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LOGIC I General methodology and introduction to formal logic

LOGIC I General methodology and introduction to formal logic

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LOGIC I General methodology and introduction to formal logic

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  1. LOGIC IGeneral methodology and introduction to formal logic DRAFT

  2. Lectures on informal logic are based on books by Fogelin & Sinnot-Armstrong, Fisher and Thomson and on lectures by Jesper Kallestrup.

  3. Lecture IInformal reasoning • Skills: - recognizing reasoning (arguments) - identifying conclusions - identifying reasons (premises) and assumptions - evaluating reasoning

  4. Logical theory Semantic relationships (relationships between true or false propositions) Argument = set of propositions Context irrelevant Logical pragmatics Use of propositions by an arguer to carry out the goal of dialogue (e.g. convince or persuade the second arguer)

  5. A seaman drafted to our ship just before we sailed form Halifaxhad never seen his new captain, who at sea often went hatless and wore a nondescript jacket. The new man had just begun a forenoon watch on the gun deck when the captain came along. The skipper suddennly stooped and picked up a butted cigarette. He trust the butt at the seaman and demanded: „I want to know who the hell owns this damned thing” The new hand considered for a moment, then said slowly to the rankless, hatless officer: „I’d say you do, mate. You found it.”

  6. Context of dialoge Seaman: the ownership of the cigarette butt Captain: the issue of keeping the ship clean

  7. Types of argumentative dialogue • Dialogue – a sequence of exchanges of messages or speech acts (typically questions and replies) between two (or more) participants • Every dialogue has a goal and requires cooperation between the participants to fulfill the goal • Each participant has an obligation to work toward fulfilling his own goal in the dialogue and also an obligation to cooperate with the other participant’s fulfillment of his own goal

  8. One context of dialogue is the personal quarrel. A quarrel is a dialogue in which one tries to trick, cheat or even attack one’s opponent directly, rather than one’s opponent’s views, using abusive language, appeal to emotions, intimidation, one-sided criticism, etc. Any means are available no matter whether they are fair or reasonable. • Aggressive personal attack • Appeal to emotions • Desire to win the argument at all costs

  9. A second context of dialogue is the (forensic) debate. In debates there are judges or referees who decide, maybe by voting, which side has the better argument. There are rules of procedure that determine who may speak and when and for how long. There are also some rules that disallow the more severe forms of personal attack, but many fallacious arguments may still be tolerated.

  10. Audience • Rules are often very permissive and may allow fallacious arguments • Goal: win a verbal victory to impress the audience

  11. A third context of dialogue is the persuasion dialogue (critical discussion). There are two participants each of whom has a thesis to prove. Internal proof by a participant means proof by inferring a proposition from the other participant’s concession in the dialogue. External proof is the introduction of new facts into the argument by appealing to scientific evidence or expert opinion. The best one can hope for is plausible commitment to an opinion based on reasoned evidence. • My goal is to persuade you of my thesis; hence I should prove that thesis from premises that you accept or are committed to • Your goal is to prove your thesis from the premises that I accept or am committed to • Goal – persuade the other party of your thesis • Method – prove your thesis

  12. A forth context of dialogue is the inquiry in which premises can only be propositions that are known to be true, that have been established to the satisfaction of all parties to the inquiry. The inquiry seeks out as much certainty as can be obtained by the given evidence. The goal is to accumulate knowledge. The participants are neutral investigators of an objective truth. The inquiry is cooperative rather than adversarial.

  13. In negotiation dialogue, the primary goal is self-interest and the method is to bargain. Bargaining makes no pretensions to be an objective inquiry into the truth of the matter. • Logical proof is not important • Frankly based on personal gain • Not neutral, not objective • Interest-based conflict

  14. Information-seeking dialogue – one party has the goal of finding infromation that the other party is believed to possess • Action-seeking dialogue – one party has the goal to bring about a specific course of action by the other party • Educational dialogue – one party (the teacher) has the goal of imparting knowledge to the other party (the student)

  15. Arguments Socrates is a man. All men are mortal. Socrates is mortal.

  16. Since Socrates is a man and all men are mortal, Socrates is mortal. Socrates is a man, since all men are mortal and Socrates is mortal.

  17. Socrates is a man. All men are mortal. Therefore Socrates is mortal. Since Socrates is a man, all men are mortal and Socrates is mortal.

  18. An argument is a train of reasoning aimed at establishing a particular claim, the conclusion, from a number of other claims, the premises. The premises are offered as reasons to believe or accept the conclusion. Arguments attempt to persuade others to accept a claim by offering reasons or evidence in support of that claim. One must do two things in propounding an argument: justify the premises by providing reasons or evidence, and show how the conclusion follows from the premises.

  19. The bus is late. It must have broke down. • That bird can’t be a robin. It doesn’t have a red breast. • You should try to appear confident in your job interview. The employers are looking for someone who can speak confidently in public.

  20. He must be older than he says. He told us he was forty-two, but he has a daughter who is at least thirty years old.

  21. She didn’t turn up for their date. She obviously doesn’t really want to be his girlfriend. If she’d wanted a serious relationship with him she wouldn’t have missed the date. • The engine won’t fire. The carburettor must be blocked.

  22. Reason indicators Because …. For …. Since …. Follows from the fact that ….. The reason being ….. Firstly, ….secondly, May be inferred from the fact that ….

  23. Conclusion indicators • Therefore • So • Hence • Thus • Accordingly • Consequently • Which proves that • Justifies the belief that • I conclude that • Which implies that • Which allows us to infer that • It follows that • Establishes the fact that • Demonstrates that

  24. (1) People who diet lose weight. Wojciech Mann cannot have dieted. He hasn’t lost weight. • (1*) People who diet lose weight. But Wojciech Mann hasn’t lost weight. (Therefore), he cannot have dieted. • (1**) People who diet lose weight. But Wojciech Mann cannot have dieted. Therefore, he hasn’t lost weight.

  25. People who diet lose weight. Wojciech Mann is a good journalist despite his weight. Wojciech Mann would be a better journalist if he dieted.

  26. (1***) People who diet lose weight. Since Wojciech Mann hasn’t lost weight, he cannot have dieted.

  27. John broke the window because he tripped. • John broke the window because he has forgotten his key. • John must have broken the window because he was the only person in the house.

  28. Indicative conditional vs. argument • If international terrorism continues to grow, there will be a worldwide crisis. • Since international terrorism continues to grow, there will be a worldwide crisis.

  29. Standard form of arguments Socrates is a man. All men are mortal. _____________________ Socrates is mortal.

  30. Since Chicago is north of Boston, and Boston is north of Charleston, Chicago is north of Charleston. • Toward evening, clouds formed and the sky grew darker; then the storm broke. • Both houses of Congress may pass the bill, but the President may still veto it.

  31. Texas has a greater area than Topeka, and Topeka has a greater area than the Bronx Zoo, so Texas has a greater area than the Bronx Zoo. • Other airlines will carry more passengers because United Airlines is on strike. • Since Jesse James left town, taking his gang with him, things have been a lot quieter.

  32. Things are a lot quieter because Jesse James left town, taking his gang with him. • Witches float, because witches are made of wood, and wood floats. • The hour is up, so you must hand in your exams. • Joe quit because his boss was giving him so much grief.

  33. Red squirrels can eat yellow berries, hawthorn berries and rosehips. Grey squirrels can eat none of these. However, grey squirrels eat acorns which red squirrels cannot eat. • In recent years, the demand for computer-literate personnel has increased. More students are graduating in computing science than before. Some companies find that these graduates require further training before embarking on a career in computing.

  34. The North American Wildlife Federation, which sponsors an annual watch for endangered species, reports that sightings of the bald eagle between 1978 and 1979 increased by 35 per cent. In 1979, 13,127 sightings were reported, 3,400 over the 1978 count. This indicates considerable growth in the bald eagle population. • To make an assessment of modern art is an impossible task. For one can assess a work of art only when there are accepted rules and conventions. Modern art has no rules and conventions.

  35. If the money supply were to increase at less than 5% the rate of inflation would come down. Since the money supply is increasing at about 10% inflation will not come down. • If Russia were unsure about American reactions to an attack on Western Europe, and if her intentions were to conquer Western Europe, she would create local casus belli (causes of war) but since she has not done this, she cannot intend to conquer Western Europe.

  36. If the civil population cannot be defended in the event of nuclear war, we do not need a civil defence policy. But, we do need a civil defence policy if ‘deterrence’ is to be a convincing strategy. Therefore deterrence is not a convincing strategy. • The materials of nature (air, earth, water) that remain untouched by human effort belong to no-one and are not property. It follows that a thing can become someone’s property only if he works and labours on it to change its natural state. From this I conclude that whatever a man improves by the labour of his hand and brain belongs to him and to him alone.

  37. The only freedom which deserves the name is that of pursuing our own good in our own way, so long as we do not attempt to deprive others of theirs, or impede their efforts to obtain it. Each is the proper guardian of his own health, whether bodily, or mental and spiritual. Mankind are greater gainers suffering each other to live as seems good to themselves, rather than by compelling each to live as seems good to the rest.

  38. Radioactive elements disintegrate and eventually turn into lead. If matter has always existed there should be no radioactive elements left. The presence of uranium etc. is scientific proof that matter has not always existed.

  39. If the ‘nuclear winter’ scientists are right the population of Britain would be virtually eliminated in a nuclear war between the superpowers even if Britain suffered no direct nuclear attack. Quite apart from the radioactive fall-out, we would suffer the darkness, the subfreezing temperatures and the mass starvation of a nuclear winter.

  40. Some people have solved their own unemployment problem by great ingenuity in hunting for a job or by willingness to work for less, so all the unemployed could do this.

  41. Evaluating arguments Validity • An argument is valid if and only if (iff) it is not possible for the premises to be true and the conclusion false.

  42. All ministers are paid. Radosław Sikorski is a minister. _________________ Radosław Sikorski is paid.

  43. All ministers are paid. Radosław Sikorski is paid. _________________ Radosław Sikorski is a ministrer.

  44. All MPs are paid. Bronisław Komorowski is paid. ___________________ Bronisław Komorowski is an MP.

  45. Truth All MPs are paid. Bronisław Komorowski is an MP. ___________________ Bronisław Komorowski is paid.

  46. Soundness An argument is sound iff it is valid and all of its premises are true.

  47. Truth and falsity are properties of claims, propositions or statements • Validity and soundness are properties of arguments • Valid arguments are truth-preserving.

  48. If the argument is invalid, it cannot establish its conclusion. • But it may still be a reasonable or persuasive argument by some other standards. It may be that the premises lend inductive support to the conclusion. • Inductive arguments do not guarantee the truth of their conclusion, but yield more or less highly probable conclusions. • Or it may be that the truth of the conclusion is the best explanation of the truth of the premises. • When we talk about validity, we typically mean deductive validity.