Logic Professor D’Ascoli HUM 200 Strayer University
LOGIC • WHAT IS LOGIC? • Lewis Carroll, Through the Looking Glass: “Contrariwise, continued Tweedledee, \if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic."
The text book type definition • Logic, from the Greek λογικός (logikos) is the study of reasoning. Logic is used in most intellectual activity, but is studied primarily in the disciplines of philosophy, mathematics, and computer science.
Some definitions of logic • the branch of philosophy that analyzes inference • reasoned and reasonable judgment; i.e. "it made a certain kind of logic" • the principles that guide reasoning within a given field or situation; i.e. "economic logic requires it"; "by the logic of war" • the system of operations performed by a computer that underlies the machine's representation of logical operations • a system of reasoning
Logic – our text • Logic is the study of reasoning: how it is done correctly, how it goes wrong, and how to distinguish between the two. • Reasoning involves constructing and evaluating arguments.
propositions • Arguments are made up of propositions. • In an argument, we attempt to establish the truth of a proposition on the basis of others. • Propositions are assertions that are either true or false. • A simple proposition makes only one assertion. • Compound propositions contain two or more simple propositions. • Compound propositions can be either disjunctive or hypothetical.
propositions There are many propositions about whose truth we are uncertain. Examples: There is life on other planets. There is a God. These may be true or false, therefore their ‘truth value’ is uncertain. However, these, like all other propositions must be either true or false.
PROPOSITIONS • Questions are not propositions as they assert no truth values (Do you like this class?) • Commands and exclamations are also not propositions as they also assert no truth values (ie, Come here. Watch Out!, etc) • Sentences can take many forms to assert the same thing, even different languages can assert the same thing • This class is stupid • Estaclaseesestúpida • Cetteclasseest stupide
propositions • Propositions and statements are not exactly the same, but they are often used in logic in the same sense. • Some logic texts even use the word statement rather than proposition. We will use proposition
propositions • Some propositions (compound) contain more than one proposition in the same sentence: China is the most populous country in the world, it produces 85% of the world’s goods and has a communist government. • The above is also an example of conjunctive propositions – though listed together , they could all be listed separately and still be true.
propositions • However, there could also be compound propositions that are disjunctive , where no one of the components is asserted. • For example, “Circuit courts are useful, or they are not useful.” • Although this example is clearly a true but one of its components might be false.
propositions • There are also hypothetical (or conditional) propositions – these are compound propositions that also do not assert that their components are true but rather that the whole is true. • Example : “If God did not exist, it would be necessary to invent him.” • Again neither claim is asserted, rather it becomes an if then hypothetical dilemma which even if both parts are wrong, may still be a true proposition – because it is hypothetical • You can never successfully argue hypotheticals • Excercises pages 9-12
Is this an argument? • http://www.youtube.com/watch?v=teMlv3ripSM • YouTube - Monty Python - Argument Clinic
Logical fallacy? • http://www.youtube.com/watch?v=yp_l5ntikaU • YouTube - monty python-witch scene
Professional Logician monologue - YouTube - Monty Python and the Holy Grail Soundtrack 3/7: Logicianhttp://www.youtube.com/watch?v=FZqs36C5sgM&feature=related • Good evening. The last scene was interesting from the point of view of a professional logician because it contained a number of logical fallacies; that is, invalid propositional constructions and syllogistic forms, of the type so often committed by my wife. "All wood burns," states Sir Bedevere. "Therefore," he concludes, "all that burns is wood." This is, of course, pure bullshit. Universal affirmatives can only be partially converted: all of Alma Cogan is dead, but only some of the class of dead people are Alma Cogan. "Oh yes," one would think. • However, my wife does not understand this necessary limitation of the conversion of a proposition; consequently, she does not understand me. For how can a woman expect to appreciate a professor of logic, if the simplest cloth-eared syllogism causes her to flounder. • For example, given the premise, "all fish live underwater" and "all mackerel are fish", my wife will conclude, not that "all mackerel live underwater", but that "if she buys kippers it will not rain", or that "trout live in trees", or even that "I do not love her any more." This she calls "using her intuition". I call it "crap", and it gets me very *irritated* because it is not logical.
"There will be no supper tonight," she will sometimes cry upon my return home. "Why not?" I will ask. "Because I have been screwing the milkman all day," she will say, quite oblivious of the howling error she has made. "But," I will wearily point out, "even given that the activities of screwing the milkman and getting supper are mutually exclusive, now that the screwing is over, surely then, supper may, logically, be got." "You don't love me any more," she will now often postulate. "If you did, you would give me one now and again, so that I would not have to rely on that rancid Pakistani for my orgasms." "I will give you one after you have got me my supper," I now usually scream, "but not before" -- as you understand, making her bang contingent on the arrival of my supper. • "God, you turn me on when you're angry, you ancient brute!" she now mysteriously deduces, forcing her sweetly throbbing tongue down my throat. "Fuck supper!" I now invariably conclude, throwing logic somewhat joyously to the four winds, and so we thrash about on our milk-stained floor, transported by animal passion, until we sink back, exhausted, onto the cartons of yoghurt. • I'm afraid I seem to have strayed somewhat from my original brief. But in a nutshell: • Sex is more fun than logic -- one cannot prove this, but it "is" in the same sense that Mount Everest "is", or that Alma Cogan "isn't". • Goodnight.
Is this an argument? • Ms. Malaprop left her house this morning. • Whenever she does this, it rains. _____________ • Therefore, the moon is made of blue cheese.
arguments • Inference is the process that may tie together a cluster of propositions, some are warranted (correct) others are not • An argument in logic does not refer to a disagreement • An argument refers strictly to any group of propositions of which one of the propositions is claimed to follow from the other propositions • For every possible inference there is a corresponding argument
arguments • Although sentences express propositions, a sentence and a proposition are not identical. • The propositions that provide evidence or support for the truth of some other proposition are called premises. • The proposition for which evidence is provided is called the conclusion.
arguments • Sometimes premise and conclusion appear in separate sentences: • “No one was present when life first appeared on earth. Therefore any statement about life’s origins should be considered as theory, not fact.” • Sometimes they appear in same sentence: • “Since it turns out that all humans are descended from a small number of African ancestors in our recent evolutionary past, believing in profound differences between the races is as ridiculous as believing in a flat earth.”
arguments • The order in which premises and conclusions can appear are also varied. This does not matter in determining validity or soundness of arguments.
arguments • Arguments often contain conclusion and premise indicators that allow one to identify them as arguments. • When indicators are lacking, the context of the passage provide cues as to whether it is argumentative in nature. P 13 – 14 let’s discuss • Once an argument is identified, care must be taken to identify premises which are not in a declarative form or premises that are unstated. P 14 -15-16-17-18-19
Conclusion indicators • Therefore - for these reasons • Hence - it follows that • So - I conclude that • Accordingly - which shows that • In consequence - which means that • Consequently - which entails that • Proves that - which implies that • As a result - which allows us to infer that • For this reason - which points to the conclusion that • Thus - we may infer
Premise indicators • Since - as indicated by • Because - the reason is that • For - for the reason that • As - may be inferred from • Follows from - may be derived from • As shown by - may be deduced from • Inasmuch as - in view of the fact that
arguments • Arguments must be distinguished from other forms of expression involving sets of propositions, for instance, expository passages and explanations. • An explanation is a group of statements that purport to account for why something happened or why something is the way that it is. P 19-20-21 excercises pages 21-26
Deductive Arguments • Some arguments are deductive, and some inductive—and all arguments are either one or the other. • Deductive arguments claim that if the premises are true, the conclusion follows with absolute necessity. That is, it cannot be false. • In valid deductive arguments, if the premises are true, the conclusion does, indeed, follow with absolute necessity. • An invaliddeductive argument is one in which, if the premises are true, the conclusion could be false. • A sound deductive argument is one that is valid and has all true premises.
Deductive arguments • The relationship between true (or false) propositions and valid (or invalid) arguments is sometimes quite complex. • The only combination of premises and conclusion whose truth-values guarantee the invalidity of the argument is when the premises are true and the conclusion false
Inductive arguments • In inductive arguments, the conclusion is claimed to follow only with high probability. • Inductive arguments are never valid or certain; they can be better or worse, more or less probable, but they can never be valid or invalid. • P 28-30
Is this argument valid? • If the moon is made of blue cheese, then pigs fly. • The moon is made of blue cheese.______________ • Therefore, pigs fly.
What we aim for • An argument is sound if and only if the argument is valid and, in addition, all of its premises are true.
Validity and truth • Valid (validity) – refers to the relation between its propositions only, if the conclusion follows with logical necessity from the premises then an argument is said to be valid • Validity can never refer to a single premise by itself • Truth – is the attribute of a proposition that asserts what really is the case • Truth cannot apply to arguments
Validity and truth • Truth and falsity are attributes of individual propositions or statements; validity and invalidity are attributes of arguments. • P 31-33 discuss samples • Excercises page 35
Key terms • Proposition Argument Premise • Statement Conclusion Probability • Validity Induction Necessity • Soundness Deduction Simple proposition • Compound proposition Disjunctive proposition Hypothetical proposition • Classical logic Modern symbolic logic Explanation • Explanation Inference Enthymemes
Some questions/ discussion • 1. Why is logic relevant to everyday life? Why should one take a course in logic? • 2. We often rely on appeals to emotion in order to persuade people rather than providing arguments. Give some examples of this from everyday contexts. Is this problematic? Are there cases when appeals to emotion are appropriate? • 3. Give an example of a simple argument you have made recently. Which statements are the premises? Which one is the conclusion? • 4. What is the distinction between deductive and inductive arguments? Give an example of each to make your explanation clear. • 5. What is the difference between validity and soundness? Why is the distinction relevant for us as students of logic?
Homework questions • 1. What is the difference between a premise and a conclusion? Provide an example of an argument from a newspaper or journal that highlights this distinction. • 2. Why is reasoning considered to be both an art and a skill and how does taking a course in logic help us to develop that skill? • 3. What is the difference between inductive and deductive arguments? What are the ramifications of this difference?
Homework continued • 4. A valid argument does not necessarily mean that the premises and the conclusion are true. In some cases, a deductive argument will be valid even when its premises and conclusion are false. If validity doesn’t mean truth, why should a logician be concerned with validity? • 5. In everyday contexts, we are confronted with argument in a variety of different spheres; political, religious, legal, medical, and so on. Why is it important to be able to analyze and assess these arguments?