Puzzles and Paradoxes Midterm
Valid versus invalid arguments
Valid 1) Kanye is a genius. 2) All geniuses are philosophers. C) Therefore, Kayne is a philosopher. Invalid 1) Everyone who lives in Calabasas lives in California. 2) Kim lives in California. C) Therefore, Kim lives in Calabasas.
Argument Ad Hominem
attacking the person instead of attacking his argument
token
is a specific instance or occurrence of a type of object or event
What is the 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.
What is one way of defending the compatibility of free will and determinism?
(1) Reject the claim that one is only free if one could have acted otherwise.• 2) Reject the claim that if every action is causally necessitated, then no one could have acted otherwise. - is to insist that a variety of options neednotbe metaphysicallyopen to us in order for our will be free. - Thus, free will is compatible with the inability to do otherwise.
What is a reason for believing in free will?
(i) Feeling or experience of freedom. (ii) We treateach 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 musttreatourselves as free.
"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) We treateach 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 musttreatourselves as free.
What is time travel?
- A traveler departs and then arrives at her destination - The time elapsed for the traveler from departure to arrival is the duration of the journey - If she is a time traveler, intuitively the time that separates her departure from her arrival does not equal the duration of her journey. - takes place when there is a discrepancy between external time and personal time - Arrival and departure are separated by two unequal amounts of time
What is Parfit's response to these puzzles about personal identity? What is one radical implication of this response? What is one reason for rejecting it?
- 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.
the paradox of the arrow
- 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 instant? - 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 - Can it move between instants? - No, because there are no times between instants. Remember time is discrete. - But if the arrow cannot move during instants, and cannot move between them, it cannot move. So motion is impossible. 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)
How can the paradox be (re)solved? (Zeno's paradox of the moving bodies and the paradox of the arrow)
- Could things move, even if they don't move either at individual instants or between them? - One might say that motion is just a matter of being in one place at one time, and another place at the next time. - Real motion then becomes a bit like the motion in a film, which is just a matter of projected objects being in one location on one frame of the film, and another on the next frame. - Russell (following Bergson) refers to this view as the "cinematographic representation of reality."38 39 - But could this really be all that there is to motion? - Consider a billiard ball in motion over some spot X on the pool table at time t, and another ball just sitting on spot X on an identical pool table at that time. - Isn't it weird to think that there is no difference between those balls at that instant?
What is the 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 - It is impossible to kill your own grandfather because it would violate the law of non-contradiction - the grandfather would somehow both survive to become a parent and not survive. - - If contradictory situations are impossible, and if time travelers would create contradictory situations, then time travel is impossible. 1)By ordinary standards of ability, the backward time traveler can kill his grandfather 2)But the time traveler cannot kill his grandfather. The grandfather lived, so to kill him would be to change the past. It is logically impossible to change the past. 3)Premises (1) and (2) contradict each other C)Therefore, backward time travel is impossible.1)
What is the memory theory of personal identity? What is Reid's objection to this theory?How does the modified memory theory respond to this problem?
- If x and y are persons, then x=y if and only if x has memories of y (or vice versa). - As Locke was aware, this theory has some surprising consequences - Here is one sort of problem that Locke raised for his own theory: - It will be useful to introduce some names to bring out the sort of example Reid has in mind: Boy = the boy at the time of the flogging Officer = the officer at the time of the standard-taking General = the general in "advanced life" - Then what Reid seems to be saying is that the following sort of scenario is possible: General has memories of the experiences of Officer, and Officer has memories of the experiences of Boy, but General does not have memories of the experiences of Boy. 1) x and y are the same person if and only if if the later has 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) C) General=Boy & General≠Boy (7,8) If x has memories of y (or vice versa), then x=y. ------------------------ = 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.
B-series
- Includes the properties of being earlier than, later than, and simultaneous with another event. - B-series expressions include such words as "simultaneously", "two years earlier than", "10/10/17" and "ten minutes later than". - But they do not include any indexicals. The present is not privileged in the B-series - The B-series 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 910/9/17 10/10/17 10/11/17event a event b event c earlier than later than - While an event must (over time) have every position on the A-series, it can only have one position vis-à-vis another event in the B-series - If two events are, say, simultaneous when in the future, then they are also simultaneous when in the past. - A sentence containing an A-series expression is true at onetime but false at another. - A sentence whose only temporal expressions are B-series expressions is true at all times if it is true at any time. - uses tenseless verbs - Non-indexical spatial descriptions: -Kyrie is at GPS Position 2°17'39"E, 48°51'30"N.-Kyrie is 1 meter east of Lebron.
A-series
- Includes the properties of being past, present and future. A-series expressions include such words as "present," "past," "future," "today," "tomorrow," and "five weeks ago" - These expressions are indexicals. - In this sense, we can think of the A-series expressions as "centered" on the present. - They describe things in relation to the time it is now. - Indexicals: Indexicals are words whose referent and meaning are determined by the context of the speaker - e.g. the time and space of speech. - Examples:-Pronouns: I, you, this, that-Adverbs: here, now, presently, today, yesterday, tomorrow -Adjectives: my, your, past, present, future, left/right, up/down7 - Besides indexicals, the A-series expressions also include tensed verbs - i.e., is, was, will be. - According to the A-series, events "move" from the future, through the present, and into the past. Events that were once future become present, and then retreat into the past - uses tensed verbs - Indexical spatial descriptions: -Kyrie stands here.-Kyrie is to the right of Lebron
Explain McTaggart's distinction between an A-series and a B-series of time. According to McTaggart, what is the status of the A-series/B-series distinction?
- McTaggart's idealism consisted largely in the claim that what we usually take to be central features of reality are merely ideal - in other words, that they are dependent on the mind, as opposed to part of objective reality. - First, we can relate various events to one another in terms of relations of "earlier than" or later than". This will provide us with a coherent ordering of these events. This gives us a B-series of events in time. - Second, 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. This gives us an A-series of events in time, centered on the present. - The B-series treats every point in time in the same way. The A-series is orientated around the time it is now - The A-series and the B-series are not independent time series. - There are links between them. - For example, the sentence "the Korea War is in the past" is true if and only if the end of the Korea War is earlier than 10/10/17.• - Are the truth-value links between the two series evidence that the A-series and the B-series are merely terminologicalvariants (like Centigrade /Fahrenheit, inch/cm, etc.)? - McTaggart says "no." He claims that the distinction between the A-series and the B-series is a metaphysical one - The two series offer different pictures of reality. On the A-series time flows - On the B-series there is no moving "now"; time does not flow; past/present/future are equally real.
Circularity
- 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
Describe Parfit's teletransporter case. Why is this case problematic for personal identity?What is one possible response to this 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. - The character in the story seems to be correct when he says "If I'm here I can't also be on Mars." But that's just: - Earth-Parfit ≠ Mars-Parfit - The problem is that both Earth-Parfit and Mars-Parfit stand in direct memory relations to Original-Parfit - Hence, if the memory guarantee is true, the following must be true: - Earth-Parfit = Original-Parfit•Mars-Parfit = Original-Parfit - But the three claims in blue cannot all be true: this trio of claims is inconsistent. - So, if the scenario Parfit describes is really possible, it looks as though the memory guarantee implies a contradiction - But then the memory guarantee must be false. - Parfit's example of teletransportation seems to show that the memory guarantee is false; and this seems to be an essential part of the memory theory.
psychological theory of personal identity (advantage and counterexample)
- 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. - A useful comparison is a comparison of persons to clubs. - Suppose that we begin a personal identity discussion club at UCI. - People gradually leave and join the club, and some of the rules change, and eventually people decide that at meetings things other than personal identity may occasionally be discussed - At one of the meetings (in 2048) someone says: "Is this really the same club as the one formed way back in 2012?" - Parfit suggests, and this seems right, that this is not a very deep question - We could decide to say that they are identical or distinct, but our choice seems arbitrary. - Parfit's suggestion is that people are, in this way, like clubs - When we ask, "Is Original-Parfit really the same person as Mars-Parfit or Earth-Parfit?" we are not asking a very deep question - Each is similar in certain ways to Original-Parfit, and that's the end of the story - There is simply no further, fundamental fact about which one is identical to Original-Parfit. - 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.
Soundness
- The argument is valid and the premises are in fact true. - deductive arguments - satisfies the following two conditions: (a) It is valid. (b) All of its premises are true - An argument's conclusion must be true
What are cases of brain bisection? Why are these problematic for personal identity?What is one possible response to such cases?
- These are studies of patients whose corpus callosum has been severed - The corpus callosum is a pathway which connects the left and right hemispheres of the human brain and, in normal subjects, allows the two hemispheres of the brain to exchange information. - If the corpus callosum is severed, the two hemispheres of the brain cannot exchange information - So any sensory data about the environment available to, for example, the left hemisphere, will not be available to guide the movements of the left hand, which is controlled by the right hemisphere - Information available only to the right hemisphere will not be reportable in speech, since speech is controlled by the left hemisphere. - 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.
Explain Zeno's Achilles paradox racetrack paradox. What do these paradoxes assume?
- This argument is supposed to show that ifspace and time are continuous, then motion is impossible - The idea is that 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 We assume two things about Achilles and the tortoise - First, Achilles always takes some amount of time to cover a given distance - Second, the tortoise, even though slow, is quite persistent; in particular, the tortoise is in constant motion, so that the tortoise covers some distance in every interval of time, no matter how small that interval of time. The tortoise, while slow, is persistent — so the tortoise has also moved some distance during the interval of time. The tortoise does not move as far as Achilles, but the tortoise does move it always takes Achilles some finite amount of time to catch up to where the tortoise was, and during that finite amount of time, the tortoise will always have covered some distance. 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)
materialist theory of personal identity (advantage and counterexample)
- We are material (physical) objects - in particular we are our bodies. - On this view, we are material objects - namely, we are our bodies - This view is natural, because it fits with many things that we are inclined to say about ourselves.(advantage) - For example, we say that we have a certain weightand height, and are in a specific place ... and what could occupy a place, and have a weight and height, other than a physical thing? - But there are problems with the idea that persons are identical with their bodies. - One important example is brought out by John Locke's example of the prince and the cobbler: - This seems to be a problem for materialist views of human persons - If Locke is right, and we can coherently imagine cases in which two persons "swap bodies", then it seems that we cannot be identical to our bodies - As we saw last time, the notion of a material object is not unproblematic; the example of the Ship of Theseus, for instance, raises problems for the idea that material objects can continue to exist over time - But there are other problems with the idea that persons, in particular, are material objects - One important example is brought out by John Locke's example of the prince and the cobbler:
Explain Zeno's paradox of the moving bodies. What do these paradoxes assume? What is the paradox meant to show?
- We are now assuming that 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. - Suppose that the following is a grid of such adjacent points. Each point is occupied with certain particles: 1 2 3 1 2 3 1 2 3 - Look at, for example, Yellow-2 and Blue-3. At Time 1, Yellow-2 is to the left of Blue-3. At Time 2, Yellow-2 is to the right of Blue-3. - But the two were never even with each other. - After all, they were not even with each other at Time 1, and were not even with each other at Time 2, and there was no time in between. - 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.
When is a sentence self-referential? How does the Dualized Liar show that this is not the root of the Liar Paradox?
- a sentence that refers to itselfas a sentence. •Examples:-Karl is reading this sentence. -This sentence contains exactly threee erors. - Self-reference isn't essential to the paradox. To see this consider the Dualized Liar Paradox... - One one side of a blank card print: "The sentence on the other side of this card is true" - On the other side of the same card print: "The sentence on the other side of this card is false" - B: The next statement by A will be false A: B has spoken truly! - Neither of these pairs of statements is self-referential, since no statement refers to itself - But they are still paradoxical!
dualist theory of personal identity (advantage and counterexample)
- according to which persons are immaterial souls. Then survival is always an all-or-nothing matter: it is just a matter of the continued existence of a soul. - This view has advantages. - Assuming that immaterial souls are indivisible, the problems of division illustrated by the examples of fission and teletransportation cannot be used against the dualist. - Of course, dualism doesn't say exactly what does happen in these cases - just that the original person survives if and only if one the post-surgery (or post-teletransportation) bodies is attached to his soul. But, souls being invisible, it might be quite hard to tell. - how could an immaterial thing, which lacks physical attributes like mass and momentum, bring about effects in the physical world?
racetrack paradox
- attempts to show directly that it is impossible for anything to move any distance at all. - 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! - The Racetrack argument is meant to show that it is impossible to move any finite distance in a finite time 1) Any distance is divisible into infinitely many smaller distances 2) To move from a point x to a point y, one has to move through all the distances into which the distance from x to y is divisible 3) To move from one point to another in a finite time, one has to traverse infinitely many distances in a finite time. (1,2) 4) It is impossible to traverse infinitely many distances in a finite time. C) It is impossible to move from one point to another in a finite time. (3,4)
deductive argument
- if the truth of the premises guarantees the truth of the conclusion - Thus, it would be self-contradictory to assert the premises but deny the conclusion - only makes explicit what is already contained, even if implicitly, in the premises. - Therefore they don't really expand our knowledge in a fundamental way, they simply make explicit what we are already committed to. - Validity and Soundness
necessary truths
- independent of the language used to express them - those that are true in allpossible worlds. - Examples: - It is not the case that it is both raining and not raining here - 2 + 2 = 4. - All bachelors are unmarried
Personal time
- is measured, say, by the traveler's wristwatch. Her journey takes, say, an hour of her personal time.
What is a proposition?
- is the meaning or content of a declarative sentence or thought - are true or false - are different from the actions (talking, thinking, drawing etc.) by which they are expressed - are different from the words, sounds, symbols, or brain states by which they are expressed - independent of the language used to express them
What is a reason for believing in 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.
What is 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 - Note: leaves it open whether there is any purpose guiding our fates.
discrete space
- not continuos - natural numbers (1,2,3,4,5) - then there are lengths which are not divisible (minimal lengths). - If time is discrete, then there are pairs of times which are such that there is no time in between them (indivisible instants) - In this case, space and time would have basic indivisible units. (Spatial-temporal atoms like pixels on a computer screen.)
continuous space
- one in which the following is true: Between every two members of the series, there is another member of that series. - rational number (1.23456, 1.234565) - 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 that time, and that in between any two moments there is another.
a priori
- prior to an experience - knowledge is independent of experience - Example: All bachelors are unmarried.
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 is causal determinism?
- the view that the state of the world at a given time (together with the laws of nature) whollydetermines 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. - Macro-level scientific theories seem to imply that macro-level events follow deterministic laws. - In particular, the laws of neurobiology and psychology seem to be broadly deterministic. - So thought of it in this way, our choices seem to be determined by prior events in accordance with these laws. - On the micro-level (the sub-atomic level), quantum mechanics tells us that the laws are non-deterministic or probabilistic. - But this doesn't seem to be much help in the present context - For being told that are choices the products of probabilistic laws is a kin to being told that they are random (within certain bounds) - And randomness also seems incompatible with free will.
synthetic
- true because of a reason - "its cloudy outside today"
contingent truths
- true propositions (often simply called contingent truths) are those that are not necessary and whose opposite is therefore possible - are those that are true in somepossible worlds and false in others. Examples: - It seldom rains in the Sahara. - There are more than twenty states in the USA. - - - Some lonely bachelors drive Maseratis.
mention
- when we talk about the word itself. Mentioned words often appear between quotation marks or in italics Example: "Tree" is spelled with two "e"s.
use
- when we talk about the world by means of it. Example: There is a tree in the garden.
Validity
-If the premises were true, the conclusion would have to be true - deductive arguments - meets this condition: If its premises are true, then its conclusion must be true. - It is impossible for there to be a valid argument which has true premises anda false conclusion. 1) Kanye is a genius. 2) All geniuses are philosophers. C) Therefore, Kayne is a philosopher. Just because it is valid, it may not be sound
inductive argument.
-if the truth of the premises supports the truth of the conclusion, but doesn'tguarantee it. - Thus, it would not be self-contradictory to assert the premises and deny the conclusion. - can take us beyond what is implicit in their premises. - Thus, they may expand our knowledge about the world in a manner that is impossible for deductive arguments. 1) Most people who live in Echo Park are hipsters. 2) Karl lives in Echo Park .C) Therefore, Karl is a hipster.
What is an 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 of an argument are its starting points. These are the claims that the argument takes for granted Example of an Argument: 1)Everyone who lives in Echo Park is a hipster. 2)Karl lives in Echo Park . C)Therefore, Karl is a hipster.
What is a paradox?
-is an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. -is an argument which has these features: (1) its premises appear to be true; (2) its conclusion appears to be false; (3) it appears to be valid. - appears to be a soundargument, which has a false conclusion - problematic because it seems to be an example of an impossible argument - is impossible for there to be a validargument which has true premises and a false conclusion
Hypothetical Syllogism
1) If p, then q 2) If q, then r C) Therefore, if p, then r - valid argument form
Explain the argument pro and con McTaggart's premise that the A-series involves a contradiction. What, if anything, is problematic about the argument the effect that the A-series involves a contradiction?
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. McTaggart's argument for premise (3): - 4) If any event has one of the following properties - being past, being present, being future - then it also has the others. - 5) No event can have more than one of the following properties: being past, being present, being future. - C) Therefore, No event has one of the following properties: being past, being present, being future. This is a valid argument. - So what we need to ask is whether its premises are true. Is the argument sound? Objection: Although an event has all of the mutually incompatible positions in the A-series, it doesn't have them all at once. - But there is nothing contradictory about something having incompatible properties at different times. - Premise (4) in effect says that, given the A-series: "Every event is past, present, and future" - But this needs to rephrased as something like: (4*) Every event was future, is present, and will be past. - The A-series is only contradictory if one attempts to interpret an A-theoretic statement such as (4*A) independent of any particular point of view in time. - In other words, the problem only arises if one attempts to give an objective (perspective-independent) account of indexical (and hence subjective) time descriptions.
Explain the argument for fatalism from foreknowledge. What is the argument meant to show? How can the conclusion of the argument from foreknowledge be resisted?
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. - 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? - It all depends on why the author of the book of my life (e.g. God) knows what he knows. - If the reason the author knows what I will do is because he controls my mind, then perhaps my will is not free. - But if the reason the author knows what I will do is because he is a time traveller from the future who closely observed me and wrote everything down then my will might still be free
State McTaggart's argument to the effect that time is unreal. Explain the arguments pro and con the premise that temporal change is possible only in the A-series.
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 - In effect, (1) and (2) together claim that time must be thought of as an A-series. And (3) claims that anything thought of in those terms is unreal. 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. - The idea here is that it is impossible for there to be an interval of time in which nothing changes. - Why would such an interval of time be inconceivable? - Well, what would conceiving of time's passage without conceiving of any change of any sort involve? - It seems to be impossible for us to experience the passage of time without experiencing change - for the experience of the passage of time is itself an experience of a sort of change. - If so, then there is no conceivable experience of the passage of time that is not also an experience of change. - But, does the possibility of time without change require the possibility of experiencing time without 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. - But B-series properties are timeless and permanent - A sentence whose only temporal expressions are B-series expressions is true at all times if it is true at any time - So the B-series cannot account for change. - Does this argument seem compelling to you?
Explain some of the solutions to the paradox of omnipotence. Which of these solutions do you find plausible and why?
1: - 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 thenlift it! 2: Def. 2: 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). 3: 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. - But how do we define the relevant acts? - An even more restricted view of omnipotence: - 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.
How can these paradoxes be (re)solved? (Zeno's Achilles paradox and his racetrack paradox)
A. Reject Premise 1: Any distance is divisible into infinitely many smaller distances. B. Reject Premise 2: To move from a point x to a point y, one has to move through all the distances into which the distance from x to y is divisible. C. Reject Premise 4: It is impossible to traverse infinitely many distances in a finite time.D. Reject the Reasoning. E. Accept the Conclusion. - Given the assumption that space (and time) is continuous, it is not possible to reject premises (1) and (probably) (2).•But what about premise (4): the assumption that it is impossible to traverse infinitely many distances in a finite time? - Why does (4) seem plausible? Because it seems that anyone who travels infinitely many finite distances will have to travel an infinite distance; and no one (who is traveling at a finite speed) can do this in a finite time. - Premise (4) assumes: The sum of any infinite collection of finite journeys is infinite - This claim has to be interpreted as follows: Taking infinitely many journeys, each of which covers somefinite distance or other, requires traveling an infinite distance. - Now we can see that premise (4) is false. In deploying the finite-infinite contrast, premise (4) neglects the matter of the size of the finite distances at issue. - The dismissal of premise (4) eliminates the inconsistency and thereby dissolves the Racetrack Paradox. But one has to take recourse to the mathematics of infinite series to see that premise (4) is false. - So premise (4) is false. One can travel infinitely many distances (each of which has some finite length) in a finite amount of time. •The reason is that the infinite series converges to 1.
Strength
An argument is strong if the truth of the premises make the truth of the conclusion very likely. - inductive arguments
Happy-face solution
Explains away the spurious appearance of a paradox by showing that the paradox-generating premises aren't really incompatible or that one of the premises isn't true
What are the various possible solutions to the paradox? Be able to what the basic idea behind these solutions is, and why they may not succeed. (Liar Paradox)
Liar Statement is Contradictory and so False - Proposal: there is nothing paradoxical about the liar paradox - Every statement includes an implicit assertion of its own truth. - Thus, for example, the statement "It is true that two plus two equals four" contains no more information than the statement "two plus two is four," because the phrase "it is true that..." is always implicitly there. - And in the self-referential spirit of the Liar Paradox, the phrase "this statements is..." is equivalent to "this whole statement is true and this statement is..." - Thus the following two statements are equivalent: -This statement is false -This statement is true and this statement is false. - - The latter statement is a simple contradiction of the form "A and not A," and hence is false. - There is therefore no paradox because the claim that this two-conjunct Liar is false does not lead to a contradiction. Problems: Is it the case that every statement includes an implicit assertion of its own truth - Imagine twirling your spoon in a bowl of alphabet soup, then looking down to discover the letters had spelled out "bad soup." - Does this random statement assert its own truth?- This solution doesn't apply to the Dualized Liar Paradox: -The next sentence is false. -The preceding sentence is true. - When these sentences are changed according to proposal: -This sentence is true and the next sentence is false. -This sentence is true and the preceding sentence is true. - We are still stuck in a paradoxical loop. The dualized liar paradox has not gone away. -------------------------------------------------------- A Hierarchical Notion of Truth? - Proposal: The liar paradox arises because the words "true" and "false" are applied to the very sentence they occur in - One solution to the liar paradox is to disallow the application of "true" and "false" to the very sentences they occur in. - This is Tarski's solution: The liar paradox does not arise if "true" and "false" cannot not apply to the very sentences these terms occur in, but instead apply only to sentences in a different language - or part of the language. - On this view, no language can contain a coherent word "true" which can apply to all of its own sentences. - If a language contains a word "true", it must apply only to sentences within a smaller part of that language, which we can call the object-language. - The words "true" and "false" may not occur in the object-language. They may only occur in what is called the meta-language. - The meta-language includes all of the object-language - plus it can talk about the truth values of the object-language. L1 = Object Language (no term for "true" - i.e. no "true1"): - E.g. "This is a classroom." L2 = Meta-language (introduces the term "true1"): - - E.g. "The sentence 'This is a classroom' is true1." L3 = Meta-meta-language (introduces the term "true2"): - E.g. "The sentence 'The sentence 'This is a classroom is true1' is true2." - And so on... Problems with Tarski's solution: - It overgeneralizes - Not all sentences that predicate truth of sentences at the same level seems to be paradoxical. - E.g. "This sentence is true" where "this sentence" refers to another sentence in the same language, e.g., the sentence "It is true that Paris is the capital of France." - Tarski's view seems to fit poorly with the commonsensical meaning of sentences like "Every statement is true or false" and "What you said just now is true". - Our ordinary understanding of true doesn't seem to involve any sort of implicit grasp of this sort of hierarchy of different senses of "true"? Rather, there seems to just be one concept of truth that applies to all sentences. ----------------------------------------------------- Degrees of Truth? - Maybe the problem here is that we have been thinking of true and falsity as all or nothing? - What if truth came in degrees - say from 0 (totally false) to 1 (totally true)? - Then we could say that sentences like the Liar sentence are "sort of true" - say .5 true. Problem: - Our conception of logic is based around the idea of truth and falsity as all or nothing - So this option would also require us to reject classical logic and come up with a new conception of logic in terms of degrees of truth - But there is some evidence that English actually works this way?
Explain David Lewis's solution to the 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 equivocationabout 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. - What I can do, relative to one set of facts, I cannot do, relative to another set of facts. - Similarly, holding fixed only the past up to the attempt to kill the grandfather, the time traveler can kill his grandfather. - However, holding fixed the past following the attempt to kill the grandfather, the time traveler cannot kill his grandfather. - There is no paradox. - To render backward time travel possible we have to assume that a time traveler cannot change the past even though he can participate in the past.
compatibilism
Reject the argument just given for Incompatibility. Accepts (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. Rejects: 3) One only has free will if one could have acted or chosen otherwise.
libertarianism
Some human actions or choices are not causally determined. Accepts: (1) If determinism is true, then every human action is causally necessitated by prior events. (3) One only has free will if one could have acted or chosen otherwise. rejects: 2) If every action is causally necessitated, no one could have acted or chosen otherwise.
hard determinism
There is no free will. Accepts: (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. Rejects: 1) If determinism is true, then every human action is causally necessitated by prior events.
What is the Liar Paradox? What role do the Principle of Bivalence and the Disquotation principle play in the 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. - 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. 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). - Are there counterexamples to the principle of bivalence? - Kale is delicious? - 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
What does it mean for a statement/proposition to entail another statement/proposition?
To say that the conclusion follows validlyfrom the premises is the same things as saying that the premises entailthe conclusion. - "p entails q" = "q is validly deducible from p."
Unhappy-face solution
an explanation of why the paradox can't have a happy-face solution. This explanation appeals to an irresolvable tension in the concepts generating the paradox
Ways to resolve
figure out which one of these appearances is the misleading one.For example: a) Find a false premise.The reject-a-premise strategy b) Show why the conclusion, which seems false, is really true.The accept-the-conclusion strategy c) Show why the reasoning employed is, contrary to appearances, invalid.The reject-the reasoning strategy. - can reject a premise by claiming that it is false, but also by instead claiming that it is incoherent or nonsensical, and so neither true nor false.
counterexample
finding a conceivable possibility (a "possible world") in which the premises are true and the conclusion false The existence of such a possibility shows the argument is invalid: 1) Everyone who lives in Calabasas lives in California. 2) Kim lives in California. C) Therefore, Kim lives in Calabasas. This argument is invalid because there is possible world in which Kim lives in California, but not in Calabasas: e.g. in which she lives in Irvine.
Genetic Fallacy
if an argument has some particular origin, the argument must be right (or wrong). (Is this always bad?)
type
is a category or class of object or event
antinomy
is a pair of arguments where: a) Each argument begins with premises that seem uncontroversially true. b) Each argument proceeds via reasoning that seems uncontroversially valid. c) The conclusion of the arguments are incompatible with each other.
aporia
is an irresolvable internal contradiction in a concept, argument, or theory. Paradox = para + doxa = beyond + belief Antinomy = anti + nomos = anti + law Aporia = a + poros = not + passing
Slippery Slope Fallacy
the assumption that something is wrong because it is similar to something that is wrong. (Is this always bad?)
Argument from Authority
the claim that the speaker is an expert, and so should be trusted. (Is this always bad?)
Explain the paradox of omnipotence.
- Let x be any being 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.
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": 1)God exists 2)If God exists, then God is omnipotent 3)If something is omnipotent, it can do anything 4)If God exists, then God can do anything. (2, 3) 5)If God exists, then God is wholly good 6)If something is wholly good, it always eliminates as much evil as it can 7)If God exists, then God eliminates as much evil as God can. (5, 6) 8)If God exists, then God eliminates all evil. (4, 7) 9)If God exists, then there is no evil. (8) 10)There is no evil. (1, 9) 11)Some evil exists.C)There is no evil and some evil exists. (10, 11) - Since the argument appears to be valid, one of the premises must be false. - We can disregard premises which follow from other premises. - Six possibilities remain: 1, 2, 3, 5, 6, and 11 - The believer in a monotheistic God has to reject 3, 6, or 11.
necessary conditions
- To say that x is a ------ condition for y is to say that it is impossible to have y without x. In other words, the absence of x guarantees the absence of y. - Example: Having four sides is necessary for being a square.
sufficient conditions
- To say that x is a ------ condition for y is to say that the presence of x guarantees the presence of y. In other words, it is impossible to have x without y. - Example: Being a square is sufficient for having four sides.
Ambiguity
- When a term can mean several different things. - - This often causes the fallacy of equivocation, when different premises of a single argument use different meanings of a term. (1) Banks contain a lot of money. (2) That muddy slope of a river is a bank. (3) Therefore that muddy slope contains a lot of money.
What is a theory of personal identity a theory of?
- a theory which tries to answer the question: what does it take forA and B to be thesame person?
a posteriori
- after an experience - knowledge or justification is dependent on experience or empirical evidence. - Example: Some bachelors are happy.
vague
- it's meaning doesn't settle exactly what it means. - Example: John is rich. The meaning of "rich" doesn't settle exactly how much money John needs to have to count as "rich" - In this sense "rich" is a vague term
analytic
- true by definition - "all bachelors are unmarried men"
Disjunctive Syllogism
1) Either p or q 2) Not-p C) Therefore, q - valid argument form
Modus Tollens
1) If p, then q 2) Not-q C) Therefore, not-p - valid argument form
Denying the Antecedent
1) If p, then q 2) Not-p C)Therefore, not-q - invalid argument form 1) If Bernie Sanders is a Republican, then he supports gun rights. 2) Bernie Sanders is not a Republican. C) Therefore, Bernie Sanders does not support gun rights.
Modus Ponens
1) If p, then q 2) p C) Therefore, q - valid argument form
Affirming the Consequent
1) If p, then q 2) q C) Therefore, p - invalid argument form 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.
False dichotomy:
1) p or q 2) p C) Therefore, not-q - invalid argument form 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
