PHIL 100 - Terms

Argument

Definition:

• A set of statements (premises) are used to support another statement (the conclusion)

Application:

Premise 1 and premise 2, therefore conclusion.

Premise

Definition:

• a reason that is used in an argument to support a conclusion.

Application:

• ex: premise 1 (vegetables dont speak), premise 2 (dogs dont speak), therefore conclusion.

Conclusion

Definition:

• the part of an argument that the premises are meant to demonstrate by means of evidence or justification.

Application:

• Premise 1, premise 2, therefore conclusion (dogs are vegetables).

Indicator words

Definition:

• words that are used within an argument to clearly indicate whether a conclusion or premise is about to be presented

Application:

• Conclusion indicator: ex: the use of the word “therefore,” which indicates a conclusion is going to be presented

• Premise indicator: ex: the use of the word “because,” which indicates a premise is going to be presented

If it is not clear where a premise or conclusion is within an argument, you can insert one yourself to make it clearer to analyze

Statement

Definition:

• the expression of a single idea or concept; it can be either true or false. Also known as a “proposition” or “claim”

Application:

• a statement can be either a premise or a claim, so essentially any single idea that is either true or false being presented in an argument

Rhetorical questions

Definition:

• a question that has an implied answer and therefore functions as a statement

Application:

• a rhetorical question is used when a person assumes the answer to it is common sense and is perceived as being obvious

Principle of charity

Definition:

• the principle of assuming an argues believes that all their premises, explicit or not, are true, and that they are reasoning logically

Application:

• its a basic default rule of communication- if we didn’t believe what other people were saying was true there wouldn’t be a conversation at all

• In an argument, we can use the principle of charity to add any missing premises to an argument to make it clearer

Ex:

P1) She makes me laugh.

MP2) I’d like a roommate that makes me laugh.

—-

C3) I should ask her to be my roommate.

Standardization

Definition:

• The rewriting of an argument in standard form, labeling its premises and conclusion(s). This is done to demonstrate the logical flow of the argument.

Application:

• to make an argument clearer, you can make an argument standardized by removing any unnecessary words and organizing its order.

Ex:

There is no milk at home, and I always have milk with my cereal, so I will have to go to the store.

P1) There is no milk at home.

P2) I always have milk with my cereal.

—-

C3) Therefore, I will have to go to the store.

Dependent premise

Definition:

• Premises that work together to establish a conclusion. Removing one of the premises removes the justification of the conclusion.

Application:

• when you use dependent premises, they work together to support the conclusion, meaning that you must assess and analyze them all together to assess their ability to sufficiently support the conclusion

• Ex:

P1) The Independent Party candidate got 1000 votes.

P2) You must obtain 2000 votes to get elected.

—

C3) Therefore, the Independent Party candidate did not get elected.

Independent premise

Definition:

• Premises that independently support the conclusion; each premise offers some degree of separate support for the truth of the conclusion.

Application:

• ex:

P1) A goldfish is small.

P2) A goldfish is quiet.

P3) A goldfish is easy to take care of.

—

C4) Therefore, a goldfish may be a suitable pet for a young child.

Missing premise

Definition:

• A premise that is unstated but is required by the logical form of the argument.

Application:

• links together the premise(s) to the conclusion within an argument

• Ex: She makes me laugh. Therefore, I should ask her to be my roommate.

P1) She makes me laugh.

MP2) I would like to have a roommate that can make me laugh.

—

C3) I should ask her to be my roommate.

Complex argument

Definition:

• an argument that includes at least one sub-argument

Application:

• each conclusion is a claim based upon the evidence provided before and for it

• Ex:

P1) Big box retailers can order massive quantities at a significantly reduced price.

P2) Small local stores can’t match the low prices of big box retailers.

—

C3) Therefore, some small local stores will go out of business.

—

C4) Therefore, there will be a reduction in business competition.

—

C5) Therefore, there will be a reduction in the variety of goods available to consumers.

—

C6) Therefore, big box retailers aren’t good for small cities.

Simple argument

Definition:

• an argument that provides a strong premise for its conclusion.

Application:

• Ex: I am wearing this perfume because it smells good.

Sub-argument

Definition:

• an argument provided to establish a statement that is then in turn used as a premise to justify another conclusion within a complex argument.

Application:

• P1 and P2 are used to support C3, making it the first sub-argument

• Again, C3 and C4 are used to support C5, making it the second sub-argument

• Again, C4 and C5 are used to support C6, making it the third sub-argument

Ex:

P1) Big box retailers can order massive quantities at a significantly reduced price.

P2) Small local stores can’t match the low prices of big box retailers.

—

C3) Therefore, some small local stores will go out of business.

—

C4) Therefore, there will be a reduction in business competition.

—

C5) Therefore, there will be a reduction in the variety of goods available to consumers.

—

C6) Therefore, big box retailers aren’t good for small cities.

Intermediate conclusions

Definition:

• a statement that is the conclusion of a sub-argument and is used as a premise for another conclusion within a complex argument.

Application:

• C3, C4, and C5 are intermediate conclusions because they are not the final conclusion.

• Ex:

P1) Big box retailers can order massive quantities at a significantly reduced price.

P2) Small local stores can’t match the low prices of big box retailers.

—

C3) Therefore, some small local stores will go out of business.

—

C4) Therefore, there will be a reduction in business competition.

—

C5) Therefore, there will be a reduction in the variety of goods available to consumers.

—

C6) Therefore, big box retailers aren’t good for small cities.

Deductive Argument

Definition:

• An argument in which the premises are intended to provide a guarantee of the truth of the conclusion.

Application:

• aims to achieve certainty

• In a successful deductive argument, the conclusion necessarily follows from the premises, and the premises are true

• Ex:

P1) All cats meow.

P2) Sam is a cat.

—

C3) Therefore, Sam meows.

Valid Argument

Definition:

• a deductive argument in which the premises necessarily lead to the conclusion; that is, it is impossible for the arguments premises to be true and its conclusion to be false. If it is possible for the premises of the deductive argument to be true and the conclusion be false, the argument is invalid.

Application:

• You dont need to actually know the content of the premises if you can recognize the arguments logical structure

• ex: of a valid argument:

P1) All dogs are mammals. (True)

P2) All mammals are warm-blooded. (True)

—

C3) Therefore, all dogs are warm-blooded. (True)

Sound Argument

Definition:

• a deductive argument that is valid and has only true premises

Application:

• all premises must be true, the conclusion also is true

• Ex:

P1) All humans are mortal.

P2) Socrates is human.

—

C3) Therefore, Socrates is mortal.

Propositional logic

Definition:

• A type of symbolic logic that deals with the relationships between propositions using the basic logical connectives: “and,” “or,” “not,” and “if… then.”

Application:

• Exploring the relationships between statements that are capable of being true or false

• Cannot be applied to inductive arguments or arguments from analogy

• Ex:

If it is raining outside, then I will need an umbrella.

Truth value

Definition:

• the truth or falsity of a statement.

Application:

• ex: the statement “Ontario is a province in Canada” is true

Negation

Definition:

• a statement of the form “Not P.” a negation is true if and only if the statement it negates is false.

• Not (-)

Application:

• when symbolizing, we always put the proposition in the positive, then we negate it

• “It is not sunny outside” is a negation of “it is sunny outside”

• Ex:

  • “That house is not suitable for my large family,” can be symbolized as -H

Conjunction

Definition:

• a statement of the form “P and Q.” A conjunction connects two statements such that it is true if and only if the connected statements are true.

• And (&)

Application:

• only true if both statements it connects are true

• Ex:

  • I & S = Isaac is tired although he got lots of sleep last night.

Disjunction

Definition:

• a statement of the form “P or Q.” A disjunction connects two statements such that it is true if and only if one or both connected statements are true.

• Or (v)

Application:

• true when either of the propositions are true or when both are true

• Ex:

  • R v U = Im going to wear a raincoat today or Im going to carry an umbrella.

  • C v S = Im going to have cream or/and sugar in my coffee

Conditional

Definition:

• a statement in the form of”If P, then Q.” A conditional does not assert that P actually is the case but states that if P is the case, then Q is also.

• If, then (>)

Application:

• claims that if something is true, then something else is also true

• The proposition before the > is called the antecedent

• The proposition after the > is called the consequent

• Antecedent > consequent

• Ex:

  • S > C = If it is snowing, then it is cold outside

Truth table

Definition:

• shows all the possible truth values for a proposition(s)

Application:

• shows the different possibilities of trues and falsies

• If you use (2^n) where n = the number of different statements, you can determine how many rows there’ll be

• Conjunction is T in a truth table when all statements are true

• Disjunction is T in a truth table when at least one statement is true

• Conditional or hypothetical is F only if P is T and Q is F (in model P>Q)

Modus ponens (valid)

Definition:

• Affirming the antecedent

  • When using conditionals

• a common valid argument form with the following structure:

  • If A, then B.

  • A.

  • Therefore, B.

Application:

If I need more money, then I will have to get a job.

I need more money.

Therefore, I will have to get a job.

A>B

A

B

VALID

Modus Tollens (valid)

Definition:

• denying the consequent

  • Working with conditionals

• A common valid argument from with the following structure:

  • If A, then B.

  • Not B.

  • Therefore, not A.

Application:

P1) If I want to help protect the environment, then I should buy an electric car.

P2) Im not buying an electrical car.

—

C3) Therefore, I dont want to help protect the environment.

A>B

-B

-A

VALID

Affirming the consequent (Fallacy)

Definition:

• this is a fallacy because it treats P as if it is necessary for Q

Application:

P>Q (if it rains, then i will need an umbrella)

Q (i need an umbrella)

P (therefore, it rained)

INVALID

Denying the antecedent

Definition:

• this is a fallacy because it treats P as if it is necessary for Q

Application:

P>Q (if it rains, then i will need an umbrella)

-P (it is not raining)

-Q (i dont need an umbrella)

INVALID

Sufficient condition

Definition:

• enough

Application:

The antecedent is sufficient enough for the consequent

Necessary conditions

Definition:

• required

Application:

• the antecedent is needed for the consequent