Logic, Philosophical Tools Quiz Review…20 minutes 10/31 With a partner or yourself, look back in your notes and textbook to review these terms and concepts Logical Consistency Logical Possibility vs. Causal Possibility Lexical and “Real” Definitions Creating a Counterexample Deductive Reasoning (Syllogisms) Validity and Soundness Inductive Reasoning Enumerative, Analogical, Abduction (Inference to best explanation) Ockham’s Razor Principle of Conservatism

Logic, Philosophical Tools Exploring the open questions in Philosophy demands that we become adept at evaluating arguments. Thus, we need to learn to use certain logical tools and techniques that may be foreign to you!

Logical Consistency Requires that all claims can be true at the same time or the result is logical inconsistency Logical inconsistency creates contradictions, which simultaneously assert and deny something. Reason demands logical consistency.

Possibility Two forms: Causal possibility Logical possibility a state of affairs that does not violate the laws of nature not useful in philosophy Logical possibility what we can conceive of in our minds as possible useful in philosophy for detecting contradictions

Logical Possibility “A good test of whether something is logically possible is to ask yourself whether you could make a movie out of it…” Try your hand at the Food for Thought exercise on page 20

Philosophical Definitions Lexical dictionary definition limited use in philosophy “Real” explains the essential nature of a thing or phenomenon established by necessary and sufficient conditions

Philosophical Definitions Necessary condition: A condition q is necessary for p if it is impossible for something to be p without being q “Being an animal (q) is a necessary condition for being a vertebrate (p).” Sufficient conditions: A condition q is sufficient for p if it is impossible for something to be q and not p “Having a segmented spinal cord (q) is a sufficient condition for being a vertebrate (p).”

The Basic Structure of Arguments The Claim (Conclusion) that the argument establishes The Reasons (Premises) offered in support of the claim

Standard Form Putting arguments in standard form is a method used to accurately assess the value of arguments Requires: listing all the premises in numbered, sequential order making a conclusion Example: “I believe that ghosts exist, because late at night. I have heard strange noises in my room” I have heard strange noises late at night in my room. Therefore: Ghosts exist.

Deductive and Inductive Reasoning Deductive The truth of the premises guarantees that the conclusion must be true. Inductive Conclusions are established only to some degree of probability.

Deductive and Inductive Reasoning Deductive 1. If my brain stops functioning, then it will not be possible for me to have any thoughts 2. When I die, my brain will stop functioning. Therefore: When I die, it will not be possible for me to have any thoughts. In a deductive argument, the premises aim to provide conclusive support for the truth of the conclusion If the premises are true…the conclusion must be true

Deductive and Inductive Reasoning Every new freshman I have talked to has been enrolled in a freshman success seminar. Therefore: All new freshman are enrolled in a freshman success seminar. If the premises are true…then it is very likely that the conclusion is true as well.

Aristotle Worked with syllogisms Formal system of thought Provides a method for connecting ideas together https://www.youtube.com/watch?v=NKEhdsnKKHs

Syllogism Ex: 1) Wood floats in water. 2) Ships are made of wood 3) Therefore ships float in water.

Syllogisms #1 and #2 are both a premise. #3 is a conclusion

Syllogism Example Reiterated Premise #1: Wood floats in water. Premise #2: Ships are made of wood. Conclusion: Therefore, ships float in water.

So? When you make or evaluate an argument, look to the premises. They should lead to a valid conclusion.

Validity and Soundness Argument

Argument: Validity A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

Argument: Validity Valid arguments do not require true premises.

Ex: Valid Argument – True premises Either Elizabeth owns a Honda or she owns a Saturn. Elizabeth does not own a Honda. Therefore, Elizabeth owns a Saturn.

Ex: Valid Argument – False premises All toasters are items made of gold. All items made of gold are time-travel devices. Therefore, all toasters are time-travel devices.

Argument - Soundness A sound argument is one that is not only valid, but begins with premises that are actually true

Soundness A deductive argument is sound if and only if 1) it is both valid, and 2) all of its premises are actually true. Otherwise, a deductive argument is unsound.

Ex: Sound argument QUANTIFIERS No felons are eligible voters. Some professional athletes are felons. Therefore, some professional athletes are not eligible voters. QUANTIFIERS

Evaluating Inductive Arguments How probable is it? Higher probability leads to stronger arguments Lower probability leads to weaker arguments If an inductive argument is strong and if its premises are true we classify the argument as COGENT. Inductive arguments do not play as big a role in Philosophy as they do in other more empirical disciplines like Psychology and Sociology

Types of Inductive Arguments Enumerative Inductive Argument Analogical Abductive (inference to the best explanation)

Type 1 Enumerative Inductive Arguments Move from specific examples or facts to a general conclusion Opposite of deduction (syllogisms) No distinctive form BUT there is a process to follow All Observed A’s have been B’s Therefore: Probably all A’s everywhere are B’s.

Type 2: Argument by Analogy Taking this philosophy class is similar to taking an English Class I always get low grades in my English classes. Therefore: I conclude that I will also get a low grade in this philosophy class.

Type 2: Argument by Analogy Evaluating an analogical argument depends on the degree to which the two compared items are similar to each other! Must be analyzed on a case-by-case basis…

Type 3: Abductive (inference to the best explanation) How can we determine whether a given explanation of an event is better than all other explanations? 1. Explanation A is better if it is simpler Ockham’s Razor = Simple theories are usually the right ones 2. Explanation A is better if it fits together better with my beliefs about the world. Principle of Conservatism = Conclusions must be compatible with preexisting beliefs