Philosphy Logic Section

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Logic

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-the organized body of knowledge, or science that evaluates arguments

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What is the aim of Logic?

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- to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own.

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Argument

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

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Two Groups of Arguments

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- Premises support conclusion (good arguments)
- Premises don’t support conclusion (bad arguments)

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Purpose of Logic

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-Distinguish between bad and good arguments

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An Argument is a group of _________

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- Statements

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Statement

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- Sentence that is either true or false (typically declarative)

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Tiger Woods plays golf and Mos Def learned to rap from Vanilla Ice. (State the amount of statements and truth value)

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- 2 statements
- last statement was false

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Truth Value

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- truth or falsity

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Types of Sentences that are not Statements

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- (question)
- (proposal)
-(suggestion)
- (command)
- (exclamation)

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Premises

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-Statements that are set forth the reasons or evidence

Premises ==+> Conclusion

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Conclusion

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- statement that the evidence is claimed to support or imply

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All humans are animals.
Clay Matthews of the Packers is a human.
Therefore Clay Matthews of the Packers is an animal.

Number of Statements?
Number of Premises?

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- 3 statements
- 2 premises

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Conclusion Indicators

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Therefore, wherefore, thus, consequently, we may infer, accordingly, we may conclude, it must be that, for this reason, so, entails that, hence, it follows that, as a result

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Premise Indicators

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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

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Break down

Expectant mothers should never do recreational drugs, since the use of these drugs can jeopardize the development of the fetus.

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2 Statements
Premise indicator:: “since”

P:: since the use of these drugs can jeopardize the development of the fetus

C:: Expectant mothers should never do recreational drugs

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“for reason that” vs. “for this reason”

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Premises vs. conclusion indicator

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Tips for when there are no indicator words present…

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- what is the main point of the passage?
-what is the arguer trying to prove?
-what single statement is claimed (implicitly) to follow from the others?

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Guide for Reconstructing Arguments

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- Close as possible to the original version
- Premises and conclusion be complete sentences and meaningful in order in which they are listed
-compound arrangements of statements in which various components are stated to be true are considered separate statements (in section 1)

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Statements not intended to support the conclusion or act as a conclusion should not be considered in the analysis of the argument

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-introductions and passing comments … counter critque…. should not be considered apart of the premises

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Inference

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-narrow sense: reasoning process expressed by an argument

-broad: interchangeable with argument

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Proposition

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- narrow sense:: meaning or information content of statement

- Interchangable with proposition and statement

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Father of Logic

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Aristotle

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What seperates Aristotle from his predecessors?

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- devised systematic criteria for analyzing and evaluating arguments

-developed syllogistic and modal logic

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Syllogistic Logic

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- terms are fundamental elements

-arguments evaluated to good or bad depending on how terms are arranged

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Modal Logic

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- logic involves concepts such as possibility, necessity, belief, and doubt

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Two conditions for a passage to purport to prove something

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1. a t least one statement claiming to present evidence

2. claim that follows from alleged evidence

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Do premisies need to present actual evidence or true reasons?

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NO.... it must CLAIM to present evidence or reasons ... there must be a claim or reasons to imply something

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Inferential Claim

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- simply a claim that the passage expresses a certain type of reasoning process

(that sumething supports or implies something or that somethign follows from something)

-objective feature os an objective feature of an argument grounded in its language or structure

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why are intentions not relevant in analyzing an inferential claim?

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-Because an inferential claim is objective

-intentions are subject in nature and usually are not accesible to the arguer

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Types of inferential CLaims

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Implicit or explicit

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Explicit Inferential Claim

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- usually asserted by premise or conclusion indicator words (thus, since, because, therefore, hence, etc...)

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What do conclusion indicator words do in terms of arguemnts

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Express that something is to be inferred

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Implicit Inferential Claim

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- exists if there is an inferential relationship but the passage contains no indicator words...

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Simple Noninferential Passages

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-Warning
-Piece of Advice
- Statement of Belief/ Opinion
-Loosely Associated Statements
-Report

-Unproblematic passages that lack calim of anything being proved

-Passages may have statements that could be premises or conclusions but lack a claim that any potential conclusion is supported by premises

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Warning Passage

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-Noninferential Claim
-intended to put someone on gaurd

ex "watch out so you don't slip"

no evidence to prove that such statements are true, no argument

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Piece of Advice

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-Noninferential Claim
- reccomendation for the future

-You should keep a few things in mind before buying a car. test drive teh car.

- there is no evidence that is intended to prove anthing ... no arguement

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Statement of Belief/ Opinion

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-Noninferential Claim
-expression about what someone happends to think or believe

ex " we believe that our friends are better than yours. We believe our friends are caring. "

-no claim is made that his or her belief or opinion is suproted by evidence or that it supprots the conclusion

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Essential to an arguement is....

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-conclusion that follows from premises that claim to evidence for conclusion

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Loosely Associated Statements

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-Noninferential Claim
- statement about the same general subject that lack claim that oneproves another

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Report

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-Noninferential Claim
-group of statements that convey information about the same topic or event
-often their are premises and even a squential flow to information but no claim is delivered.. none of the statements act as evidence in a struturally valid casual relationship that implies a process of reasoning
-Reports might contain arguements such as in direct quotes but given that the author does not make a claim directly it is recognized as a passage with an argument in it not an argument in itself

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Expository Passages

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-Noninferential Claim
- Topic sentece that is expounded
- "flesh out an idea"
-"show how" vs "prove that"

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Illustration Passages

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-Noninferential Claim
-intended to show what someting means or how it is done
- they do not claim anything is being proved

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Arguements from Example

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- example to prove a claim
- typically claims are not common knowledge

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Explainations

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-Noninferential Claim
- expression that purports to shed light on some even tof phenonmenon

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Two parts of Explanation

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Explanas (claims that shed light on something)

Explanadum (Accepted fact)

-"showing why" vs. "proving that"

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Conditional Statement

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- an "if... then" statement what contains an antecedent and consqeuent
-not an arguement because it fails to have a statement taht claims to present evidence for another
- no assertion that either antecedent or consquent is true
-Premises in an arguement are claimed to be true
-inferential content of conditional statements can often be rewritten as infrential arguments

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3 Rules for relating conditional statement to arguments

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1. A single conditional statement is not an argument

2. A conditional statement may serve as either the premise or the conclusion of an argument

3. The inferential content of a conditional statement may be reexpressed to form an argument

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Necessary and Sufficient Conditions

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-A necessary condition of a statement must be satisfied for the statement to be true

A sufficient condition is one that, if satisfied, assures the statement's truth

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Deductive Argument

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- is an argument incorporating the claim that it is impossible for the conclusion to be false
given that the premises are true

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Inductive Argument

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- an argument incoporating the claim tht it is impropable that the conclusion be false given that teh premises are true

-probabilistic reasoning

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Inductive vs Deductive

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-Improbable vs Impossible

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Objective Features of an Argument to determine it to be Inductive or Deductive

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1. the occurence of special indicator words

2. actual strength of the inferential link between premises and conclusion

3. for or style of argumentation

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Special Indicator Words

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- Inductive Indicators :: probable, improbable, plausible, implausible, likely, unlikely and reasonable to conclude

Deductive Words:: certainly, absolutely, definitely

((it must be the case is a conclusion indicator that can appear in either arguments))

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Forms of Deductive Arguments

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- mathmatics
- definition
- categorical
- hypothetical
- disjunctive syllogisms

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Argument Based on Mathmatics

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depends on purely arithmetic or geometric computation or measurement

- all arguements based on pure mathmatics are deductive

((exception /// statistics))

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Argument from Definition

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- Conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion

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Syllogism

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-Argument consistenof exactly two premises on one conclusion

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Categorical Syllogism

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- a syllogism in which each statement begins with on of the words "all," "no," or "some"

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Hypothetical Syllogism

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- syllogism having a conditional statement for one or both of its premises

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Disjunctive Syllogism

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- having a disjunctive statement ("either ... or" statement)

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Disjuntive Definition

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1. Serving to separate or divide.
2. Grammar Serving to establish a relationship of contrast or opposition. The conjunction but in the phrase poor but comfortable is disjunctive.
3. Logic
a. Of a proposition that presents two or more alternative terms.
b. Of a syllogism that contains a disjunction as one premise.
n. Grammar

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Inductive Forms

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content of the Con. is in come was intended to "go beyond" the content of the Pres...

-Predictions about the future
-Arguments from analogy
-Inducitve Generalizations
- Argu. from authority
- Argu. based on signs
- Casual inference

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Prediction

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- argu. that proceeds from our knowledge of the past to a claim about the future

- whenever an argument is arguing the future that argument is inductive

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Argu. from Analogy

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- is an argu. that depends on the existenceof analogy, or similarity, between two things or states of affairs

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Generalization

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- an argu. that proceeds from the knowledge of a selected sample to some claim about the whole group

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Argu. from Authority

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- an argument that concludes something is true becase a presumed expert or witness has said that it is

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Casual Inference

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- procedes form knowledge of a cause to a claim about an effect conversely from knowledge of an effect to a claim about a cause

-because specific instances of cause and effect can never be known with absolute certainty, one may usually interpret such arguments as inductive

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Complete certainty

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deductive

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Probablistic Reasoning

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inductive

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Two claims found in every argument

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Inferential and Factual

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Factual Claim

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- a claim that evidence or reasons exist

-(premises which present genuine evidence)

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Inferential Claim

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- a claim that the alleged evidence or reasons support something

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Two types of Deductive Argu.

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Valid or invalid

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Valid Deductive Argu.

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- impossible for conclusion to be false given that the premises are true

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Invalid Deductuve Argu.

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- deductive argu. in which it is possible for the conclusion to be false given that the premises are true

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If te conclusion follows strictly from prems. the argument is ...

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argument is valid

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To test an argument for validity we begin by assuming ...

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all the premises are true and try to find possible contradiciton in conclusion

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Is validity determined by true statements?

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No... validity is determined by the relationship between premises and conclusion

(ask the question do the prem. prove the conclusion )