2. The Possibility of the Impossible A Prelude to Logic, Ch 1 and “Logical Possibility”

3. The Agenda The concept of logical possibility as distinct from physical possibility Necessity, contingency and possible worlds Are there really necessary truths: a puzzle

4. Is ESP impossible? All descriptions of ESP imply violations of conservation of energy…as well as violations of all principles of information theory and even of the principle of causality…Strict application of physical principles requires us to say that ESP is impossible. ---------Milton Rothman Impossible? It depends on what you mean by impossible…

5. Does ESP actually occur? Is there any scientific evidence for or against ESP? –During the 1930s J. B. Rhine and colleagues at Duke University conducted a series of experiments to determine whether ESP phenomena actually occurred using Zener cardsZener cards –You may have observed experiments like those Rhine conducted…

7. What’s wrong with the experiment (and with Rhine’s original one)? Face-to-face situation with minimal screening allows for “sensory leakage” –In original, subjects could read figures from backs of cards –Subjects could see reflection in experimenter’s glasses, or eyes –Subjects could read experimenter’s expression, and voice No double-blind Rhine’s results not duplicated when more rigorous eperimental methods adopted

8. Logical Possibility vs. Physical (“Nomological”) Possibility Logically possible –“conceivable” –consistent: doesn’t imply a contradiction Reducio ad absurdem (“If you can show that a position has absurd consequences, you’ve provided a powerful reason for rejecting it.”) Physically possible –consistent with “laws of nature”

9. Actuality, physical possibility and logical possibility Whatever is actual is possible …but not vice versa Whatever is physically possible is logically possible …but not vice versa

10. Logically Impossible Physically Possible Logically Possible Actual Round Square P and not-P Having your cake and eating it (simultaneously) Trisecting an angle with only compass and straight-edge Precognition? Time Travel?

11. possible world: a way things could have been actual world: the way things actually are necessarily : at all possible worlds. Has the same truth value at all possible worlds. contingently : at the actual world but at some other possible world. Not necessary, i.e. “could have been otherwise.” Possible Worlds

12. Necessary and Contingent Contingently true The earth goes around the sun. On earth, things fall at 32 feet per second per second. The first day Fall 2013 classes at USD was Sep 4 San Diego is in California. Contingently false The sun goes around the earth. There’s no such thing as gravity--everything just floats. The first day of Spring 2013 classes at USD was Sep 3 San Diego is in Texas.

13. Could San Diego have been in Texas? San Diego, Texas “San Diego is in California” is contingently true if there’s some possible world at which the city in which we now are isn’t in California.

14. San Diego could be somewhere else!

15. What’s the point? A proposition is contingently true if there’s some possible world at which it’s false. But what seems to be a possible world that makes the proposition false may not really be one

16. Necessary and Contingent Necessarily true All bachelors are unmarried. Que sera sera. [Whatever will be, will be.] 2 + 2 = 4 Either San Diego is entirely in California or San Diego is not entirely in California. Necessarily false Some bachelors are married Some things that will happen will not happen 2 + 2 = 5 San Diego is both entirely in and not entirely in California

17. San Diego at 3 Possible Worlds San Diego is entirely in California San Diego is not entirely in California Either San Diego is entirely in California or San Diego is not entirely in California

18. True in virtue of language Be careful to distinguish between sentences which are true in virtue of language and those that are about language! (1) is necessarily true but (2) is contingently true: (1)All bachelors are unmarried. (2)“Bachelor” means “unmarried male.”

19. Are mathematical truths necessary? The course of maintaining that the truths of logic and mathematics are not necessary or certain was adopted by Mill. He maintained that these propositions were inductive generalizations based on an extremely large number of instances. 2 + 2 = 4 Lucky for Mill things aren’t nailed down.

20. About time… Is precognition logically possible?Is precognition logically possible? Is God’s foreknowledge compatible with free-will?Is God’s foreknowledge compatible with free-will?Is God’s foreknowledge compatible with free-will?Is God’s foreknowledge compatible with free-will? Is time-travel possible?Is time-travel possible?Is time-travel possible?Is time-travel possible?

21. Precognition & Psychic Predictions If the psychic was right, then it was true at t1 that e was going to happen at t3 But you immediately take action a in order to prevent e from happening You’re successful! So at t2 it isn’t true that e was going to happen at t3 Is this possible??? In the future, e will happen. Watch out!

22. Time Viewed Timelessly

23. The man who was his own mother “Jane” is left at an orphanage as a foundling. When “Jane” is a teenager, she falls in love with a drifter, who abandons her but leaves her pregnant. Then disaster strikes. She almost dies giving birth to a baby girl, who is then mysteriously kidnapped. The doctors find that Jane is bleeding badly, but, oddly enough, has both sex organs. So, to save her life, the doctors convert “Jane” to “Jim.”

24. And then... “Jim” subsequently becomes a roaring drunk, until he meets a friendly bartender (actually a time traveler in disguise) who whisks “Jim” back way into the past. “Jim” meets a beautiful teenage girl, accidentally gets her pregnant with a baby girl. Out of guilt, he kidnaps the baby girl and drops her off at the orphanage. Later, “Jim” joins the time travelers corps, leads a distinguished life, and has one last dream: to disguise himself as a bartender to meet a certain drunk named “Jim” in the past…

25. The Man Who Was His Own Mother Jane is born Baby Jane Is born Jane becomes Baby Jane’s mother Jim meets Bartender who whisks him back to the past Jim meets Jane Jim becomes Baby Jane’s father Drops Baby Jane off At orphanage Baby Jane dropped Off at orphanage Jim becomes distinguished Time-Traveler Disguised as Bartender meets Jim The Drunk Bartender takes Jim Back to the past where he meets Jane

26. 1945- A baby is an orphan who then grows up into a girl 1963- The girl becomes pregnant by a drifter who than disappears. The girl becomes a guy after labor complications and the baby is kidnapped. The girl who is now a guy becomes a drifter. 1970- The drifter walks into a bar and a bartender offers him a time machine ride to go back in time and change his past. 1963- the drifter meets a girl and gets her pregnant. 1985- the bartender drops the drifter off to enlist in the time travelers corps. 1963- the bartender kidnaps the newborn baby girl 1945- the bartender drops the baby off at an orphanage 1985- the drifter becomes a member of the corps and gets a mission to meet a drifter at a bar as a bartender in 1970

27. Is time travel logically possible? Suppose you travel back into the past to kill your baby-self…

29. But... Just because something’s logically possible doesn’t mean we’re off the hook! There are lots of things that are logically possible which we ought not to believe. And it is not entirely straightforward, even given careful observations what we should believe because science is not mere fact-collection!

30. What science does Science seeks to understand the world by identifying general principles that are both explanatory and predictive Explanation: answer to a “why” question Prediction: allows a hypothesis to be tested A good explanation enables us to make accurate predictions

31. What about ESP? Some beliefs are more central than others—more hangs on them. –these include, e.g. conservation of energy and the principle of causality as cited by Rothman –which are inconsistent with claims about ESP These scientific principles are deeply embedded in the “Web of Belief”

32. The Web of Belief Logic Scientific Theories Ordinary Empirical Claims

33. But we could be wrong! It is logically possible that the laws of nature be different from what they actually are. It is logically possible that we be mistaken about the way they actually are! In the interests of explanation and prediction we may need to revise our scientific theories!

34. UNPAID ADVERTISEMENT Philosophy of Science Philosophy of science clarifies both the quest for scientific knowledge and the results yielded by that quest…by exploring the logic of scientific evidence; the nature of scientific laws, explanations, and theories; and the possible connections among the various branches of science. How, for instance, is psychology related to brain biology, and biology to chemistry? And how are the social sciences related to the natural sciences. USD offers this course!

35. Confirming and Confuting Hypotheses Scientific hypotheses cannot be conclusively confirmed (though they can be shown to be true beyond reasonable doubt!) Scientific hypotheses cannot be conclusively refuted (thought they can be shown to be false beyond reasonable doubt!) Consider the flat earth hypothesis…

36. The Greeks knew the earth was round! Eratosthenes of Cyrene (Greek Ἐ ρατοσθένης; c. 276 BC [1] – c. 195 BC [2] ) was a Greek mathematician, poet, athlete, geographer, and astronomer. He made several discoveries and inventions including a system of latitude and longitude. He was the first Greek to calculate the circumference of the Earth (with remarkable accuracy), and the tilt of the earth's axis (also with remarkable accuracy); he may also have accurately calculated the distance from the earth to the sun and invented the leap day. [3] He also created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.Greek [1] [2]Greekmathematician poetathletegeographer astronomerlatitudelongitude circumference of the Earthdistance from the earth to the sunleap day [3]map of the world

37. The Flat Earth Hypothesis What would refute it? Circumnavigation? Objects disappearing over the horizon? A flat-earther can keep his theory going forever by introducing ad hoc hypotheses.

38. Flat Earth Circumnavigation

39. But wouldn’t ships fall off the edge if the earth were flat?

40. No! Flat Earth is surrounded by a massive ice wall which Round-Earthers call “Antarctica.” It keeps people from falling off if they stray too far into the Southern Ocean!

42. But what about ships disappearing over the horizon? And the sun setting?

43. Zeltic Law of Perspective Earth is flat but light travels in tight curves Ad Hoc hypothesis: can’t be verified independently of the phenomenon it’s supposed to explain

44. Zeltic Law of Perspective Earth is flat but light travels in tight curves Ad Hoc hypothesis: can’t be verified independently of the phenomenon it’s supposed to explain

45. Ptolemaic Astronomy Time for a paradigm shift?

46. Epicycles explain retrograde motion of planets http://astronomy.nmsu.edu/nicole/teaching/AST R110/lectures/lecture11/slide01.html

47. Epicycles

48. So what should we do about Ptolemeic astronomy? In favor –Conservatism Against –Simplicity –Fruitfulness

49. Criteria of Adequacy Creationism, Intelligent Design or Evolution?

50. The Flat Earth hypothesis is clearly crazy but... We can defend a crazy hypothesis if we’re willing to make lots of other changes to the Web of Belief. ESP is not logically impossible but, like the Flat Earth hypothesis, Ptolemaic astronomy and Creationism it’s highly, highly, highly improbable And for the empirical sciences, that’s the most we can establish! The Flat Earth hypothesis is clearly crazy but... We can defend a crazy hypothesis if we’re willing to make lots of other changes to the Web of Belief. ESP is not logically impossible but, like the Flat Earth hypothesis, Ptolemaic astronomy and Creationism it’s highly, highly, highly improbable And for the empirical sciences, that’s the most we can establish! The Moral

51. Back to Logic...

52. Logic deals with logical possibility The possibility of propositions being true (necessity and contingency) The possibility of groups of propositions all being true together (consistency) The impossibility of the premises of an argument being true and the conclusion being false (validity)

53. A puzzle: necessary truths & falsehoods How can there be necessary truths? Take "all bachelors are unmarried": I can describe a world were "bachelor" means "male under 30" and such a world is one in which there are married bachelors, right? Similarly "2+2=4" and "2+2=5": it's just a matter of how you define the symbols, right?

54. To Be Continued…