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It’s logical!

It’s logical!. Do you remember the three kinds of reasoning we talked about before?. Deductive…inductive…and…informal!. Vs. Deduction. Induction . Reasoning from particular to general Metal ‘A’ expands when hated; metal ‘B’ expands when heated; metal ‘C’ expands when heated.

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It’s logical!

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  1. It’s logical!

  2. Do you remember the three kinds of reasoning we talked about before? Deductive…inductive…and…informal!

  3. Vs. Deduction Induction Reasoning from particular to general Metal ‘A’ expands when hated; metal ‘B’ expands when heated; metal ‘C’ expands when heated. ∴ all metals expand when heated. More informative, but less certain than deduction. • Goes from general to particular All metals expand when heated. ‘A’ is a metal. ∴ ‘A’ expands when heated. • More certain, but less informative than induction.

  4. As a WoK… can logical reasoning be doubted? No! because of these three laws: Law of identity a=a b) Law of non-contradiction nothing can be a and -a c) Law of the excluded middle everything is either a or -a

  5. Can DEDUCTIVE reasoning be doubted? Can INDUCTIVE reasoning be doubted? Why?

  6. Give a rational explanation to the following… A man walks into a bar and asks the barman for a glass of water. The barman pulls out a gun and points it at the man. The man says ‘Thank you’ and walks out. What happened?

  7. Fallacies A fallacy is a kind of error in reasoning. Fallacies should not be persuasive, but they often are. Fallacies may be created unintentionally, or they may be created intentionally in order to deceive other people. The vast majority of the commonly identified fallacies involve arguments, although some involve explanations, or definitions, or other products of reasoning. Sometimes the term “fallacy” is used even more broadly to indicate any false belief or cause of a false belief. 

  8. ≠ Truth Validity All bull-fighters are brave people. Some brave people are compassionate. All bull fighters are compassionate. All dogs are mammals. Fido is a dog. Fido is a mammal.

  9. Property of STATEMENTS concernedwithwhatisthe case. TRUTH - Property of thewhole SYLLOGISM whentheconclusionsfollowthepremises. VALIDITY - ∴ The validity of an argument is independent of the truth of falsity of the premises it contains.

  10. - No human being can run as fast as a thunderbolt. - If someone can run as fast as a thunderbolt, he is either non-human, or has been scientifically modified. - The Flash can run as fast (or even faster) than a thunderbolt. - Therefore, the Flash is either non-human, or has been genetically modified.

  11. We can construct valid arguments for almost any combinations of true and false premises and conclusions. The only situation that is impossible is a valid argument with true premises and a false conclusion.  [ T ] 1. All men are mortal. [ T ] 2. Socrates is a man. [T ] Therefore, Socrates is mortal. [ F ] 1. All cups are green. [ F ] 2. Socrates is a cup. [ F ] Therefore, Socrates is green.   [ T ] 1. All men are mortal. [ T ] 2. Socrates is mortal. [ F ] Therefore, Socrates is a man.

  12. [T] [T] [T] Allwhales are mammals Allmammalshavelungs. Therefore, allwhaleshavelungs. Valid All spiders have six legs. All creatures with six legs have wings. Therefore, all spiders have wings. [F] [F] [F] Valid [T] [T] [F] If I owned all the gold in Fort Knox, I would be very rich. I do not own all the gold in Fort Knox. Therefore, I am notveryrich Invalid

  13. Two true premises and a true conclusion. One true premise, one false premise and a true conclusion. One true premise, one false premise and a false conclusion. Two false premises and a true conclusion. Two false premises and a false conclusion.

  14. The Four Aristotelian Propositions In the system of Aristotelian logic, the square of opposition is a diagram representing the different ways in which each of the four propositions of the system are logically related ('opposed') to each of the others.

  15. Propositions are contradictory when the truth of one implies the falsity of the other, and conversely. Propositions are contrary when they cannot both be true.  For example, if the proposition “all industrialists are capitalists” (A) is true, then the proposition “some industrialists are not capitalists” (O) must be false. Similarly, if “no mammals are aquatic” (E) is false, then the proposition “some mammals are aquatic” must be true. An A proposition, e.g., “all giraffes have long necks” cannot be true at the same time as the corresponding E proposition: “no giraffes have long necks.” The truth of the A proposition “all plastics are synthetic,” implies the truth of the proposition “some plastics are synthetic.” However, the truth of the O proposition “some cars are not American-made products” does not imply the truth of the E proposition “no cars are American-made products.”  Two propositions are said to stand in the relation of subalternation when the truth of the first (“the superaltern”) implies the truth of the second (“the subaltern”), but not conversely. Because “some lunches are free” is false, “some lunches are not free” must be true. Propositions are subcontrary when it is impossible for both to be false. 

  16. What can yousayabouttheTruth and Falsehood of thefollowingpropositionsgiventheinformationstated in thefirst of them? • 1. • Everyaminoacidisanorganiccompound. [T] • No aminoacidisanorganiccompound. [ ] • Some aminoacids are organic compounds. [ ] • Someaminoacids are notorganiccompounds. [ ] • 2. • No reptileis a hot-blooded animal. [T] • Some reptiles are hot-bloodedanimals. [ ] • Some reptiles are nothot-bloodedanimals. [ ] • Everyreptileis a hot-blooded animal. [ ] • 3. • Some NY senatorshavebeentrimphantcandidatestothe US presidency. [F] • Some NY senatorshavenotbeentrimphantcandidatestothe US presidency.[ ] • Every NY senator has been a trimphantcandidatetothe US presidency. [ ] • No NY senator has been a trimphantcandidatetothe US presidency. [ ] • 4. • Somefuels are notpollutingagents. [T] • Every fuel is a pollutingagent.[ ] • No fuel is a pollutingagent. [ ] • Somefuels are pollutingagents.[ ]

  17. A man is lying dead in a field. Next to him there is an unopened package. There is no other creature in the field. How did he die? Anthony and Cleopatra are lying dead on the floor of a villa in Egypt. Nearby is a broken bowl. There is no mark on either of their bodies and they were not poisoned. How did they die? A man rode into town on Friday. He stayed three nights and then left on Friday. How come? A landscape gardener is given instructions to plant four special trees so that each one is exactly the same distance from each of the others. How would he arrange the trees? Connect the crosses using only four straight lines and without taking your pencil off the paper.

  18. http://www.youtube.com/watch?v=vRJUvFG8gbE http://www.youtube.com/watch?v=ytWGiOuzpe4&feature=related http://www.youtube.com/watch?v=k0xgjUhEG3U http://www.youtube.com/watch?v=GNN6-OekWvI&feature=related http://www.youtube.com/watch?v=Dln3DJEcghY http://www.youtube.com/watch?v=DQ24HdCPN9E&feature=related http://www.youtube.com/watch?v=ZsoMIbXfA0g&feature=related http://www.youtube.com/watch?v=m4foH4HCzKA&feature=related http://www.youtube.com/watch?v=im4TYITM0VE

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