Intro to Logic Flashcards
What is Logic?
The analysis and appraisal of arguments
What is Philosophy?
Reasoning about the ultimate questions of life
What is an Argument?
a set of statements consisting of premises and a conclusion
What is a Premise?
supporting evidence
What is a Conclusion?
a statement made based on supporting evidence
What is true/false?
statements can either be true, correct, or false, incorrect
What is the Law of Non-Contradiction?
contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions “A is B” and “A is not B”
What is the Law of Excluded Middle?
the law of excluded middle states that for any proposition, either that proposition is true or its negation is true
What is valid/invalid?
Valid is if the premises support the conclusion, invalid if the premises do not
What is the difference between true and valid?
true is connected to statements, valid is connected to agruments
What is “sound”?
A “sound” argument is both valid (conclusion follows the premises) and all the premises are true
What is “.˙.”?
Therefore
What is “wff”?
A well formed formula is a finite sequence of symbols from a given alphabet that is part of a formal language
What is a deductive argument?
A deductive argument has a tight connection between premises and conclusion, it would be impossible for the premises to all be true but have a false conclusion
What is an inductive argument?
An inductive argument has a loose connection between premises and conclusion, the conclusion relative to the premises is only a good guess (could be true or false)
What is a definition?
a rule of paraphrase intended to explain the meaning of a word or phrase
What is an interchange test?
A definition test where if A=B is true, then B=A must be true
What is a lexical definition?
a definition explaining current usage of a word or phrase
What is a stipulative definition?
a definition specifying your own usage of a word or phrase
What is a clarifying definition?
a definition that stipulates a clearer meaning for a vague term
What is a recursive definition?
a definition that first specifies some things that the term applies to and then specifies if the term applies to certain things
What is a logical positivism?
using the verifiability criterion of meaning
Who is A.J. Ayer?
a logical positivist who appealed to the verifiability criterion of meaning
What is an analytic sentence?
a statement that is self-contradictory to deny
What is a synthetic sentence?
any statement which cannot be determined true or false by linguistic meaning alone
What is verifiability criterion of meaning?
(LP) If there is no way to test a statement, then it has no meaning– nothing in it could be true or false
Who is William James?
Logistician who suggests to determine the “cash-value” of a statement
What is pragmatism?
if the truth of a statement has no practical meaning to anyone, then it has no meaning at all
What is a logically necessary truth?
the same idea as analytic statements, a truth that is self-contradictory to deny
What is “a priori” knowledge?
rational knowledge based on reason
What is “a posteriori” knowledge?
empirical knowledge based on experience
What is synthetic?
not self-contradictory to either affirm or deny
What is traditional logic?
A combination of Aristotle’s logic and the Stoic’s additions
What is Buddhist logic?
deductively valid, yet tend to lean towards pursuing mystical thinking
Who is Artistotle?
Greek who studied Logic, formulated a correct principle of inference, to use letters for terms, and to construct a axiomatic system
Who were the Stoics?
Studied modial logic, used numbers, divided logic into philosophy
Who is Boethius?
Christian thinker, explained modal box-inside/outside ambiguity while defending divine foreknowledge and human freedom.
Who is Anselm and Peter Abelard?
Latin translators of Aristotle’s works
Who is Thomas Aquinas?
influential medieval philosopher, little impact on logic but used it a lot. Likely produced more philosophical arguments than anyone who has ever lived.
Who is William of Ockham?
developed modial logic and avoided metaphysics
What is Ockham’s razor?
“Accept the simplest theory that adequately explains the data”
Who is Jean Buridan?
formulated standard rules for valid syllogisms
Who is Immanuel Kant?
said Aristotle invented and perfected logic, nothing else more could be added
Who is Gottfried Leibniz?
co-inventor of calculus, proposed idea of symbolic language
Who is George Boole?
Boolean algebra, father of mathematical logic
Who is Gottlob Frege?
created modern, showed how to analyze arguments with relations and used a formal system
Who is Bertrand Russel?
praised Frege’s work, fixed it after showing its flaws with the Russel Paradox
Who is Alfred North Whitehead?
Russels teacher, worked with him to avoid the Russel Paradox, developed a more intuitive symbolic system with Russel
What are three reasons to study logic?
- Logic builds our minds
- Logic increases our understanding of philosophy
- Logic is fun
What are the five major areas of philosophy?
- Logic
- Metaphysics
- Aesthetics
- Epistemology
- Ethics
What are the four types of sentences?
Declarative, Interrogative, Imperative, Exclamatory
What are the five rules for good lexical definitions?
- neither too broad nor too narrow
- avoids circularity and poorly understood terms
- matches the vagueness of the term defined
- matches the emotional tone of the term defined
- includes properties only essential to the term
What are the five qualities of a stipulative definition?
- use clear terms that will be understood
- avoid circularity
- let us paraphrase out the defined term
- accord with how the term is used
- aid understanding and discussion of subject matter
What is the difference between an analytic and synthetic sentence?
analytic sentences use “a priori”, while synthetic sentences use “a posteri”
What sentence is this?
“Michigan beat Ohio State.”
Declarative
What sentence is this?
“Did Michigan win?”
Interrogative
What sentence is this?
“Beat Ohio State.”
Imperative
What sentence is this?
“LETS GO MICHIGAN.”
Exclamatory
