Symbolic Logic: Ch. 1

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Logic

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-Organized body of knowledge, or science, that evaluates arguments
-Aim: develop a system of methods and principles that we may uses as criteria for evaluating arguments and creating our own.

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Argument

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-a group of statements including
PREMISES and CONCLUSION
-purports to prove something--requirements:
1) factual claim: At least one of the statements must CLAIM to present evidence or reasons (they don't have to be actual evidence or true reasons)
2) inferential claim: There must be a CLAIM that the alleged evidence or reasons supports or implies something--i.e. a claim that something follows from the alleged evidence (The premises don't ACTUALLY have to support the conclusion)

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explicit inferential claim

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asserted by premise or conclusion indicator words
*BUT, the mere occurance of an indicator word does NOT GUARANTEE the presence of an argument

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implicit inferential claim

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exists if there is an inferential relationship b/t the statements, but no indicator words

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Premises

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In an argument, the STATEMENTS claimed to provide support for, or reasons to believe, the conclusion

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Conclusion

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In an argument, the STATMENT that the evidence (premises) is claimed to support or imply; i.e. the statement claimed to follow from the premises

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Truth Value

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Truth or falsity of a STATEMENT

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Statement

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A sentence that is either true or false (typically declarative)

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Extraneous statements

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Statements that are neither premises nor conclusions should not be inlcuded in the list of premises

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inference

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the reasoning process expressed by an argument; used interchangeably with 'argument'

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syllogistic logic

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-a kind of logic in which the fundamental elements are terms
-arguments are evaluated as good or bad depending on how the terms are arranged in the argument

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modal logic

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

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Types of Nonarguments

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Simple Noninferential Passages
Expository Passages
Illustrations
Explanations
Conditional Statements

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Deductive Argument

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an argument in which it is claimed that it is IMPOSSIBLE for the conclusion to be false given that the premises are true
-The conclusion is claimed to follow NECESSARILY from the premises

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Inductive Argument

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an argument in which it is claimed that it is IMPROBABLE for the conclusion to be false given that the premises are true
-The content of the conclusion goes beyond the content of the premises
-The conclusion is claimed to follow PROBABLY from the premises

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Three criteria used to distinguish between deductive and inductive arguments

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1. Indicator words
2. Actual strength of the inferential link b/t premises and conclusion (whether conclusion ACTUALLY follows necessarily or probably)
3. Form of argument

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Deductive Argument Forms

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1. Argument based on mathematics
2. Argument from definition
3. Categorical Syllogism
4. Hypothetical syllogism
5. disjunctive syllogism

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Argument based on mathematics

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The conclusion depends on some purely arithmetic or geometric computation or measurement

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Argument from definition

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The conclusion is claimed to depend merely upon the definition of some word or phrase used in the premise or conclusion

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Categorical syllogism

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Each statement begins with "all," "no," or "some"

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Hypothetical syllogism

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a syllogism that has a conditional statement for one or both of its premises

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Disjunctive syllogism

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A syllogism having a disjunctive statement (either...or...)

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syllogism

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An argument consisting of exactly two premises and one conclusion

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Inductive Argument forms

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Prediction
Argument from analogy
Generalization
Argument from authority
Argument based on signs
Causal Inference

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Scientific Arguments

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Inductive: Aimed at discovery of a law
Deductive: application of known laws to specific circumstances (But watch out for predictions!)

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Causal Inference

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Inductive: Argument that proceeds from knowledge of a cause to a claim about an effect or vice versa

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Argument based on signs

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Inductive: proceeds from knowldege of a sign t a claim about the thing or situation the sign symbolizes (an intelligent message)

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Prediction

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Inductive: Argument that proceeds from knowledge of the past to a claim about the future.

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Valid Argument

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(For deductive)
an argument in which it is impossible for the conclusion to be false given that the premises are true
PASSES TEST 2

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Test for Validity

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1. Are the premises true?
2. Does the conclusion follow necessarily from the premises?

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Sound Argument

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(Deductive)
Argument is valid and has all true premises
PASSES TEST 1 AND 2

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Test for Strength

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(inductive)
1. Are the premises true?
2. Does the conclusion follow probabalistically from the premises?
3. Is there info available to me that affects negatively the probability of the conclusion?

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Strong Argument

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(Inductive)
The conclusion follows probably form the premises
PASSES TEST 2

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Cogent Argument

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-The premises are true
-The conclusion follows probably form the premises
-There is no more info that would negatively affect the probability of the conclusion
PASSES TEST 1, 2, 3

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Explanandum

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the statement that describes the event or phenomenon to be explained (the second part)

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Explanans

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the statement or group of statements that purports to do the explaining

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Necessary condition

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B is said to be a necessary condition for A whenever A cannot occur without the occurence of B
ex. being an animal is a necessary
condition for being a dog
If X is not an animal, then X is not a dog.

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sufficient condition

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A is a sufficient condition for B whenever the occurrence of A is all that is needed for the occurrence of B
ex: Being an animal is a necessary condition for being a dog
If X is a dog, then X is an animal

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invalid deductive argument

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actually true premises and actually false conclusions

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weak inductive argument

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true premises and probably false conclusion