Introduction to Paradoxes Philosophy 20229 rts Greek philosopher - PowerPoint PPT Presentation

Introduction to Paradoxes Philosophy 20229

❙♦❝r❛t❡s � Greek philosopher (470-399 BC) � Referred to himself as a “gadfly" “Socrates, I certainly used to hear, even before meeting you, that you never did anything else than exist in a state of perplexity yourself and put others in a state of perplexity. And now you seem to be bewitching me and drugging me and simply subduing me with incantations, so that I come to be full of perplexity." –Meno � In addition to taking down the learned and powerful, Socrates main opposition was to the sophists.

❙♦♣❤✐sts � Teachers in ancient Greece, specializing in philosophy and rhetoric � Specialized in teaching the ability to influence one’s fellow citizens in political gatherings through rhetorical persuasion � They are strongly associated with the pursuit of winning arguments and looking smart, rather than the pursuit of truth.

P❛r❛❞♦①❡s � A paradox is an argument designed to frustrate people � Our job in this class is to figure out what is going on with the various paradoxes so that we can determine which are helping us see fundamental and important truths about reality, and which are mere rhetoric (and no one agrees about which are which)

❉❡✜♥✐♥❣ ❛ P❛r❛❞♦① “An apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises." –R. M. Sainsbury

❆r❣✉♠❡♥ts You may recall from your intro class that an argument is a series of statements, one of which is called the conclusion and the others of which are called the premises. Analyzing arguments is easier if we put them into explicit premise-conclusion form. 40 years ago, we had Pong, two rectangles and a dot...That is what games were. Now, 40 years later, we have photorealistic 3D sim- ulations with millions of people playing simultaneously, and it’s getting better every year. And soon we’ll have virtual reality, aug- mented reality. If you assume any rate of improvement at all, the games will become indistinguishable from reality. It would seem to follow that the odds that we are living in base reality is one in billions.

▼❛❦✐♥❣ ❆r❣✉♠❡♥ts ❊①♣❧✐❝✐t 40 years ago, we had Pong, two rectangles and a dot...That is what games were. Now, 40 years later, we have photorealistic 3D sim- ulations with millions of people playing simultaneously, and it’s getting better every year. And soon we’ll have virtual reality, aug- mented reality. If you assume any rate of improvement at all, the games will become indistinguishable from reality. It would seem to follow that the odds that we are living in base reality is one in billions. ✭✶✮ Video games improve at a very fast rate. ✭✷✮ If video games continue to improve at a very fast rate, the games will be indistinguishable from reality. ✭❈✮ Therfore, the odds are very strong that we are in a simulation. Is this a good argument?

▼❛❦✐♥❣ ❆r❣✉♠❡♥ts ❊①♣❧✐❝✐t ✭✶✮ Video games improve at a very fast rate. ✭✷✮ If video games continue to improve at a very fast rate, the games will be indistinguishable from reality. ✭❈✮ Therfore, the odds are very strong that we are in a simulation. Is this a good argument? There are several things one could mean by this: � Is it a fair representation of the original non-premise-conclusion form argument? � Are the premises true? Yes+Valid=Sound � Do the premises imply the conclusion? Yes=Valid

❱❛❧✐❞✐t② ✭✶✮ Video games improve at a very fast rate. ✭✷✮ If video games continue to improve at a very fast rate, the games will be indistinguishable from reality. ✭❈✮ Therfore, the odds are very strong that we are in a simulation. � An argument is valid if and only if it is impossible for all the premises to be true and the conclusion to be false. � Thus, this argument is invalid as written. � Showing a way for the premises to be true and the conclusion false shows an argument to be invalid; valid (for our purposes) just means there is no way to do that. � When an argument is invalid, we often want to try to find ways to make it valid.

Validity ✭✶✮ Video games improve at a very fast rate. ✭✷✮ ■❢ ✈✐❞❡♦ ❣❛♠❡s ✐♠♣r♦✈❡ ❛t ❛ ✈❡r② ❢❛st r❛t❡✱ t❤❡♥ t❤❡② ✇✐❧❧ ❝♦♥t✐♥✉❡ t♦ ✐♠♣r♦✈❡ ❛t ❛ ✈❡r② ❢❛st r❛t❡ ✭✸✮ ❱✐❞❡♦ ❣❛♠❡s ✇✐❧❧ ❝♦♥t✐♥✉❡ t♦ ✐♠♣r♦✈❡ ❛t ❛ ✈❡r② ❢❛st r❛t❡ ✭✶✱ ✷✮ ✭✹✮ If video games continue to improve at a very fast rate, the games will be indistinguishable from reality. ✭✺✮ ❱✐❞❡♦ ❣❛♠❡s ✇✐❧❧ ❜❡ ✐♥❞✐st✐♥❣✉✐s❤❛❜❧❡ ❢r♦♠ r❡❛❧✐t② ✭✸✱ ✹✮ ✭✻✮ ■❢ ✈✐❞❡♦ ❣❛♠❡s ✇✐❧❧ ❜❡ ✐♥❞✐st✐♥❣✉✐s❤❛❜❧❡ ❢r♦♠ r❡❛❧✐t②✱ t❤❡♥ t❤❡r❡ ✇✐❧❧ ❜❡ ❝♦♥s❝✐♦✉s ♣❡♦♣❧❡ ✐♥ ✈✐❞❡♦ ❣❛♠❡s ✭✼✮ ❚❤❡ ♥✉♠❜❡r ♦❢ ♣❡♦♣❧❡ ✐♥ ✈✐❞❡♦ ❣❛♠❡s ✇✐❧❧ ✈❛st❧② ♦✉t♥✉♠❜❡r t❤❡ ♥✉♠❜❡r ♦❢ ♣❡♦♣❧❡ ♥♦t ✐♥ ✈✐❞❡♦ ❣❛♠❡s ✭✽✮ ❚❤❡r❡❢♦r❡✱ t❤❡ ♥✉♠❜❡r ♦❢ ❝♦♥s❝✐♦✉s ♣❡♦♣❧❡ ✐♥ ✈✐❞❡♦ ❣❛♠❡s ✇✐❧❧ ✈❛st❧② ♦✉t♥✉♠❜❡r t❤❡ ♥✉♠❜❡r ♦❢ ♣❡♦♣❧❡ ♥♦t ✐♥ ✈✐❞❡♦ ❣❛♠❡s ✭✺✱ ✻✱ ✼✮ ✭✾✮ ❲❡ ❤❛✈❡ ❡q✉❛❧ ♦❞❞s ♦❢ ❜❡✐♥❣ ❛♥② ❝♦♥s❝✐♦✉s ♣❡rs♦♥✳ ✭✶✵✮ ❱✐❞❡♦ ❣❛♠❡s ❛r❡ s✐♠✉❧❛t✐♦♥s ✭❈✮ Therefore, the odds are very strong that we are in a simulation.

❱❛❧✐❞✐t② We often want to try to simplify and clarify when possible, so consider this version of the argument: ✭✶✮ Simulations are able to replicate human consciousness ✭✷✮ The number of conscious creatures in simulations is much higher than the number of conscious creatures not in simulations ✭✸✮ I have an equal chance of being any conscious creature ✭❈✮ Therefore, there is a high probability that I am in a simulation.Valid Sound?

❲❤❛t ✐s ❛ P❛r❛❞♦①❄ A paradox is an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. Returning to our definitions of paradoxes, this means a paradox is an argument which is apparently valid in which the premises are apparently true and the conclusion is apparently false − which is impossible. For any given argument, one can either deny a premise, deny that it is valid, or accept the conclusion. Analyzing paradoxes this semester will involve two steps: ✭✶✮ Determining what is being argued for, what it is being argued from, and how the argument is supposed to work ✭✷✮ Figuring out the best option between rejecting a premise, rejecting validity, or accepting the conclusion. As you will see, the latter often involves developing complex theories regarding the concepts in the paradox.

Proof that 1=2 ✭✶✮ a �= ✵ � In a lot of arguments (like this one), ✭✷✮ a = b some premises are mini-conclusions a ✷ = ab ✭✸✮ ( ✷ ) following from previous premises. a ✷ − b ✷ = ab − b ✷ Like the final conclusion, you can only ✭✹✮ ( ✸ ) reject them if you either reject the ✭✺✮ ( a + b )( a − b ) = b ( a − b ) ( ✹ ) premise(s) they are derived from, or if ✭✻✮ ( a + b ) = b ( ✺ ) you reject the reasoning by which they ✭✼✮ ( b + b ) = b ( ✷ , ✻ ) were derived. ( ✼ ) ✭✽✮ ✷ b = b � Call the mini-conclusions ❞❡r✐✈❡❞ ✭✾✮ ✷ = ✶ ( ✽ ) ■ ♣r❡♠✐s❡s � Call the others ✐♥❞❡♣❞❡♥❞❡♥t ♣r❡♠✐s❡s .

Proof that 1=2 ✭✶✵✮ a �= ✵ � Obviously the conclusion of this ✭✶✶✮ a = b argument is false. a ✷ = ab ✭✶✷✮ ( ✷ ) � Whenever the conclusion of an a ✷ − b ✷ = ab − b ✷ ✭✶✸✮ ( ✸ ) argument is false, it means that ❡✐t❤❡r t❤❡r❡ ✐s ❛ ❢❛❧s❡ ✐♥❞❡♣❡❞❡♥❞❡♥t ♣r❡♠✐s❡ ✭✶✹✮ ( a + b )( a − b ) = b ( a − b ) ( ✹ ) ♦r ❛♥ ✐♥✈❛❧✐❞ ❧♦❣✐❝❛❧ st❡♣✳ ✭✶✺✮ ( a + b ) = b ( ✺ ) � There does not seem to be any ✭✶✻✮ ( b + b ) = b ( ✷ , ✻ ) problem with introducing two ✭✶✼✮ ✷ b = b ( ✼ ) variables, saying they are equal, and ✭✶✽✮ ✷ = ✶ ( ✽ ) ■ saying that they are not 0, so the problem must be with the validity.

Often paradoxes do not come to us in organized premise-conclusion form. Simpson’s paradox: Homer is trying to figure out whether or not he should take Drug H for baldness. Here are the statistics he is faced with (with the percentages being the percent of people in that group who regrew hair): Men Men 40 Men under 40 and over Drug H 40% 20% 38% Placebo 50% 25% 27% How could these numbers happen, and what should Homer do?