Formal Logic Systems

Logic

the organized body of knowledge or science that evaluates arguments

Argument

a group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion)

Statement

a sentence thats true or false (a declarative sentence)

Truth value

the truth or falsity of a statement

premises

the statements that set forth the reasons or evidence

conclusion

the statement that the evidence is claimed to support or imply

conclusion indicators

therefore, wherefore, thus, consequentyl, we may infer, accordingly, we may conclude, it must be thaat, for this reason, so, entails that, hence, it follows that, implies that, as a result

premise indicators

since, as indicated by, because, for, in that, may be inferred from, as, given that, seeing that, for the reason that, inasmuch as, owing to

inference

the reasoning process expressed by an argument (interchangeable with argument)

proposition

the meaning or information content of a statement (interchangeable with statement)

syllogistic logic

a kind of logic that fundamental elements are terms, and arguements are evaluated as good or bad depending on how the terms are arranged in the argument

modal logic

a kind of logic that involves such concepts as possibility, necessity, belief, and doubt

Warning

a form of expression that is intended to put someone on guard against a dangerous or detrimental situation (“watch out that you dont slip on the ice”) no evidence its true = no argument

piece of advice

form of expression that makes a recommendation about some future decision or course of conduct (similar to warnings)

a statement of belief or opinion

is an expression about what someone happens to believe or think about something (no argument)

loosely associated statements

about the same general subject, but they lack a claim that one of them is proved by the others (no argument)

report

consists of a group of statements that convey information about some topic or event

expository passage

a kind of discourse that begins with a topic sentence followed by one or more sentences that develop the topic sentence (if used to elaborate = no argument)

illustration

an expression involving one or more examples thats intended to show what something means or how it is done (no argument but misleading)

arguments from example

illustrations taken/interpreted as arguments

explanation

an expression that purports to shed light on some event or phenomenon

If it rains, the ground gets wet. It rained. Therefore, the ground is wet. What does this illustrate?

Modus Ponens

If a person is a bachelor, he is unmarried. John is married, so he is not a bachelor. What does this illustrate?

Modus Tollens

Which is invalid?

Modus ponens/tollens, affirming the consequent, or denying the consequent?

Affirming the consequent

If the lamp is plugged in, then it will turn on. The lamp does not turn on. Therefore, is it not plugged in. What does this illustrate?

Modus tollens

Deductive reasoning aims for conclusions that are:

Necessarily true if premises are true

Inductive reasoning aims for conclusions that are:

Probably true given premises

Every swan I’ve seen is white. Therefore, all swans are white. This illustrates?

Inductive

All humans are mortal. Socrates is a human. Therefore, Socrates is mortal. This illustrates?

Deductive

Which type of reasoning is tested for validity?

Defuctive

An argument is valid if:

It’s conclusion follows logically from premises

An argument is sound if:

It is valid and all premises ar

An argument can be valid even if:

Its premises are false or its conclusion is false

Truth applies to:

statements (propositions)

validity applies to:

entire arguments

When is an argument cogent?

If it is strong and has true premises

“90% of students at this university own laptops. Maria is a student here. So Maria probably owns a laptop” What does this illustrate?

Strong inductive argument

An inductive argument is strong if:

the conclusion is probably true given the premises

A cogent argument must have:

have true premises and be inductively strong

what is an uncogent argument?

a weak inductive with at least one false premise

“The car wont start because the battery is dead” is this an argument or an explanation?

an explanation

“The ground is wet because it rained” is this an argument or an explanation?

an explanation

The intension of “bachelor” is:

The meaning: an unmarried adult

The extension of “bachelor” is:

All unmarried adult males

Which focuses on meaning or sense: intension or extension?

intension

Which focuses on the members on the actual members of a set? intension or extension?

extension

The word “triangle” meaning “a three-sided polygon” is its:

intension

Where is the definiendum and the definien in the def “a bachelor is an unmarried adult male”

definiendum- bachelor

definien- an unmarried adult male

Definiens

word or words doing the defining

Definiendum

the term being defined

What is this argument?

If P then Q. Q. Therefore, P.

Affirming the consequent (fallacy/invalid)

“If you study, you pass. You did not study. Therefore, you did not pass.” This is what argument?

Denying the antecedent (invalid)

“If you study, you pass. You did not pass. Therefore, you did not study.” This is:

Modus Tollens (valid)

What is necessary for an argument to be cogent?

deductive validity

Extension:

the class of objects to which the term conventionally applies

Intension:

the set of properties shared by all objects in the term’s extension

(def by extension) Ostensive:

you point out members of the definiendum’s extension

(def by extension) Enumeration:

list some or all members of the term’s extension

(def by extension) subclass:

listing the subclasses included in the term’s extension

(def by intension) definition by synonym:

“panther” means “leopard.” If youre learning german it may be helpful to know that Hirn means “brain

(def by intension) definition by etymology:

you might explain that the word “orthodox” comes from the Greek word “ortho” meaning “right” or “straight” along with “doxa” which means opinions or belief

(def by intension) definition by genus and species:

specify a broad category and then separate members within

Fallacy:

an error in reasoning that renders an argument logically invalid or weak. often appear persuasive on the surface, but they fail to provide logically sound support for their conclusions

Informal Fallacy:

occurs when the reasoning in an argument is flawed due to its content, language, or assumptions, rather than a formal structural error. These fallacies often exploit emotions, irrelevant points, or improper appeals

Appeal to force F

occurs when someone attempts to persuade by using threats or force instead of logical reasoning

Appeal to pity F

attempts to win support for an argument by exploiting the aduiences sympathy or pity

Appeal to the people F

relies on popular opinion or the feelings of a crowd to support a conclusion

Appeal to fear F

tries to instill fear in the audience to persuade them to accept a conclusion

Bandwagon argument F

suggests that a claim is true or right simply because many people believe or do it

Appeal to snobbery F

attempts to persuade by appealing to the desire to be special or part of an elite group

Appeal to tradition F

claims something is correct or better simply because it has been done that way in the past

Ad Hominem (general) F

attacks the person making the argument rather than the argument itself

Ad hominem abusive F

attacks a persons character in a direct way instead of addressing the argument

Ad hominem circumstantial F

dismisses a persons argument by pointing out circumstances that supposedly bias them

Tu quoque F

dismisses criticism by accusing the critic of hypocrisy

Fallacy of accident F

applies a general rule to a specific case where the rule is not applicable

Straw man F

misrepresents or distorts an opponents argument to make it easier to attack

Missing the point

when the premises support a conclusion, but a different, unrelated conclusion is drawn

Red herring F

introduces an irrelevant topic to divert attention from the main issue

Ostensive def:

defining something by pointing to an example

Lexical def:

the standard dictionary meaning of a word

Enumeration def:

listing all the members or parts of a category

genus and species def:

defining by placing the term within a larger category (genus) and then specifying its distinguishing features (species)

stipulative def:

assigning a new meaning to a word for a particular context

If P then Q.

P.

Therefore, Q.

what argument is this?

Modus Ponens (valid, affirm antecedent)

If P then Q.

Not Q.

Therefore, not P.

what argument is this?

Modus Tollens (valid, deny consequent)

If P then Q.

Not P.

Therefore, not Q.

what argument is this?

denying the antecedent (invalid)

An example of increasing intension and decreasing extension:

animal, mammal, feline, tiger

An example of increasing extension and decreasing intension:

tiger, feline, mammal, animal

Defeasibility:

the idea that a persons justification for a belief can be overturned (or defeated) by new information or additional evidence

Rebutting defeater:

provides evidence directly against your belief (ex- you believe it sunny outside, then you see its raining)

Undercutting defeater:

attacks the reliability of the evidence supporting your belief (ex- you believe its 3 because the clock says so, then you learn the clock is broken)

If P, then Q.

Q.

Therefore, P.

what argument is this?

Affirming the consequent (invalid)

P or Q.

Not P.

Therefore, Q.

What argument is this?

disjunctive syllogism (valid)

If P, then Q.

If Q, then R.

Therefore, if P, then R.

what argument is this?

hypothetical syllogism (valid)

Deductive reasoning is classified as either:

valid or invalid

Sentences are classified as either:

true or false

Inductive reasoning is classified as either:

strong or weak

Inductive reasoning:

a type of reasoning that moves from specific observations to general conclusions

An inductive argument is cogent if it meets what 3 conditions?

1. argument is strong

2. the premises are actually true

3. the argument is not defeated by additional information