What is an argument? PHIL 110. Is this an argument? Is this an argument? What about this? And what about this?

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1 What is an argument? PHIL 110 Lecture on Chapter 3 of How to think about weird things An argument is a collection of two or more claims, one of which is the conclusion and the rest of which are the premises. Whoever mounts the argument intends the premises to support the conclusion. 1 2 Is this an argument? John: Abortion is Evil. Bill: No It s not. John: If you think abortion s not criminal, you re a jerk. Bill: Want a punch in the nose? Is this an argument? Abortion is evil. I firmly believe this. Anyone who thinks otherwise is just deluded. 3 4 What about this? And what about this? Abortion is evil, for it is evil to take an innocent life and abortion involves the taking of an innocent life. The idea of God is the idea of the most perfect of possible beings. A being that didn t exist wouldn t be perfect. Thus God exists, for the idea of God is the idea of a thing that exists. 5 6

2 And this? The hypothesis that humanity will go extinct before colonizing other planets offers a good explanation for why one finds oneself living here, on Earth, before the colonization of other planets has started. The hypothesis that humanity won t go extinct so soon doesn t explain this fact. And so the first hypothesis is the most plausible. I.e., our days are probably numbered. Arguments are usually written like this: 1. Socrates is a man. 2. All men are mortal. 3. Socrates is mortal. 7 8 Conclusion indicator words thus so consequentially it follows that which means that hence therefore as a result we can conclude that which implies that Premise indicator words since because the reason being assuming that given that for the reason that for in view of the fact as indicated by due to the fact that 9 10 What sorts of arguments are there? There are two main kinds of arguments: Deductive arguments have premises that are intended to provide conclusive support for their conclusions. Inductive arguments have premises that are intended to provide probable support for their conclusions. Which is deductive? Which is inductive? 99 percent of females have a thing about Brad Pitt. So, probably, Sally has a thing about Brad Pitt. John Key lays eggs, and anything that lays eggs isn t human, so John Key isn t human

3 Validity If the premises of a deductive argument really do provide conclusive support for its conclusion, in the sense that the logical form of the argument is such that it is impossible for both the premises to be true and the conclusion to be false, then the argument is valid. Otherwise it is invalid. Validity and invalidity are properties of deductive arguments, not inductive arguments. Which argument is valid? 1. Sally lays eggs. 2. Anything that lays eggs isn t human. 3. Sally isn t human 1. Sally doesn t lay eggs. 2. Anything that lays eggs isn t human. 3. Sally is human Strong and weak inductive arguments If the premises of an inductive argument really do provide probable support for the truth of its conclusion, then the argument is strong. Otherwise it is weak. Strength and weakness are properties of inductive arguments, not deductive arguments. Which argument is strong? Which is weak? 1. There is life on Mercury, Venus, Earth, Mars, Jupiter, Saturn, and Uranus. 2. Probably, there is life on Neptune 1. There is life on Earth and Mars 2. Probably, there is life on Neptune Soundness and Cogency If a deductive argument satisfies both thee conditions then it is sound: (1) It is valid; (2) Its premises are true. If an inductive argument satisfies both these conditions then it is cogent: (1) It is strong; (2) Its premises are true. All good arguments are either sound or cogent. Classify this argument: 1. Either Jim or Ben will go to the party. 2. Ben won t go to the party. 3. Jim will go to the party

4 Classify this argument: Classify this argument: 1. If Jim is human, then Jim is a mammal. 2. If Jim is a mammal, then Jim is warmblooded. 3. If Jim is human, then Jim is warmblooded. 1. John Key lays eggs. 2. If John Key lays eggs, then John Key isn t human. 3. John Key isn t human Classify this argument: Classify this argument: 1. There is life on Mercury, Venus, Earth, Mars, Jupiter, Saturn, and Uranus. 2. Probably, there is life on Neptune 1. The sun has risen every day in the past. 2. Probably, the sun will rise tomorrow How do you tell if a deductive argument is valid? Step 1. Identify the argument s premises and its conclusion. Step 2. Replace every statement is the argument with meaningless letters, leaving just the logical words (if... then, or, and, not). Step 3. Having thereby revealed the logical form of the argument, now see if it is impossible for any argument sharing this logical form to have true premises and a false conclusion. If two arguments share the same logical form, and one of the arguments has got true premises and a false conclusion, then both arguments are invalid

5 Example. What are the premises and conclusion of this argument. What is its logical form? Is it valid or invalid? Sally is warm-blooded. For Sally is human, and if Sally is human then Sally is warmblooded. Modus ponens Any argument having the following, very common logical form is valid. 2. P 3. Q This form of argument is called modus ponens or affirming the antecedent Is this argument valid? 1. If Sally is human, then Sally is warmblooded. 2. Sally isn t human. 3. Sally isn t warm-blooded Denying the antecendent Any argument having the following logical form is invalid. 2. Not P 3. Not Q This invalid argument-form is called denying the antecedent Is this argument valid? 1. If Sally is human, then Sally is warmblooded. 2. Sally isn t warm-blooded. 3. Sally isn t human. Modus tollens Any argument having the following logical form is valid. 2. Not Q 3. Not P This form of argument is called modus tollens or denying the consequent

6 Is this argument valid? 1. If Sally is human, then Sally is warmblooded. 2. Sally is warm-blooded. 3. Sally is human. Affirming the consequent Any argument having the following logical form is invalid. 2. Q 3. P This invalid argument-form is called affirming the consequent Hypothetical syllogism Any argument having the following logical form is valid. Disjunctive syllogism And any argument having the following logical form is also valid. 2. If Q then R 3. If P then R This form of argument is called a hypothetical syllogism. 1. P or Q 2. Not P 3. Q This form of argument is called a disjunctive syllogism There are three main kinds of inductive argument. Enumerative induction involves drawing the conclusion that a group of things will have a certain property from the premises that observed members of the group have this property. E.g., 55% of surveyed NZers think MMP is good. So probably about 55% of NZers think MMP is good. When are enumerative inductions strong? When are they weak? 35 Analogical Induction Analogical induction involves concluding that a pair of things that share many properties in common will probably share a further property in common. E.g., Sarah and Anne like the same books, the same films, the same music, the same sort of people, and the same clothes. Sarah likes going to Auckland. So, probably, Anne likes going to Auckland too. When are analogical inductions strong? When are they weak? 36

7 Abduction (or inference to the best explanation ) Abduction involves inferring that the hypothesis that provides the best explanation of a certain phenomenon is probably correct. E.g., Copernicus sun-centered theory of the solar system provides a better explanation of the movements of Celestial bodies through the heavens than does the Ptolemaic, Earth-centered theory. So the former theory is probably true. When are abductions strong? When are they weak? 37 Fallacies involving unacceptable premises Begging the Question. The conclusion is one of the premises. E.g., God exists because God told me that he exists in a dream. I can trust my dream, because God wouldn t let me have delusional dreams. False Dilemma. The premises assert that only two alternatives exist, when there are really more than two. E.g., You either support the right for everyone to have guns, or you are against freedom. You don t support the right for everyone to have guns. So you are against freedom. 38 Fallacies involving irrelevant premises Equivocation. One word is used in two different ways in the same argument. E.g., Only man is rational, and no woman is a man, and so no woman is rational. Composition. The argument falsely assumes that what holds of the parts must hold of the whole. E.g., My child would benefit from not being vaccinated. So it would be best for all children if vaccination were stopped. Division. The argument falsely assumes that what holds of the whole must hold of the parts. E.g., We are alive and we are made out of subatomic particles. So they must be alive too. Ad hominem (or appeal to the person). The argument attacks the conclusion of another argument by attacking the person who presents the other argument, rather than by attacking the argument itself. E.g., The theory of anthropogenic climate change is nonsense, because its argued for by Al Gore, and Al Gore is a hypocrite who flies in planes a lot and has a really big house Genetic Fallacy The argument attacks a theory by criticizing its origins. E.g., The theory of Relativity came to Einstein in a dream, so it is probably false. Appeal to authority. The argument cites the views of someone who isn t a genuine expert. E.g., Freeman Dyson thinks the threat of climate change is overblown. So the threat of climate change is probably overblown. Appeal to the masses. The argument relies on the idea that a proposition must be true because most people believe it. Appeal to tradition. The argument relies on the idea that something must be true or good because it is part of an established tradition.e.g., Astrology has been around for ages, so there must be something to it. Appeal to ignorance. The argument relies on the idea that a claim must be false (or true) because there is no proof that it is true (or false). E.g., Scientists haven t proved that the theory of anthropogenic climate change is true, so there is no reason why we should take it seriously

8 Straw Man The argument misrepresents someone s claim to make it easier to reject. E.g., The theory of anthropogenic climate change implies that temperatures will go up as CO2 levels go up. But CO2 levels go up every year, while temperatures don t go up every year. And so the theory of anthropogenic climate change is false. 43 Fallacies involving insufficient premises Hasty generalization. The argument draws a conclusion about all members of a group based on evidence about an excessively small number of things in that group. Faulty analogy. The argument assumes that two things will be similar in a certain respects but doesn t provide sufficient reason to think that they will be. E.g., Both Sarah and Anne are two legged and warm blooded, and Sarah likes going to Auckland, so Anne probably likes going to Auckland too. 44 Slippery slope The argument falsely assumes that an initial action must lead inexorably to some very bad result. E.g., If you deny the existence of God, then you deny the existence of an afterlife. And if you do this, then you have no reason to behave morally. And if you have no reason to behave morally, then you will probably murder people whenever it serves your selfish interests to do so. And murdering people is plainly a really terrible thing to do. So you shouldn t deny the existence of God. The end! 45 46