Why Logic? One way to support a theory is to offer an argument in its favor. One way to criticize a theory is to offer an argument against that theory. Which arguments should we take seriously? Logic answers this Question!
Talking about Arguments We need to have a specific vocabulary for talking about different kinds of arguments and when an argument works and when it doesn’t work. We will use different terms to describe failures of structure and failures of content.
Deduction In DEDUCTIVE ARGUMENTS the CONCLUSION is supposed to follow NECESSARILY from the PREMISES. A DEDUCTIVE INFERENCE is one which takes us from evidence or reasons to a conclusion with necessity.
A Deductive Argument All Cars have engines My Honda is a car Therefore, … My Honda has an engine. THE CONCLUSION! Premise 1 Premise 2 Conclusion INDICATOR Note: If I tell you what the premises are, you know what the conclusion would be before I told you!!! It is impossible for the conclusion to be false, given these premises!
Induction In INDUCTIVE ARGUMENTS the CONCLUSION is supposed to follow with HIGH PROBABILITY from the PREMISES. An INDUCTIVE INFERENCE is one which takes us from evidence or reasons to the likelihood of the conclusion.
An Inductive Argument Every person I have met from Poland loves potato soup. Karlov is from Poland. Therefore,… i) Karlov will love potato soup. ii) Karlov will probably love potato soup.
A Quick review… Deductive vs. Inductive Arguments Deductive: The truth of the premises is supposed to require the truth of the conclusion (Necessary Support) Inductive: The truth of the premises is supposed to increase the probability of the conclusion (Probability)
Good vs. Bad Arguments Deductive Validity – IF the premises are true THEN the conclusion MUST be true. Inductive Strength – IF the premises are true THEN the conclusion WILL BE PROBABLE. Deductive Soundness – the deductive argument is valid AND premises are all true Inductive Cogency—The inductive argument is strong and the premises are all true
Argument Family Tree Argument Deductive Valid Sound Invalid Inductive Strong Cogent Weak
Deductive Arguments Deductive Validity – IF the premises are true THEN the conclusion MUST be true. Deductive Soundness – the deductive argument is valid AND premises are all true Failure of Structure: INVALID Failure of Content: UNSOUND
Validity Validity is the central concept in deductive logic. Validity is related to structure or form. Validity = df A deductive argument is valid iff it is impossible for the premises to be true and the conclusion false (at the same time).
Soundness Soundness is the secondary mode of evaluation in deductive logic. Soundness is related to content. Soundness =df A deductive argument is sound iff the argument is valid and the premises are all true (at the same time).
Kinds of Deductive Arguments Arguments from Mathematics Arguments from Definition Categorical Syllogism Hypothetical Syllogism Disjunctive Syllogism
Argument Family Tree (D) Argument Deductive Valid Sound Invalid Inductive Strong Cogent Weak
Evaluating Deductive Arguments To determine VALIDITY you must first identify the form of the argument. – Try to develop counter-examples with the same logical form, or… – Employ methods of formal logical analysis. Determining SOUNDNESS depends upon the truth of the premises (beyond logic)
Inductive Arguments Inductive Strength – IF the premises are true THEN the conclusion WILL BE PROBABLE. Inductive Cogency—The inductive argument is strong and the premises are all true Failure of Structure: WEAKNESS Failure of Content: NON-COGENT
Strength Inductive STRENGTH is the central mode of evaluation for inductive arguments. Strength=df An inductive argument is strong iff it is improbable that the conclusion is false when the premises are all assumed to be true.
Cogency Inductive COGENCY is the secondary mode of evaluation for inductive arguments. Cogency=df An inductive argument is cogent iff it is inductively strong and the premises are all true.
Kinds of Inductive Arguments Prediction Arguments from Analogy Generalization Arguments from Authority Arguments based upon signs Causal Inferences
Argument Family Tree (I) Argument Deductive Valid Sound Invalid Inductive Strong Cogent Weak
Evaluating Inductive Arguments To determine STRENGTH you must evaluate whether the truth of the premises would in fact enhance the probability of the conclusion. This requires knowledge of how things work and how they are related. To determine COGENCY you must know the truth of the premises (beyond logic)
Induction? The evaluation of inductive arguments is less clear. If you can give determinate quantitative values to probabilities, then the rules of statistics apply. Otherwise you need to try and reflect on the probabilities to the best of your ability.
Induction Some factors to keep in mind about inductive data: Typicality (How common?) Generality (How General?) Frequency (How Frequent?) Analogy / Dis-analogy?
Arguments 1.All ARGUMENTS have a CONCLUSION and PREMISES that are supposed to support the conclusion. 2. Deductive and Inductive arguments differ with respect to the type of support they are intended to provide. 3. Deductive arguments provide NECESSARY SUPPORT 4. Inductive arguments provide PROBABLE SUPPORT
Pause and reflect…
New Topic: Informal Fallacies The study of informal fallacies goes back to Ancient Greece, where the first philosophers and logicians sought to control the demagogues and their teachers (the so-called Sophists).
What is a Fallacy? A fallacy is a mistake in an argument which consists in something other than merely false premises.
Formal Fallacies A formal fallacy is simply an invalid deductive argument form.
Informal = Material Informal fallacies depend on the content of the fallacious argument: either the argument depends upon a shift or ambiguity in linguistic meaning or the substitution of an non-logical basis for a logical justification. There are many varieties.
Fallacies of Relevance The conclusion is logically irrelevant to the premises, even if it is psychologically or emotionally relevant. The key to spotting a fallacy of relevance is to distinguish genuine evidence from emotional appeal.
1. Appeal to Force (Argumentum Ad Bacculum) Arguing via threat: "I deserve a good grade, wouldn't you agree? If you don't agree, I'm afraid about what might happen: I just can't control Bruno here".
2. Appeal to Pity (Argumentum ad Misericordium) Trying to support a conclusion by evoking pity in the listener. I need to pass this class in order to graduate, if I don't graduate,, my parents will kill me. Therefore, I should receive a passing grade in the class".
3. Appeal to the People (argumentum ad populum) Attempting to convince by appealing to the natural desire we all have to be included, or liked, or recognized. This type of fallacy breaks down into several sub-types. Bandwagon: Of course God exists. Every real American believes that. Other related types: Appeal to Vanity; Appeal to Snobbery ("Of course you should cheat; all the cool people are doing it").
3. Appeal to the People (argumentum ad populum) (2) In general, accepting a claim only because someone else believes it is a fallacy (not because you find them to be a credible source for instance...). So, we could say that another example of an ad populum is: Appeal to Belief. Example: "90% of those surveyed think we should not convict Clinton, so you should too". Closely related is the … Appeal to Common Practice. Example: "Hey, everyone speeds. So speeding isn't wrong".