Sample Questions for the Final Exam

You should attempt to review the material by ensuring that you have a good grasp on the main arguments that appeared in the readings and discussed in class.

The format will involve short paragraph answers to a list of perhaps 16-20 questions.

Here are some of the kinds of questions you may be asked:

• What is the difference between changing the past and affecting the past?
• What is the main claim of the A-theory of time, and how does this distinguish it from the B-Theory? (Lockwood ch. 1, pp. 4-10; Dainton ch. 1, pp. 6-12.)
• State the thesis of presentism, and give one objection to the view. (Dainton ch. 6, pp. 80-92.)
• In ‘The Myth of Passage’ D.C. Williams criticized the notion of “absolute becoming” that played a prominent role in the growing-block theory of C.D. Broad, claiming that the “true and literal passage” of time just consists in the ordered occurrence of events along the temporal dimension of an unchanging, tenselessly existing four-dimensional manifold. Later, in ‘On Absolute Becoming and the Myth of Passage’, Steven Savitt claimed that “there is no difference whatsoever between [Broad’s] understanding of absolute becoming and Williams’s true and literal passage.” What was Savitt’s reasoning in making this claim? (Savitt, ‘On Absolute Becoming and the Myth of Passage’.)
• Explain Tooley’s causal argument for the growing block theory of time. (Dainton ch. 6, pp. 74-8.)In ‘Remarks on the Passage of Time’ Tim Maudlin responds to D.C. Williams’s argument that the phenomenology of our experience does not provide evidence for the claim that time genuinely passes, since even if there were such passage it would always be conceivable, given the Time Reversal Invariance of physics, that there exist a ‘time-reversed Doppelgänger’ whose experiences were qualitatively just like ours, but ordered in the opposite direction from that of the real passage of time – and we have no independent evidence that we are not in such a situation. Explain Maudlin’s response to Williams’s argument. (Maudlin, ‘Remarks on the Passage of Time’ pp. 269-73.)
• Describe Newton’s ‘rotating bucket’ argument, and what it was intended to show about the nature of space. (Dainton ch. 11, pp. 169-80; SEP article on Newton’s views on space and time, section 5.3.)
• Explain Einstein’s Principle of Relativity. (Dainton ch. 16, pp. 255-8; Also see advanced relativity notes, p. 46-48.)
• What is the Minkowski spacetime interval, and what is its significance for the philosophical interpretation of time? (Dainton ch. 16, pp. 264-8.)
• Explain Putnam’s argument for the claim that Special Relativity is incompatible with dynamic theories of time. (Dainton ch. 17, pp. 269-71.)
• What arguments can be given against fatalism about the past?
• Explain the three principles that Dummett puts forth as sufficient to rule out backwards causation. (Located at the end of Dummett's ‘Bringing About the Past’, pp. 349-57.)
• According to Lewis in ‘Paradoxes of Time Travel’, the problem presented by the grandfather paradox is that it appears that it both is and is not within the time traveler’s power to kill his grandfather. How does Lewis suggest we resolve this apparent contradiction? (Lewis, ‘Paradoxes of Time Travel’ pp. 6-8; Lockwood ch. 7, pp. 156-8.)
• What is entropy? What are some arguments for why the direction of entropy increase does not explain the direction of time?
• What is the (Loschmidt/Zermello) reversibility objection?
• What is Albert's characterization of the epistemic asymmetry?
• What is the Asymmetry Experiment and what does it have to do with the direction of causation? (Notes)

Fourth Essay Assignment

The fourth paper is due Thursday May 6. It should be about 1500 words (minimum 900, maximum 2000).

Topic 1: Explain and critically analyze the argument in pages 13-18 of the "Knowledge and Intervention" chapter that is posted in the course reserves.

Third Essay Assignment

The third paper is due Thursday April 20. It should be about 1500 words (minimum 900, maximum 2000). You have a choice of two topics.

Topic 1: Diagnose Taylor's argument for fatalism. That means you explain the core structure of the argument and then identify the weakest premise or step in the reasoning and discuss why it is problematic.

Topic 2: Dummett's essay explicitly attacks one argument for fatalism regarding the past. But does he demonstrate that fatalism towards the past is incorrect? Discuss. (You should be considering whether he successfully rules out all other reasonable arguments for fatalism regarding the past.)

Second Essay Assignment

The second paper is due Thursday March 25. It should be about 2000 words (minimum 1500, maximum 2300). You have a choice of two topics.

Topic 1: Present an explanation of the lessons of special relativity for our understanding of time. The target audience is not expected to be knowledgeable about classical physics or relativity, but is generally interested in science. About the level of a Scientific American article (of the past 10 years). Specifically detail what about time in Einstein's theory is different from classical physics. You will be graded on your ability to present the material clearly to non-experts and your accuracy. This is not intended to be a philosophy paper where you defend a controversial thesis against other philosophers; it is a popularization.

Topic 2: Discuss whether point-relativized dynamism, as discussed by Dainton, pp. 274-276, and Stein, "On Relativity Theory and Openness of the Future" can accomplish the goal of removing (or mitigating) the alleged tension between the traditional growing block theory and special relativity. In doing so, clarify what the tension is and what would count as a satisfactory mitigation of it. You may want to have a look at Callender's "Shedding Light on Time," and Dorato's "Putnam on Time and Special Relativity."

Help on Writing Philosophy Papers

Here is some approved advice from Horban and Pryor.

First Essay Assignment

The first paper is due Thursday March 4. It should be about 2000 words (minimum 1500, maximum 2300). You have a choice of two topics.

Topic 1: Explain the difference between the growing block theory and presentism. Contrast their relative merits. Specifically, consider whether the principles motivating moving from a static block theory to a growing block theory also motivate moving further to a form of presentism. Similarly, do any principles motivating moving from presentism to a growing block theory also motivate moving further to a static block theory?

Topic 2: Critically assess the argument Maudlin offers in the 'epistemological objections' section of "On the Passing of Time" (p. 269-end). After explaining Maudlin's objection to Price and Williams, provide one possible response. (This could include arguing, against Maudlin, that the arguments of Price and Williams are not question-begging; or if you agree that they are question-begging, you could provide a different argument for the claim that we cannot know whether time has a direction just from the subjective character of experience.) Then evaluate your reply, and say whether you believe it is ultimately convincing.

For both topics, it is important for you to get your own opinions laid out in the paper, but whatever contentious claims you make also need to be defended. So it is key to limit the scope of your claims so that you are not putting yourself in the position of having to defend too a broad thesis.

Course Description

Course Hours: 10:30 AM - 11:50 PM Tuesday and Thursday.

Office Hours: Tuesday and Thursday 12:10 PM to 1:10 PM.

Textbooks: Time and Space by Barry Dainton and The Labyrinth of Time by Michael Lockwood.

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 two most important questions we will be discussing are, “Does time flow?” and “What is the difference between past and future?”

In the first half of the course, we will discuss the standard literature in the philosophy of time, covering notions of change and flow, and then see how classical and relativistic physics bears on the passage of time 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 four papers each worth 18% of your final grade, a comprehensive final exam worth 28% of your final grade. The topics of the papers will be assigned to you based on the course readings.

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.