Puzzles & Paradoxes - Schafer - Midterm

Basic Argument for their incompatibility

(1) If determinism is true, then every human action is causally necessitated by prior events. (2) If every action is causally necessitated, no one could have acted or chosen otherwise. (3) One only has free will if one could have acted or chosen otherwise. (4) Therefore, Casual Determinism is incompatible with the Existence of Free Will.

paradox of omnipotence

- 1) Either x can create a stone which x cannot lift, or x cannot create a stone which x cannot lift. 2) If x can create a stone which x cannot lift, then, necessarily, there is at least one task which x cannot perform (namely, lift such a stone). 3) If x cannot create a stone which x cannot lift, then, necessarily, there is at least one task which x cannot perform (namely, create such a stone). 4) Hence, there is at least one task which x cannot perform. 5) If x is an omnipotent being, then x can perform any task. C) Therefore, x is not omnipotent.

Reason for believing in free will

- (i) Feeling or experience of freedom. - (ii)We treat each other as if we were free. - We hold each other morally responsible for our actions. And we generally do not hold people responsible when they are not in control of their actions or those actions were not chosen freely. - Free will seems to be a condition on deserving credit for one's accomplishments. - Free will seems to be a condition on the value we accord to love and friendship. - (iii)In deciding what to do, we must treat ourselves as free.

what is parfit's response to these puzzles and personal identity

- At this stage, both materialism and the memory theory might seem to be in pretty bad shape. - Parfit suggests a radical response to these problems. According to Parfit, when we talk about "personal identity" or "being the same person", we aren't really talking about an all-or-nothing thing. - Rather, we are just talking about degrees of psychological similarity. So when I say that A and B are the same person, what I really mean is just: A and B are psychologically connected in certain interesting ways. - So, in some sense, there's really no personal identity at all.

Resolved Moving Bodies Paradox

- But it seems impossible for objects to switch left-right orientations without at some point being "even" with each other. And if this really is impossible, then it seems to follow that motion is impossible if space and time are discrete.

Reason for believing in causal determinism

- Causal determinism is the view that the state of the world at a given time (together with the laws of nature) wholly determines the state of the world at - Every event that occurs, including human action, is entirely the result of earlier causes and natural laws. - The state of the universe, plus the laws of nature, determine a single unique future.

Resolved Arrow Paradox

- Consider an arrow shot from a bow, and imagine that space and time are discrete. - Consider an indivisible moment in time. Does the arrow move during that -It seems that it cannot since, if it did, the instant would be divisible — the arrow would have to be in one place for one part of the instant, and in another part for another. But if instants have parts, then they are not indivisible.

Argument for fatalism from foreknowledge

- God's omniscience does not require us to accept premise (2), that necessarily God knows you will do x tomorrow. - When premise (2) is rephrased as follows:then the argument from foreknowledge becomes invalid - But isn't God's omniscience a necessary attribute of God? - And doesn't that imply that necessarily Gods knows what I will do before I choose to do it - Does this rule out free will?

modified memory theory response to reids objection

- If A and B are the same person, and B and C are the same person, then A and C are the same person. -x and y are the same person if and only if either: (1) x has memories of y (or vice versa), or (2) there is some series of persons connecting x and y which is such that each person in the series has memories of the immediately preceding person in the series.

why are these problematic for personal identity

- Ownership: Every conscious experience must be an experience of someone. - Awareness: If someone has a conscious experience, it must be at least in principle possible for them to be aware of that experience.

what are various solutions to the paradox

- The liar statement is neither true nor false - The liar sentence is both true and false (Dialetheism - Buddhism) - The liar statement is just meaningless b/c it is self-referential - The liar statement is false - The liar statement is ill-formed or meaningless b/c it uses a non- hierarchical notion of truth - The liar sentence is "kind of true".

what radical implication of this response

- This view has some surprising consequences. One is that questions about death and survival also do not have all- or-nothing answers. - Think about Earth-Parfit after he comes out of the New Scanner. One naturally thinks that he should be very upset about the fact that he is going to die soon. - But, if Parfit is right, he should be much consoled by the fact that Mars-Parfit, who is psychologically extremely similar to him, will continue to live — after all, ordinary survival just is a matter of there being someone psychologically quite similar to me who continues to exist. -No line between personal identity / identities of others, personal identity is flexible, our memories are not just localized to our bodies

One way of defending the compatibility of free will and determinism?

- is to insist that a variety of options need not be metaphysically open to us in order for our will be free. - Thus, free will is compatible with the inability to do otherwise.

Assumption of the Arrow

-1) During any one instant, an arrow does not move, since instants do not have any parts. 2) Nothing happens between one instant and the next instant. 3) The arrow does not move between instants. (2) 4) Therefore, the arrow does not move during instants and it does not move between instants. (1,3) C) Therefore, the arrow does not move. (4)

Grandfather Paradox

-Grandfather paradoxes arise whenever a time traveler goes into the past and prevents an event that is a pre- condition of the traveler making the backward time journey in the first place -A time traveler goes back in time and kills his grandfather before the grandfather has fathered children. If the grandfather dies at this point, then one of the time traveler's parents never exists. Hence the traveler can't be born and travel back to kill the grandfather ... and so on.

reid's objection to memory theory

-It assumes only the transitivity of identity and the possibility of the sort of scenario described above. It is difficult to deny that such scenarios are, in fact, possible. -• 1)xandyarethesamepersonifandonlyififthelaterhas memories of the earlier. (The Memory Theory) • 2) General has memories of the experiences of Officer. • 3) General=Officer (1,2) • 4) Officer has memories of the experiences of Boy. • 5) Officer=Boy (1,4) • 6) General does not have memories of the experiences of Boy. • 7) General≠Boy (1,6) • 8) General=Boy (3,5, transitivity of identity)

A-Series Time

-McTaggart -we can build a sequence of events by beginning with the present and then describing the other events in terms of how far in the past or future they lie, measured from the present -these events in time are centered on the present -includes properties of being past, present, and future -indexicals are words whose referent and meaning are determined by the context of the speaker, ie the time and space of speech *pronouns: I, you, this that adverbs: here, now, presently, today, yesterday, tomorrow adjective: my your, past, present, future, left/right, up/down -presents the history of time from a point of view that is located within that history.

B-Series Time

-McTaggart -we can relate various events to one another in terms of relations of "earlier than" or lather than. This will provide us with a coherent ordering of these events. -Includes the properties of being earlier than, later than, and simultaneous with another event. -presents the whole history of time from a point of view that is outside of time, i.e. one that is not located at any particular point in that history.

David Lewis Solution to Grandfather Paradox

-Premises (1) and (2) on slide #24 are both true. They do not contradict one another. The term "can" in both premises mean different things. -The Grandfather paradox rests on an equivocation about the meaning of "can." -When we say that somebody "can" do something, we mean that they have the capacity to do it, holding certain things fixed. Which things we hold fixed will depend upon context.

Some claim that there is tension between God's omnipotence, his omnibenevolence, and the fact that the world contains some evil. Explain the tension.

-Some arguments try to show that the idea that God is omnipotent and omnibenevolent contradicts a very obvious fact about the world: the fact that it contains evil. This is what philosophers call the "Problem of Evil": -

what role does the principle of bivalence principle play in the paradox

-The Liar Paradox contradicts the principle of bivalence. -Principle of Bivalence: Every declarative statement has exactly one truth value, either true or false. -Motivation: "Any non-defective representation of how things are in the world must be either accurate or inaccurate, true or false" (Sainsbury, p. 113).

what is the liar paradox

-This sentence is false // L1:L1 is false -Suppose L1 is true; then it is as it says it is - i.e. it is false. So L1 is false. -Suppose L1 is false. Well, false is just what it says it is, and a sentence that tells it the way it is is true. So L1 is true. This sentence is false L1: L1 is false -So, if L1 is true, it is false; and if it is false, it is true. So it seems that L1 is neither true nor false. For if it were either, it would be both! -This is a paradox if we assume the principle of bivalence. This principle states that declarative sentences such as L1 are either true or false.

advantage of materialist theory

-This view is natural, because it fits with many things that we are inclined to say about ourselves.

Achilles Paradox

-Zeno -Achilles and a tortoise are having a race. Since Achilles is very fast, and the tortoise is very slow, the tortoise is given a head start. -The race starts, and Achilles makes it to the point where the tortoise started to race, but by that time the tortoise has moved some distance, so by the time Achilles reaches where the tortoise used to be, even though the distance is shrinking, he has yet to pass the tortoise -it always takes Achilles a finite amount of time to catch up to where the tortoise was, and during that finite amount of time the tortoise has covered some distance

Racetrack Paradox

-Zeno Imagine that you are trying to move from point A to point B. Suppose C is the midpoint of the distance from A to B. It seems that you have to first get from A to C, before you can get from A to B. Now suppose that D is the midpoint between A and C; just as above, it seems that you have to first get from A to D before you can get from A to C. Since we are assuming that space is infinitely divisible, this process can be continued indefinitely. So it seems that you need to complete an infinite series of journeys before you can travel any distance - even a very short one!

Type

-a category or class of object or event

Token

-a specific instance or occurence of a type of object or event

Mention

-a word is this when we talk about the word itself -these words often appear between quotation marks or italics ex) "tree" is spelled with two "e"s

Use

-a word is this when we talk about the world by means of it ex) there is a tree in the garden

Example of an Invalid Argument

-affirming the consequent -1) If p, then q 2) q C) Therefore, p 1) If Bernie Sanders is a Republican, then he supports gun rights. 2) Bernie Sanders supports gun rights. C) Therefore, Bernie Sanders is a Republican.

What is a paradox?

-an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. -premises of an argument are apparently acceptable if and only if they are apparently true -the conclusion of an argument is apparently acceptable if and if only if it is apparently false -appears to be a sound argument, which has a false conclusion -has three features: its premises appear to be true, its conclusion appears to be false, and it appears to be valid

advantage of dualist theory

-assuming that immaterial souls are indivisible, the problems of division illustrated by the examples of fission and tele-transportation cannot be used against the dualist

Discrete Space

-comprised of moments -if space is this, then there are lengths which are not divisible (minimal lengths) -there are pairs of times which are such that there is no time in between them (invisible instants) -in this case, space and time would have basic indivisible units

disadvantage of materialist theory

-doesn't take into account the soul/conscious of a person. -what if there was a case where two souls that switched bodies. Would they be the same person?

solutions of the paradox

-first solution: Why should an omnipotent being not be able to perform tasks whose description is self-contradictory? If that being is capable of performing one task whose description is self- contradictory - that of creating the stone in question - why should it not be capable of performing another - that of lifting the stone? • An omnipotent being x can do things whose description is self-contradictory. Such a being can render necessary truths false. It can make 2 + 2 = 5. • And so it can make a stone that is too heavy for it to lift and then lift it! second solution: A being x is omnipotent if and only if x can bring about anything which is logically possible. Arguably it is contradictory and hence logically impossible that an omnipotent being makes a stone so heavy that an it cannot lift it. So given Def. 2, not being able to do something that is impossible is fully compatible with being omnipotent. • To show that being x is not omnipotent one would have to show that a certain task is (i) logically possible and (ii) cannot be performed by x. But the task of making a stone too heavy for an omnipotent being to lift violates (i). -third solution: Def. 3: A being x is omnipotent if and only if for anything that it is possible for x to bring about, x can bring it about. • Def. 3 restricts omnipotence not only to what is logically possible but also to what is possible for the particular agent. This takes care of counterexamples regarding relational properties of objects.

Example of a Valid Argument

-hypothetical syllogism 1) If p, then q 2) If q, then r C) Therefore, if p, then r 1) If Kim lives in Irvine, she lives in California 2) If Kim lives in California, she lives in the U.S. C) Therefore, if Kim lives in Irvine, she lives in the U.S.

Compatibilism

-if determinism is true, then every human action is causally necessitated by prior events -if every action is causally necessitated, no one could have acted or chosen otherwise -reject the argument just given for incompatibility -One way to be reject Incompatibility, and defend Compatibilism, is to insist that a variety of options need not be metaphysically open to us in order for our will be free. Thus, free will is compatible with the inability to do otherwise. -is the view that every event that occurs, including human action, is entirely determined by earlier causes (plus laws).

Hard Determinism

-if every action is causally necessitated, no one could have acted or chosen otherwise -one only has free will if one could have acted or chosen otherwise -there is no free will

Continuous Space

-if space is this, then between any two points in space there is a third -thus for any length, there is a length that is half as long -applied to time, the idea would be that for any amount of time, there is period of time that is half the time, and that in between any two moments there is another

Deductive Argument

-if the truth of the premises guarantees the truth of the conclusion -it would be self contradictory to assert the premises but deny the conclusion -in this kind of argument, the conclusion only makes explicit what is already contained, even if implicitly, in the premises -these arguments do not expand our knowledge in a fundamental way, they simply make explicit what we are already committed to -in this kind of argument, it is important to look for two key concepts: -validity: if the premises were true, the conclusion would have to be true. -soundness: the argument is valid and the premises are in fact true

Inductive Argument

-if the truth of the premises supports the truth of the conclusion, but does not guarantee it -it would not be self contradictory to assert the premises and deny the conclusion -can take us beyond what is implicit in their premises -these arguments may expand our knowledge about the world in a manner that is impossible for deductive arguments -in this kind of argument, it is important to look for this key concept: -strength: an argument is strong if the truth of the premises make the truth of the conclusion very likely

Argument

-is a series of statements where the last statement supposedly follows from or is supported by the initial statements. -the last statement is called the conclusion, and the initial statements are called the premises. -the premises are the starting point ex) 1) Everyone who lives in Echo Park is a hipster. 2) Karl lives in Echo Park C) Therefore, Karl is a hipster

How can the conclusion of the argument from foreknowledge be resisted

-is it necessary that god will know what you will do -necessarily omniscience -God has controlling/influencing or is he just observing -Is there a way to think of god's foreknowledge as controlling/influencing what we will do or is he more of an observer -God knows that you will do *contra argument*

Personal Time

-is that which is measured, say, by the traveler's wristwatch -her journey takes an hour of her time

Causal Determinism

-is the view that the state of the world at a given time (together with the laws of nature) wholly determines the state of the world at the next moment. -Every event that occurs, including human action, is entirely the result of earlier causes and natural laws. -The state of the universe, plus the laws of nature, determine a single unique future.

Fatalism

-is the view that whatever happens now and will happen in the future happens necessarily. -because the present and future is fixed, or pre-ordained, our choices about what to do in a situation seem inconsequential.

A priori/a (knowledge)

-knowledge is independent of experience ex) all bachelors are unmarried

Proposition

-meaning or content of a declarative sentence or though -they are true or false -are different from the actions by which they are expressed -are different from words, sounds, symbols, or brain states by which they are expressed -are independent of the language used to express them

Validity

-meets this condition: If its premises are true, then its conclusion must be true -a key concept in deductive arguments ex) 1)Kanye is a genius 2)All geniuses are philosophers C)Therefore, Kanye is a philosopher

Example of a Valid Argument

-modus tollens 1) If p, then q 2) Not-q C) Therefore, not-p 1) If Kanye is human, he is mortal. 2) Kanye is not mortal. C) Therefore, Kanye is not human.

Assumption of Achilles Paradox

-motion is impossible because time is continuous -The Achilles paradox attempts to show that nothing can ever catch anything else from behind (so long as the former is moving at a finite speed and the latter never stops moving)

Assumption of Racetrack Paradox

-motion is impossible because time is continuous -The Racetrack Paradox attempts to show directly that it is impossible for anything to move any distance at all.

Paradox of the Arrow

-motion is impossible because time is discrete -to move at a moment, you would have to be changing space at that moment, which is impossible, -you can't move between the moments because nothing is there, -moments are the smallest unit and can therefore not be changed, and nothing can move between it -as a result, the arrow cannot move through it

Necessary Truths

-must be true/whose opposite is impossible ex) all bachelors are unmarried

Contigent Truths

-not necessary and whose opposite is therefore possible ex) there are more than twenty states

Circular Argument

-one or more of the premises relies for its truth on the truth of the conclusion -logical form: X is true because of Y. Y is true because of X

Assumption of the Moving Bodies

-space and time are discrete, which means that there can be points in space which are genuinely adjacent, in the sense that there are no points in between them.

personal identity

-suppose that there is a person, A, who exists at some time, and a person, B, who exists at some later time -a theory of personal identity is a theory which tries to answer the question: what does it take for A and B to be the sam person?

Soundness

-the argument is valid and the premises are in fact true -satisfies these two conditions 1) It is valid 2) All of its premises are true -therefore, an argument's conclusion *must* be true -a key concept in deductive arguments

External Time

-the arrival is more than an hour after the departure in external time, if she travels toward the future; or the arrival is before the departure in external time if she travels toward the past

What does it mean for a statement/proposition to entail another statement/proposition?

-to say that the conclusion follows validity from the premises is the same thing as saying that the premises entail the conclusion -"p entails q" = "q is validly deducible from p."

Necessary Conditions

-to say that x is a necessary condition for y is to say that it is impossible to have y without x -the absence of x guarantees the absence of y ex) having four sides is necessary for being a square

Sufficient Conditions

-to say that x is a sufficient condition for y is to say that the presence of x guarantees the presence of y -it is impossible to have x without y ex) being a square is sufficient for having four sides

Synthetic

-true in virtue of how their meaning relates to the world ex) bachelors are lonely and unhappy

Analytic

-true in virtue of their meaning ex) an unmarried man is a bachelor

Example of a Circular Argument

1) Karl is all-knowing and truthful and wrote these lecture slides. 2) If Karl is all-knowing and truthful and wrote these lecture slides, then everything these lecture slides say is true. 3) Everything these lecture slides say is true. 4) These lecture slides say that Karl is all-knowing and truthful and wrote these lecture slides. C) Therefore, Karl is all-knowing and truthful and wrote these lecture slides.

What is the argument meant to show?

1)Necessarily, if God (or anyone else) knows you will do x tomorrow, then you will do x tomorrow. 2)Necessarily, God knows that you will do x tomorrow. C)Therefore, it is necessary that you do x tomorrow. - The argument is valid. But is it sound? - Note that this argument (unlike the argument from Determinism), does not rely on a scientific conception of reality.

how does the dualized liar show the root of the liar paradox

A: B is true B: A is not true Suppose A is true 1) A is true 2)A 3) B is true 4)B C) A is not true (1) & (C) form a contradiction Assumption (1), Disquotation (2), Def of A (3), Disquotation (4), Def of B -this sentence refers to itself

what are cases of brain bisection

Now think about a case in which a split-brain patient has a red stimulus presented to the right half of their visual field, and a blue stimulus presented to the left half of their visual field. • If you ask the subject what color they see, they will say "Red", since this was the color presented to the part of the eye which feeds input to the left hemisphere of the brain, which controls speech. • So it is clear that there is a conscious experience of red; so, by Ownership, there must be someone who is having this experience. Let's call this person "Mr. Red." • If you put a pen in the left hand of the subject, and ask what color was just seen, that hand will write "Blue." So it seems that there must have been a conscious experience of blue - otherwise, how would the hand know what color to write? • But if there is a conscious experience of blue, by Ownership someone must have had this experience. Let us call the person who has this experience "Mr. Blue."

describe parfit's teletransporter case

Original-Parfit = Parfit before he stepped into the teletransporter. Earth-Parfit = the person who gets out of the teletransporter on Earth. Mars-Parfit = the person who gets out of the teletransporter on Mars.

Con Premise on Temporal Change

Premise (1): No Time w/o ChangeReminder of the Argument: 1)Time necessarily involves change. 2)Change is possible only in the A-series. 3)The A-series involves contradiction and is therefore unreal. C) Therefore, time is unreal.

Pro Premise on Temporal Change

Premise (2): No Change w/o A-Series•Argument: Time flows. This is what allows for genuine change. - Genuine change occurs when the events or facts that exist now change - In other words, change occurs when we move from a present at which (say) a poker is cold to a present at which it is hot.

disadvantage of psychological(memory) theory

ex) sober man v drunk man -should a person be blamed for doing something drunk if he cannot remember what he did when he was drunk now that he's sober?

"Subject S's will is free with respect to performing action A if and only if S could have chosen to do other than A." Explain this definition of free will.

• (i) Feeling or experience of freedom. • (ii)Wetreateachotherasifwewerefree. • Weholdeachothermorallyresponsibleforour actions. And we generally do not hold people responsible when they are not in control of their actions or those actions were not chosen freely. • Freewillseemstobeaconditionondeserving credit for one's accomplishments. • Freewillseemstobeaconditiononthevalue we accord to love and friendship. • (iii)In deciding what to do, we must treat ourselves as free.

Resolved Racetrack Paradox

- The problem is not whether adding an infinite number of items gives us a finite quantity. Instead the problem is whether we can go through an infinite number of intervals of space in a finite time. - In any case, Zeno took himself to have shown by means of the Achilles Paradox and the Racetrack Paradox that motion is impossible if space and time are continuous.

what role does the principle of disquotation play in the liar paradox

-It seems to be part of the meaning of the word "true" that one can move freely between the claim that S and the claim that "S" is true. -For example, to say that Karl is a professor and to say that it is true that Karl is a professor seems to be to say the same thing. -This is formalized by philosophers in terms of the principle called disquotation, which says that one can infer that "S" is true from the claim that S and that one can infer that S from the claim that "S" is true: • S <—> "S" is true

Example of an Invalid Argument

-false dichotomy 1) p or q 2) p C) Therefore, not-q 1) Either Karl is a professor or he is unqualified to teach this course. 2) Karl is a professor. C) Therefore, Karl is qualified to teach this course.

disadvantage of dualist theory

-how could an immaterial thing, which lacks physical attributes like mass and momentum, bring about effects in the physical world? -Counterexample: brain bisection: ownership and awareness

Libertarianism

-if determinism is true, then every human action is causally necessitated by prior events -one only has free will if one could have acted or chosen otherwise -some human actions or choices are not causally determined

psychological (memory) theory

-if x and y are persons, then x=y, if and only if x has memories of y (or vice versa)

when is a sentence self referntial

-is a sentence that refers to itself as a sentence. -ex) dualized liar sentence

Paradox of Moving Bodies

-motion is impossible because time is discrete

dualist theory

-persons are immaterial souls

Time Travel

-takes place when there is a discrepancy between external time and personal time

materialist theory

-we are material (physical) objects - in particular we are our bodies -John Locke objects to this theory, using the conscious (soul) and the body as an example ex)prince and cobler

McTaggart Argument that Time is Unreal

1) Time necessarily involves change. 2) Change is possible only in the A-series. 3) The A-series involves contradictions and is therefore unreal. C) Therefore, time is unreal.

Resolved Achilles Paradox

But we know that this is absurd. Indeed, it seems that if motion is possible at all, it is possible for one thing to catch another thing from behind. But this seems to be what Zeno has shown to be impossible!