Unit 1

Logic: Chapter 1: Logical Concepts

Logic: the study (analysis, evaluation, and criticism) of arguments.

Argument: a series of sentences that are intended to provide reasons to support a conclusion.

Entailment: the strategy employed in logic, starting with some statements the person does believe–say, A, B,
and C–and then showing them that if they believe A, B, and C, then they have to accept Z!

-​ In what sense do they “have to” accept Z? The technical notion that we will explore is that A, B, and C
together imply or entail Z.

Conclusion: the main goal, target, or purpose of the argument

Premise: a statement intended to be accepted by both parties and not to be argued over

Intermediate Conclusion: an inference to a claim not obvious from the premises, found through arguing
-​ Not the main conclusion the argument is working towards
-​ Not every argument has an intermediate conclusion

Key Words:
-​ Premise:
-​ Because, Since, Due to the fact that, As, Given that, Furthermore, In addition, Besides
-​ Conclusion:
-​ So, Hence, Therefore, Thus, Consequently, As a result, It follows that

Factual vs. Practical

-​ If the conclusion of an argument is a statement of fact, it is a factual argument.
-​ Some arguments don’t provide reasons for truthfulness, instead providing reasons for what’s practical
to do.

Deductive vs. Inductive

Deductive and inductive arguments differ in the kind of support the argument is supposed to provide for the
conclusion.
-​ In a deductive argument, the premises are meant to provide conclusive, indisputable reasons for
accepting the conclusion: if the premises are true, the conclusion must be true, and there’s no possible
way for it to be false.
-​ Basically, you follow theories to find a true conclusion
-​ An inductive argument is one in which the premises are intended to provide evidential support for the
conclusion, but not definitive proof.
-​ Basically, you make observations to find an open-ended conclusion

-​ Inductive arguments often have a similar flavor – X, Y, and Z have some property (flying, being
tall, etc.), therefore other things that are like X, Y, and Z will also have that property.
-​ Inductive reason typically involves using information about a specific subset of entities, and then
extrapolating or generalizing that information to other similar entities.

Practice:
-​ Argument Analysis
-​ Factual vs. Practical Arguments
-​ Deductive vs. Inductive Arguments
 Logic: Chapter 2: Validity, Soundness, Strength, Cogency

Validity and soundness are used when evaluating deductive arguments.

Valid Argument: a deductive argument in which the premises entail the conclusion
-​ If the premises are true, then the conclusion is true

-​ Valid argument preserves truth—if the premises are all true, then the truth will be “transmitted” to the
conclusion as well
-​ It’s impossible for the premises to be true and the conclusion to be false

-​ When interpreting validity:

-​ Assume the premises are true and see if they entail the conclusion
-​ Disregard whether the premises are true or false; you are judging validity, not correctness

Sound Argument: a valid deductive argument with true premises

-​ False premises may end up at a false conclusion
-​ A sound argument must have true premises and a true conclusion

-​ If you can imagine a hypothetical situation with true premises and a false conclusion, then you have
come up with a counterexample that can invalidate the argument

Strength and cogency are similar terms used to discuss inductive arguments.

Strong Argument: an inductive argument with premises providing good evidence for the conclusion
-​ Strength is a matter of degree
-​ An argument can be stronger than another argument if it supplies stronger evidence to support the
conclusion, but there is no absolute standard of what counts as a "strong" vs. a "weak" argument. This
contrasts with validity, which is not a matter of degree—an argument is either valid or it is not.

-​ A strong argument may have false premises. When judging strength, we simply assume that the
premises are true, even if we know they are false
-​ A strong argument may have a false conclusion if it starts from false premises, but also even if it starts
from true premises (strong arguments only make the conclusion probable, not certain)

-​ An argument may be weak even if every statement in the argument is true. As with deductive reasoning,
if an argument does not follow a logical “train of thought,” but instead consists of unconnected (but true)
statements, then it would not be a strong argument, even if all the statements happened to be truths.

Cogent Argument: a strong inductive argument with true premises

-​ A cogent argument doesn’t need a true conclusion. Since inductive reasoning is probabilistic, even
strong inductive reasoning can sometimes lead to a false conclusion.

Deductive Argument:
-​ Valid: when the premises support the conclusion
-​ Sound: when the premises support the conclusion and are true

Inductive Argument:
-​ Strong: when the premises support the conclusion
-​ Cogent: when the premises support the conclusion and are true

Practice:
-​ Validity - Informal Arguments
 Logic: Chapter 3: Logical Fallacies

Appeal to Force
-​ Threatening people to make them join your side
Appeal to Pity
-​ Using pity to make people join your side
Appeal to Majority
-​ Everyone says so, so it must be true
Appeal to Authority
-​ An authority said so, so it must be true
Appeal to Ignorance
-​ No one has found something to refute this, so it must be true

Tu Quoque
-​ The person speaking is hypocritical to their own argument, so they’re wrong
Ad Hominem
-​ Your background can be slandered, making your argument false
Composition
-​ The parts of something is true, so the whole thing must be true
Division
-​ The whole thing is true, so its parts must be true

Straw Man
-​ Focusing only on one part of an argument and then overly simplifying it
Slippery Slope
-​ Thinking one thing will lead to another
Weak Analogy
-​ Making an analogy of two things that lack correlation
Hasty Generalization
-​ A couple samples revealed this, so the conclusion must be that
Begging the Question
-​ You lay down a premise and act like it’s accepted to be true
False Alternative
-​ You can either do this, or that
Equivocation
-​ Something sounds similar to a true thing, so it must be true
Subjectivism
-​ I personally believe it’s true, so it must be true
Missing the Point (Non Sequitur)
-​ Establishing premises and finding a conclusion uncorrelated to the premises
 Unit 2

Logical Operators in English and Symbolic Notation:

Operator Usage Symbolic Notation

Not Not ~P
And And P&Q
Or Or PvQ
If … Then If P then Q P→Q
If P if Q
If and only if P if and only if Q P↔Q
Unless P unless Q ~Q → P

Valid Argument: for every row in which every premise is true, the conclusion is true at that row as well.
-​ (All other rows can be ignored.)

Tautology: if the complete truth table shows that its value is “True” at every row of the truth table.
-​ (Intuitively, it is a statement that is “always” true “no matter what the circumstances.")

Contradiction: if the complete truth table shows that its value is “False” at every row of the truth table.
-​ (Intuitively, it is a statement that is “always” false “no matter what the circumstances.")

Contingency: if the complete truth table shows that its value is “True” at some rows and “False” at others.
-​ (Intuitively, it is a statement whose truth value may change depending on the circumstances.)