Logic
Deductive Validity- the form of the argument is such that if the premises are true, then the conclusion must be true.
Validity vs. Soundness: soundness is valid form plus true premises, validity refers to the form only, not the truth of the premises.
We assess validity by distilling the form of the argument with letters standing in for the key terms:
All A are B
All B are C
Thus, all C are A
Categorical Syllogisms
· Can be composed of:
o Universal affirmatives (all A are B)
o Universal negative (no B are C)
o Particular affirmative (some A are B)
o Particular negative (some B are not C)
All A are B [major premise]
All B (middle term) are C [minor premise]
Thus, all C (minor term, subject term) are A (major term, predicate term)
A term is distributed if and only if that statement makes a claim about each and every member of the class denoted by that term.
Salmon’s Rules for testing the validity of categorical syllogisms
1. The middle term of the syllogism must be distributed exactly once
2. The subject and predicate terms of the syllogism may not be distributed exactly once
3. The number of negative statements must match the number of negative conclusions in the premises
Counter-instance: test the argument for validity by coming up with an instance of the form in which the premises are true and the conclusion false. Example:
Some cats are black
Some dogs are black
Thus, some cats are dogs
Venn Diagrams
Test for validity by illustrating the claims of the two premises in a Venn diagram. Shade out areas in which there can be no instances of the term to demonstrate universal claims. Use and x to demonstrate particular claims. If the syllogism is valid, the conclusion will be visible on the Venn diagram.
Hypothetical Syllogisms
Modus ponens (affirming the antecedent, valid)
If A, then B
A
Thus, B
Affirming the consequent (invalid)
If A, then B
B
Thus, A
Modus Tollens (denying the consequent, valid)
If A, then B
Not B
Thus, not A
Denying the antecedent (invalid)
If A, then B
Not A
Thus, not B
Disjunctive Syllogisms
X or Y
Not X
Thus, Y
This form of argument is always valid as long as one term is denied and one affirmed.
Fallacy of False Dichotomy: occurs when the two terms of a disjunctive syllogism are not mutually exclusive
Enthymeme
The instrument of logic distinctive to rhetoric. An abbreviated syllogism in which one of the premises is implied Example:
He will not pass the test because he did not study.
Enthymemes, unlike syllogisms, deal with probabilities rather than logical necessity
Signs: indications of that something has occurred, can be fallible or infallible
American Rhetorical Tradition 8/7
Three kinds of Persuasive Discourse
· Deliberative
o Aims to persuade someone to do something or believe something
o Concerned with the future
· Judicial
o Aims to defend or condemn someone’s actions
o Concerned with the past
· Ceremonial
o Aims to please or inspire
o Concerned with the present
The Five Canons of Rhetoric
· Inventio (Invention or discovery)
o The skill of creating or discovering arguments
o Differs from arguments which do not require rhetorical invention, such as witnesses in a court case
· Dispositio (arrangement or organization)
o The proper organization of an argument
· Elocutio (style)
o Difficult to define precisely, but concerned with the choice of words and the arrangement of sentences
· Memoria (memory)
o The ability to memorize a speech
· Pronuntiatio
o The proper pronunciation of words, also the overall delivery of the speech (hand gestures, etc.)
8/10
3 Kinds of Rhetorical Appeal
· Logos
o Rational/logical argument. Can be either:
§ Deductive- drawing conclusions from general propositions
§ Inductive- making generalizations based on observed facts
· Pathos
o Emotional appeal to the passions
· Ethos
o An appeal based on the character of the speaker, especially as evinced by the speech
8/12
Invention: Topics (topoi)
· Topics
o Strategies or stock ideas to help discovery/invent arguments
o Divided into two types, common and special
· Common topics
o Apply to all situations
o All common topics have sub-topics
§ Definition
· Genus
· Division
§ Comparison
· Similarity
· Difference
· Degree
§ Relationship
· Cause and Effect
· Antecedent and Consequent
· Contraries
· Contradictions
§ Circumstance
· Possible and impossible
· Past Fact and Future Fact
§ Testimony
· Authority
· Testimonial
· Statistics
· Maxims
· Laws
· Precedents
· Special Topics
o Grouped according to the three kinds of persuasive discourse: deliberative, judicial, and ceremonial
o Deliberative
§ Worthy: what is good in itself
§ Advantageous: what is useful to get some other good
o Judicial
§ Justice/injustice
o Cermonial
§ Virtues and Vices
§ Personal Assets and Achievements
8/13
Arrangement/Organization
· Introduction
o Informs the audience of the ends or objects of the discourse
o Disposes the audience to be receptive to the speaker
o At the end of the introduction, the reader should be attentive/benevolent/docile
· Statement of Fact
o Inform or remind the audience of essential information
o Should be lucid/brief/plausible (Quintilian)
8/14
Arrangement/Organization
· Confirmation
o the statement of your argument
· Refutation
o Rebuttals to counterarguments
o Refutation by
§ Reason (logos)
§ Emotion (pathos)
§ Character (ethos)
§ Wit
o Each of these has advantages and disadvantages
· Conclusion
o Remind the audience of your overall argument