Last updated April 10, 2022

#literature/books/implemented Links: Finished-Implementing List

Introduction

• Logical thinking is difficult and rare

• Helps evaluate thinking and arguments of others

• We tend to make similar mistakes in reasoning

• Logic helps us understand relationships, deduce information from relationships, analyze and evaluate arguments, identify hypotheses, and draw sound inferences

Chapter 1 - Proof

• Proofs help reason for why something is

• The law of the excluded middle states that something is either x or not x

• The law of noncontradiction is where a thing cannot be and not be at the same time

Proof by Contradiction

• If your statement is false, then the opposite must be true

• You intentionally take the opposing position to debunk it

Chapter 2 - All

• Propositions can either be true or false, but not both at the same time

• Quantifiers make propositions (every, all, some none, many, etc)

• A and any could also represent all

All S are P

• All (subject) are (predicate)

• Universal affirmations are the above but with only one instance

• People may tend to substitute it with All (predicate) are (subject)

• Conversion mistake

Familiarity

• The more unfamiliar a material, the harder it is to draw correct inferences

Chapter 3 - Not

• Affirmations are assertions, while negations are denials

ex) “all humans are imperfect” vs “No human is perfect”

• When “No S are P” is true, then “No P are S” is also true

• Consider double negatives

Chapter 4 - Some is Part or All of All

• Some is an existential quantifier

• Some S are P is a type I proposition

• Some S are NOT P is a type O proposition

• A and I propositions are affirmations

• A and E propositions are universal propositions

Chapter 5 - Syllogisms

• Syllogisms accepts only conclusions that are inescapable from the stated premises

• Each proposition in a syllogism is one of AEIO

• First two lines are premises, while third line is a conclusion

• Syllogisms require a middle term, M

• “Some lawyers are men.

• Some women are lawyers.

• Therefore, some women are men.”

• Our emotions tend to sway us from interpreting the premises

• Knowledge interferes with logic

• If “all seniors were forged to go to the gym”, we know that other grades shouldn’t go, even if the statement doesn’t say so

Chapter 6 - If

• A conditional

• “If p then q”

• P is the antecedent, q is the consequent

• If p is true, q is true

• Subjects have difficulty applying a rule to logic when counterexamples in the subject’s experience are unavailable or difficult to recall, and if the task fails to cue individuals to search for counterexamples

• “If p then q” does not translate to “if q then p”

• People may tend to see p as the only unique cause of q, which is false

• “if p then q” is equal to “p only happens if q”

Contrapositive

• Contrapositive of the converse is called the inverse

ex) The inverse of “If you are breaking the law then you are exceeding the speed limit”

“If you are not exceeding the speed limit, then you are not breaking the law”

Chapter 7 - If/And/Or

• Or means either or both in logical terms

Syllogisms

• If p then q

• p

• Therefore q

• If p and q, then r and s

• If p then q

• If not p then r

• Therefore, q or r

• If p then q

• Not q

• Therefore, not p

• If p then q

• q

• Therefore, no solution

• Same can be said to not p not q

Chapter 8 - Series Syllogisms

• “A ham sandwich is better than nothing.

• Nothing is better than eternal happiness.

• Therefore, a ham sandwich is better than eternal happiness

• Series syllogisms are linear syllogisms that elicit a relational inference (better than, older than, less than)

• The hand is touching the oen

• The pen is touching the paper

• Therefore, the hand is touching the paper

Chapter 9 - Symbols

• Leibniz created mathematical symbols and equations, while Boole connected it to logic

Chapter 10 - Logic Machines and Truth Tables

Three-Value Logic System

• If a result is uncertain, it is marked as ½

Chapter 11 - Fuzzy Logic, Fallacies, Paradoxes

• Fuzzy logic is when the result is vague/gray compared to concrete/black and white

• Degrees of truth

Fallacies

• Fallacies can distract us from the true issue at hand

• Something is proven false because it can’t be proven true, and vice versa

• Errors in deduction don’t mean we are not logical, it may be because:

• We fail to accept the task

• The intended meaning is distorted

• The omission of a premise

• The Introduction of outside knowledge as a new premise

• Errors in deductive reasoning

• Adding to, altering, or ignoring items from the premise

• Allowing fractal content to supersede the inference pattern

• Everyday patterns override logic

• Language difficulties, number and location of negations, sentence and word length, cognitive overload

• Inability to accept the hypothetical

Paradoxes

• Persons, things, or situations that exhibit a contradictory nature

• Vague measurements allow for paradoxes

Chapter 12 - Common Logic and Language

• Modern logic overlaps semantics

• Modern language skips out on premises due to mutual understanding

Chapter 13 - Thinking Well Together

• Humans tend to choose the most satisfactory option out of many choices rather than waiting to seek all possible alternatives

Human Reasoning

• Humans reason from an unconscious set of logical rules

• Reasoning errors are from the matter being reasoned about rather than the form of thought

• We tend to only use the information we find relevant to base our conclusions, which can alter our conclusion, even if our logical thinking was correct

• We tend to not seek counterexamples to form conclusions, and we tend to stick to our instincts rather than logical decisions

• After learning a logics class, university students can still have troubles with conditionals and biconditionals

• We don’t always have the time to carefully analyze everything, so we must learn to pay attention to the right things

• When explaining ourselves or teaching others, we need to be clear and precise to make our ideas clearer

Application

• I think this just shifted my mindset towards logical questions in school

• Further emphasizes the importance of understanding the question through the word choice

• I can be more clearer and concise when saying things to prevent confusion

• Try to be more skeptical in my everyday life

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