Intro To Logic

Front 1

Inductive Argument

Back 1

Decitates how we can infer from observed events to generalizations we can rely on.

Hint 1

An inductive argument can't guarantee that the truth of its premises will transfer to its conclusion.

Front 2

Logic

Back 2

The science which addresses the validity of inference and demonstration.

Hint 2

So it's an attempt to explain in as systematic way as possible what the principles of valid reasoning are.

Front 3

Deductive Argument

Back 3

An argument on which the conclusion is entailed by the premises. The conclusion follows because of the form of the argument rather than the meaning the terms.

Hint 3

The conclusion is deduced by the premises. The premises serve to prove the conclusion. Cannot lead from true premises to false conclusions. The arguments validity is completely independant of the truth of the statements that make it up. An argument whose premises are false and conclusion is true can be valid. An argument whose premises are false and conclusion are false can also be valid. But a deductive argument that has true premises but a false conclusion is invalid.

Front 4

Law of Noncontradiction

Back 4

No proposition can be both true and false.

Hint 4

Aristotelian logic fundamental principle. One of two.

Front 5

Law of the Excluded Middle

Back 5

A proposition must either be true or false.

Hint 5

Aristotelian logic fundamental principle. One of two.

Front 6

Syllogism

Back 6

A form of argument with two premises and a conclusion, such as all men are mortal; Socrates is a man, therefore Socrates is mortal.

Hint 6

All A's are B's, all B's are C's, therefore all A's are C's. The conclusion is deduced by the premises. The premises serve to prove the conclusion. Aristotelian syllogism is based mostly on deductive syllogism but also touches on inductive argument as part of the science of reasoning.

Front 7

Indicator Word

Back 7

Indicates the logical relationship of claims that come before or after it.

Hint 7

Because, therefore, so, hence, thus, it follows that, as a result, consequently, etc. indicate conclusion statements. Since, if, because, from which it follows, for these reasons, etc. indicate premises.

Front 8

Good Arguement

Back 8

An argument that gives us good reasons (premises) to believe the conclusion. Depends on whether the premises are true and the conclusion follows from the premises.

Hint 8

Two conditions: Truth Condition - All premises must be true. Logic Condition - The conclusion must follow from the premises.

Front 9

Valid Argument

Back 9

An argument where if all the premises are true, the conclusion cannot be false. If all the premises are true, the conclusion follows with certainty.

Hint 9

One of the ways to fulfill the logic condition. Validity is a logical property of whole arguments, not of individual claims. All A are B. X is an A. Therefore, X is a B.

Front 10

Invalid Argument

Back 10

If all the premises are true, the conclusion can be false.

It is logically possible for the premises to be true and the conclusion false.

The truth of the premises does not guarantee the truth of the conclusion.

Front 11

Strong Argument

Back 11

An argument in which the if the premises are true, they strongly suggest the truth of the conclusion. If all the premises are true, the conclusion follows with high probability.

Hint 11

One of the ways to meet the logic condition. A strong argument can be invalid. The distinction between strong and week arguments is a matter of degree based on conventional choice. Most A are B. X is an A. Therefore, X is a B. Almost all A are B. X is an A. Therefore, X is a B.

Front 12

Weak Argument

Back 12

An argument where the if the premises are true, they do not strongly suggest the truth of the conclusion. If all the premises are true, the conclusion follows neither with certainty nor with high probability. They do not follow the logic condition.

Hint 12

In this case, the premise is not strong enough to imply the conclusion. Some A are B. X is an A. Therefore, X is a B.

Front 13

Claim

Back 13

Declarative statement. When one claim is made and other claims are added as evidence to support the truth of another claim then the claims together become an argument.

Hint 13

Bats are mammals. Good exists. There are two inches of snow on my car.

Front 14

Argument

Back 14

One or more claims (premises) intended to support the truth of another claim (conclusion).

Front 15

Inferences

Back 15

Evaluations that can be made regardless of whether the premises are true.

Front 16

Technical Definition

Back 16

Stipulate technical definitions to define how you intend to use the word.

Front 17

Argument Form

Back 17

The logical structure of an argument which are templates into which meaningful claims can be inserted.

Front 18

Modus Ponens

Back 18

Logical structure whereas: if P, then Q. P. Therefore, Q.

Front 19

Modus Tollens

Back 19

A logical structure whereas: if P, then Q. Not Q. Therefore, not P.

Front 20

Sentences

Back 20

In logic, they are the statements that can be true or false and are put together to form the premises and conclusion of an argument.

Hint 20

The sentences can reflect either fact or opinion. Questions, imperatives, and exclamations do not count as logical sentence claims.

Front 21

Questions

Back 21

In logic, questions themselves do not count as sentences, but answers will because answers are true or false.

Front 22

Imperatives

Back 22

Commands are neither true or false and do not count as sentences in logic. Not all commands are phrased as imperatives which allows them to be true or false and recognized as sentences in logic. 'You will respect my authority.'

Front 23

Exclamations

Back 23

Exclamations do not add to logical sentences and do not make up logical sentences. Sentences are focused on statements that can either be true or false. 'Oouch!' is neither true or false.

Front 24

Extraneous Material

Back 24

Anything in a passage that does not do rational work in an argument, that is, words or phrases that do not play a role in a premise or the conclusion.

Front 25

Set Up / Background Phrases

Back 25

Type of extraneous material.

Hint 25

Once again... to begin... let me say a few words about... as you are well aware...

Front 26

Expressions of Personal Feeling or Commentary

Back 26

Type of extraneous material.

Hint 26

It happens over and over... some of the worst... rears its ugly head... its pretty obvious... it should be clear that... i can't believe... it's really sad that... i would like to propose that...

Front 27

Transition Phrases

Back 27

Type of extraneous material.

Hint 27

In addition... which leads me to my next point... on one hand... on the other hand... insofar as... naturally... of course... didn't you know... you know... that raises the question... which leads us to ask...

Front 28

Buzz Words

Back 28

Words or phrases that seem meaningful, even technical and academic, but that have no meaning at all.

Hint 28

When buzz words are not explicitly defined in a particular context, they have only the pretense of meaning.

Front 29

Ambiguous

Back 29

A word or phrase that has more than one clear meaning.

Hint 29

There are two types: lexical ambiguity, and syntactic ambiguity.

Front 30

Lexicaly Ambiguous

Back 30

A word that has more than one clear meaning.

Hint 30

Match, pen, chip, suit, virus, hard, draw, head, mouse, bank.

Front 31

Syntactically Ambiguous

Back 31

A phrase in which the arrangement of words allows for more than one clear interpretation.

Hint 31

I cancelled my travel plans to play golf.

My travel plans included playing golf but I cancelled those plans.

I cancelled my travel plans in order to play golf.

Front 32

Vagueness

Back 32

A weird or phrase that has clear meaning, but does not precisely define truth conditions.

Hint 32

Tall, short, close, far, weak, strong, soft, hard, fat, thin, pile, heap.

Front 33

Truth Conditions

Back 33

Conditions on which we could say for sure that the claim in which the word is used is true or false.

Front 34

Propositional Logic

Back 34

Deals with logical relationships between propositions taken as wholes. It is interested in how the truth value of compound claims depends on the truth value of the individual claims that make it up. The compound claim as a whole can be true or false and the individual statements in the compound claim can be individually true or false. If either component is false the entire compound claim is false.

Hint 34

Sometimes called sentential logic or statement logic. In logic we use letters to symbolize propositions (statements, sentences, assertions).

Front 35

Compound Claims

Back 35

Claims that are made up of more than one statement that can be true or false. If one statement in the compound claim is false then the whole claim is false. The compound claim is true when all claims are true.

Hint 35

Basic claim structures:

A and B (conjunction)

A or B (disjunction)

If A then B (conditional)

Not-A (contradictory)

Front 36

Conjunctions

Back 36

A and B

A but B

A however B

A yet B

A and B and C but D and E

Hint 36

Only true if all of the individual claims are true.

Front 37

Disjunctions

Back 37

A or B

A or B or C or D or E

Inclusive Or claims are only false if all claims are false.

Exclusive Or claims are false if either all claims are false or all claims are true since one claim negates the other in a valid exclusive or claim.

Hint 37

Asserts that at least one claim of a set of claims is true. There are inclusive or statements and exclusive or statements. Inclusive or statements do not negate the truth values of the other claims in a sentence, meaning they are not mutually exclusive. In an exclusive or statement only one of the claims can be true.

Front 38

Conditionals

Back 38

If A then B (A -> B)

Assert a logical relationship between A and B. Does not assert that A is true or B is true, just the logical relationship between the two. The only time a conditional is not true is when the antecedent is true and the conditional is false.

Hint 38

Conditional claims have two parts consisting of the antecedent and the consequent. The antecedent is the claim that comes right after the if in a conditional claim and the consequent is the claim that comes after the then.

Front 39

Conditional Fallacy

Back 39

Fallacies that occur in interpreting conditional statements.

Hint 39

Affirming The Consequent: If A then B. B so A. Just because B is true doesn't mean A is true.

Front 40

Bioconditionals

Back 40

A if and only if B

A iff B

A<-->

A=B

(If B then A) and (if A then B)

Joins two conditionals using the if rule and only if rule.

It asserts two things: that A is true if B is true. And that A is true only if B is true.

Hint 40

The truth of the claims has to run both ways. If A then B and if B then A.

Front 41

Sentence Letters SL

Back 41

Capital letters are used to represent basic sentences. Whatever logical structure a sentence might have is lost when it is translated as an atomic sentence.

Hint 41

Requires the use of a symbolization key which provides and English language sentence for each sentence letter used in the symbolization.

Front 42

Atomic Sentences

Back 42

The sentences that can be symbolized with sentence letters. If A is true, then -¡A is false. If -¡A is true, then A is false.

Hint 42

A subscript is added after the letter since the English alphabet is finite and there is no limit to the number of atomic sentences.

Front 43

Connectives

Back 43

Logical connectives are used to build complex sentences from atomic components.

Hint 43

There are 5 logical connectives in SL:

‐¡ negation "it is not the case that"

& conjunction "both... and..."

V disjunction "either... or..."

--> conditional "if... then..."

<-> biconditional "... if and only if..."

Front 44

Negation

Back 44

A sentence can be symbolized as -¡A if it can be paraphrased in English as "it is not the case that A."

B: Mary is in Barcelona

-¡B: Mary is not in Barcelona. Mary is somewhere besides Barcelona.

R: The widget is replaceable.

-¡-¡R The widget is not irreplaceable.

H: Elliot is happy.

Incorrect: -¡H Elliot is unhappy. Just because Elliot is not happy doesn't mean Elliot is unhappy. So to represent Elliot is unhappy would require a new letter symbol. -¡ would have to mean it is not the case that Elliot is happy. He could be not happy but that doesn't imply he's unhappy. He could be in between.

Front 45

Conjunction

Back 45

Two claims joined by 'and.' A sentence can be symbolized as A & B if it can be paraphrased in English as "both A, and B." Each of the conjuncts must be a sentence. Sentences that can be paraphrased "A, but B" or "although A, B" are best symbolized using conjunction A & B. A & B is true if and only if both A and B are true.

Hint 45

The individual claims in a conjunction are called conjuncts. Words like both and also do not add to the logical structure of claims so they do not require symbols.

Front 46

Disjunctive

Back 46

Claims separated by 'or.' A sentence can be symbolized as A V B if it can be paraphrased in English as "either A, or B." Each of the disjuncts must be a sentence. There are exclusive 'or' sentences that imply that the truth of one claim results in the negation of the other claim. Inclusive 'or' sentences allow room for both claims to be possible in the existence of the truth of an individual claim. It implies that at least one of the claims are true and that doesn't make the other claims false. A disjunct is only false if all claims are false.

Hint 46

Like conjunction, disjunctions are also logically symmetrical.