Logic

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Argument

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- group of Statements, one or more of which is meant to support the conclusion

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Premises

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- statements that set forth reasons for the conclusion

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Statement

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- sentences that are either T or F

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Inference

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- reasoning process thats set forth by the argument

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Conclusion Indicators

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- therefore, thus, wherefore, hence, it follows that, for this reason, accordingly, consequently, so, as a result, implies that

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Premise Indicators

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- Since, because, for, as, given that, seeing that, owing to, for the reason that,

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No Indicators

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- Identify the main point of the argument (Conclusion) Everything else is a premise

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Argument features:

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1. One of the Statements must claim to present evidence or reason

2. Must be a claim that something follows from alleged evidence or reasons

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Types of Non Arguments

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1. Simple

2. Illustrations

3. Explanations

4. Conditional

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Simple Non Argument

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non inferential passage - warning - advice- often but not always - beliefs and opinion

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Illustrations non argument

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- expressions involving one or more examples

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Explanations non argument

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- expressions that shed light on something, usually a fact

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Conditional non argument

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- a hypothetical statement - if… then - not presenting evidence

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Sufficient Conditions

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- A is a sufficient condition for B whenever A is all thats needed for B

Ex: being a dog is a sufficient condition for being an animal

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Necessary Conditions

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- B is a necessary condition for A whenever A cannot occur without B

Ex: being an animal is a necessary condition for being a dog

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Deductive Arguments

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- Rely on necessary reasoning: Conclusion defintely follows from the premises

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Inductive Arguments

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- rely on probabilistic reasoning: Conclusion probably followss from the premises

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Indicators - Inductive

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- probably, most likely, plausibly, unlikely

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Indicators - Deductive

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- necessarily, certainly, absolutely

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Deductive Arguments:

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Argument from a definition

Categorical syllogisms

Hypothetical Syllogism

Disjunctive Syllogism

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Argument from a definition

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- conclusion depends on a definition

Ex: Tom is a bachelor. Therefore, Tom is an unmarried man

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Categorical syllogisms

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- in which statements begins with “all”, “no”, or “some”

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Hypothetical Syllogism

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- with a conditional statement for one r both of its premises

Ex: P: If t rains, I get wet / P: It rains = C: I get wet

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Disjunctive Syllogism

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- contains an either/or statement (either A or B), one option is eliminated, the other is concluded

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Inductive Argument forms:

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Predictions

Arguments from analogy

Generalizations

Argument from authority

Argument based on signs

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Predictions

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Arguments from analogy - the argument depends on similarity between 2 things

Ex: Because my iphone works well your iphone works well too

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Generalizations

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- proceed from a claim about a sample to claim about the whole (lots of statistical claims)

Ex: because one drink from starbucks is good therefore all drinks from starbucks are good

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Argument from authority

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- x is true because expert said so

Ex: smoking is bad because the surgeon general said so

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Argument based on signs

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- Conclude something is true based on a sign

Ex: there is road work ahead because a sign said so

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Valid Deductive Argument

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- it is impossible for the conclusion to be false when it is assumed that all of the premises are true

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Invalid Argument

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- conclusion can be false when its assumed all the premises are true

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How to Check for Validity:

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Assume the truth of premises -Can conclusion be false?

MUST ASSUME THE PREMISES ARE TRUE TO DETERMINE VALIDITY EVEN IF IN REALITY THEY ARE NOT

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Sound Argument:

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if it is both Valid and has all true premises in reality!

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Unsound Argument:

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if it is invalid or it has one or more false premises (or both)

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Strong Inductive Arguments:

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it is improbable that the conclusion is false when it is assumed all premises are true

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Weak Inductive Arguments:

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probable that the conclusion is false when its assumed all premises are true

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Cogent Inductive Argument:

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Strong and has really all true premises

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Uncogent Inductive Argument:

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Weak or has one or more false premises

A weak Inductive Argument is always uncogent

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Substitution Instance

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= an argument or statement that has the same form as another argument or statement.

Ex: P1 If it rains, I get wet. P2 It Rains C I get wetP1: If R then W P2: R C: W - Isolate the argument form and be able to replace it

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Counter example Method to find validity

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1. State argument form

2. Select terms to substitute

3. Replace letters to create premises, to create an obviously false conclusion

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implicit claim

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exists if there is an inferential relationship between the statements in a passage, but the passage contains no indicator words

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Warning

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is a form of expression that is intended to put someone on guard against a dangerous or detrimental situation

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Piece of Advice

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is a form of expression that makes a recommendation about some future decision or course of conduct

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Statement of Belief or Opinion

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is an expression about what someone happens to believe or think about something

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causal inference

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is an argument that proceeds from knowledge of a cause to a claim about an effect, or, conversely, from knowledge of an effect to a claim about a cause

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particular statement

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is one that makes a claim about one or more particular members of a class

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general statement

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makes a claim about all the members of a class.) It is true, of course, that many inductive and deductive arguments do work in this way; but this fact should not be used as a criterion for distinguishing induction from deduction

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Deductive or Inductive

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1. arguments in which the premises provide absolute support for the conclusion. such arguments are always deductive.

2. arguments having a specific deductive character or form (e.g., categorical syllogism). this factor is often of equal importance to the first, and, when present, it provides a clear-cut indication that the argument is deductive.

3. arguments having a specific inductive character or form (e.g., a prediction). arguments of this sort are nearly always best interpreted as inductive.

4. arguments containing inductive indicator language (e.g., “it probably follows that . . .”). since arguers rarely try to make their argument appear weaker than it really is, such language can usually be trusted. But if this language conflicts with one of the first two factors, it should be ignored.

5. arguments containing deductive indicator language (e.g., “it necessarily follows that . . .”). arguers occasionally use such language for r hetorical purposes, to make their argument appear stronger than it really is, so such language should be evaluated carefully.

6. arguments in which the premises provide only probable support for the conclusion. this is the least important factor, and if it conflicts with any of the earlier ones, it should probably be ignored.