same time (surfaces of simultaneity), matters of fact about distances between objects in space, and matters of fact about distances in time between events. Galilean spacetime goes further by having an affine connection. An affine connection 'glues' the spatial slices together in such a way that there is a matter of fact about what paths in spacetime count as straight lines. This is just enough structure to accommodate classical physics, including the bucket phenomena. (You can see that classical physics prima facie needs a notion of straight line because Newton's first law of motion says that a particle will travel in a straight line unless acted on by a force.) Galilean spacetime, unlike Newtonian spacetime, does not posit any spacetime structure that can lead to unanswerable questions, like "Where is this particle located in space?" Thus, it is immune to Leibniz's shift arguments.

In the end, Newton's and Leibniz's theories had deficiencies. However, in an important sense, Newton was more the winner than Leibniz because Leibniz didn't have enough structure to explain the bucket phenomena, there was a real physical phenomena that Newton could explain that Leibniz couldn't. Newton's theory had superfluous structure, but it is far preferable to have superfluous structure than not enough.

New Links

I've added some links on the left to some books that discuss the absolute vs. relational accounts of space and time in classical physics. Some of them are quite a bit more technical than what we discussed in class.

Course Hours: 2:30 PM - 3:50 AM Tuesday and Thursday.

Office Hours: Wednesday 2:00 PM to 4:00 PM. (plus Katia in 1st floor of Gerard House, Tuesday 1:30-2:20)

Course Description

Conceptions of time play critical roles in our understanding of our origin, the creation of the universe, our ultimate fate, and our sense of purpose and progress. The three most important questions we will be discussing is, “Is there a beginning and ending to time?” “Does time flow?” and “What is the difference between the past and the future?”

 We will first blaze through the history of philosophy of time, covering ancient Greek and medieval Judaic philosophy of time. We will use modern mathematics, notions of topology, density, ordering, and metric, in order to analyze these ancient theories. We will discuss the standard literature in the philosophy of time, covering notions of change and flow, and then see how relativistic physics bears on the notion of flow by way of relativity of simultaneity and time travel. Finally, we will investigate the second law of thermodynamics to see what relationship it has to temporal asymmetries such as the asymmetry of influence, the causal asymmetry, the asymmetry of knowledge.

Tasks and Evaluations

Your grade for the course will be determined by three (roughly five-page) papers worth 15% each, a final exam worth 25%, and a 10-12 page paper worth 25% of your final grade. There is an additional 5% of your grade based on your evaluating other students’ long papers.

For the short papers, the exact writing topics will be determined in part by chance. I will create 3 or 4 topics and then you will be randomly assigned to one of the topics. For the longer paper, you will get to choose topics, subject to my approval and suggestions for adjustment. I will also provide some potential paper topics.