Expository Writing--Food: Article, Critical Thinking, Analyitical Essay

All,
   After reviewing the film "Forks Over Knives", please begin the two-fold process of critique.  1) Read through the following critique of the movie (Forks Over Knives Critique); 2) determine which of the arguments presented from the movie and the critique are better and why. 

You will be writing an analytical essay comparing the relative worth of the two sets of arguments.  This is the beginning of an argumentative essay.  The paper will be due Monday.

Expository Writing: Food--Logical Reasoning Dilemma

Please give a detailed response to the following dilemma.  Give your reasons.

One day, you may be called upon to fire one of your three equally qualified assistants in order to save your department money.

• Do you fire the one with the least experience, but whom you personally recruited away from his previous job, with a promise that ditching to his other job would be good for his career?
• Do you fire the one who brought in the least money this year, but who just had a baby with a serious medical condition?
• Do you fire the one who is hardest to get along with, but who has been with the company for thirty-five years and plans to retire in 18 months?

Logic 5.3

Valid syllogisms conform to certain rules, as evidence by Aristotle. There are five rules from the Boolean perspective, and four from the Aristotelian perspective. (The fifth rule does not apply in the Aristotelian perspective, but the first four remain.)

Rule 1: The middle term must be distributed at least once.

Rule 2: If a term is distributed in the conclusion, then it must be distributed in a premise.

Rule 3: Two negative premises is not allowed.

Rule 4: A negative premise requires a negative conclusion, and a negative conclusion requires a negative premise.

Rule 5: If both premises are universal, the conclusion cannot be particular.

Logic 5.1

The major, minor, and middle terms of a standard categorical correspond directly to the conclusion of a standard categorical syllogism:

Major Premise: contains the predicate term of the conclusion
Minor Premise: contains the subject term of conclusion
Conclusion: Contains the major term of the major premise as its subject; contains the minor term of the minor premise as its predicate.

The conclusion is a the standard indicator of the major and minor terms of an argument. The middle term is that term that appears twice in the premises.

Mood: The standard categorical notation for the three propositions in a standard categorical syllogism: AAA, EAO, AII, etc.

Figure: The four possible distributions of terms in the premises of a standard categorical syllogism:

MS(1) SM(2) MS(3) SM(4)
PM PM MP MP

Unconditionally Valid Forms
AAA-1
EAE-1,2
AII-1,3
EIO-1,2,3,4
AEE-2,4
AOO-2
IAI-3,4
OAO-3


Conditionally Valid Forms
AAI-1,3,4
EAO-1,2,3,4
AEO-2,4

Logic 4.5

Traditional Square of Opposition:

Contradictory: Complete opposition between propositions. One of the contradictory set must be true and the other must be false.
Contrary: Expresses only partial opposition; at least one must be false, however, both might be false.
Subcontrary: Expresses only partial opposition; at least one must be true, however, both might be true.
Subalternation: Truth transmits only downward; falsity transmits only upward.

Inferences that do not transmit their truth-values are said to be illicit.
Illicit Contrary:
It is false that all A are B
Therefore, no A are B
It is false that no A are B.
Therefore, all A are B.

Illicit Subcotrary:
Some A are B.
Therefore, it is false that some A are not B
Some A are not B.
Therefore, some A are not B.

Illicit Subalternation:
Some A are not B.
Therefore, no A are B.
It is false that all A are B.
Therefore, it is false that some A are B.

Remember the Existential Fallacy and distinguish between unconditionally valid inferences and conditionally valid inferences.

Logic 4.4

“No cats are dogs” = “No dogs are cats”
“Some dogs are black” ≠ “Some dogs are not black”

Conversion, Obversion, and Contraposition yield new propositions that may or may not have the same truth-value depending on the starting proposition.

Conversion: Switching the subject and predicate terms. E and I propositions are Logically Equivalent, while A and O propositions are not.

Conversion for E and I propositions can be used to make immediate inferences. A and O propositions cannot, and are therefore Illicit Conversions.
Ex:
“All cats are dogs. Therefore, all dogs are cats”
“Some animals are not dogs. Therefore, some dogs are not animals.” Both of the these arguments commit the fallacy of illicit conversion.

Obversion: 1) Change the quality; 2) replace the predicate with its term opposite.
Ex: All S is P
Step 1: No S is P; Step 2: No S is non-P
“All cats are animals” becomes “No cats are non-animals.”

The class complement is the opposite of class term.

When an obversion is made then made again, the proposition will be the same as the starting proposition:
“All presidents of the United States are citizens”
Obversion:
“No presidents of the United States are non-citizens”
Obversion:
All presidents of the United States are citizens”

All obversions retain their truth-value.

Ingenuity is required to find a term’s complement. All immediate inferences from obversion are valid.


Contraposition: 1) switch the subject and predicate terms; 2) Replace the subject and predicate terms with their complement.

All S is P—All non-P is non-S

A and O propositions retain their truth-value in contraposition, while E and I propositions do not.

Inferences from E and I props are logically licit, while inferences from A and O propositions are logically illicit.

In order to remember which propositions retain their truth value for conversion and contraposition remember the second and third vowels of each word:

ConvErsIon
ContrApOsition

Logic 4.3

A and E propositions are considered to have existential import by Aristotle if their subject terms denote existing things. The Boolean (George Boole) position is that no universal propositions imply existential import. Basically, existential import is a limiting factor on what counts as a proposition.

“All dogs are animals” has existential import
“All unicorns are wild” has no existential import.

Venn Diagrams: A diagram to indicate the distribution of the terms of a proposition. No E import for A and E (there is no X).

The Modern Square of Opposition
A and O propositions are exactly opposite, since A asserts that the entire subject class is part of the predicate class, while O asserts that there is something of the subject class that is not in the predicate class. A and O are contradictories. E and I propositions are also contradictories, since E asserts that the overlap is empty, while I asserts there is at least one thing in the overlap.

Contradictory relationships establish the modern square of opposition:


Contradictory relations necessarily have the opposite truth-value. If A is true, then O is false and vice versa; If E is true, then I is false and vice versa. No other inferences, however, are possible; they are logically undetermined.

Immediate Inferences have one proposition and follow necessarily from the logically determinable opposition.
“Some students are gifted at math.
Therefore, it is false that all students are gifted at math.”

Immediate inferences are unconditionally valid regardless if they assert anything about existing things. Once we assume the truth or falsity of a proposition, we can immediately infer the truth value of its claimed inference.

If we use a Venn diagram to show the relationship between a proposition and its immediate inference, then if the two diagrams are the same (or the conclusion shows at least as much as the premise), then the inference is valid; otherwise it is not.

Existential import is key if we are to make the case for a valid immediate inference from all to some. From the Boolean standpoint, since we cannot assume Existential Import, A to I and E to O inferences commit the Existential Fallacy.

Logic 4.1-4.2

4.1
A Categorical Proposition relates that either all or part of one class denoted by the subject term is included in or excluded from the class denoted by the predicate term

•Note that the subject term and predicate term are not the same things the subject and predicate respectively.

All A is B: (the whole subject class is included in the predicate class)
No A is B: (the whole subject class is excluded form the predicate class)
Some A is B: (part of the subject class is included in the predicate class)
Some A is not B: (part of the subject class is excluded from the subject class)

A Categorical Proposition is in Standard Form if it expresses these relations clearly.

Standard Form: Quantifier—Subject Term—Copula—Predicate Term

All S are not P is not standard form because it is ambiguous (No S is P v Some S is not P)

4.2
Quality (Universal or Affirmative), Quantity (Universal or Particular), and Distribution (make up the essential parts of a standard categorical proposition.

A (Universal Affirmative): All S is P
E (Universal Negative): No S is P
I (Particular Affirmative): Some S is P
O (Particular Negative): Some S is not P

Distributions
A= Only the S term is fully distributed
E= S and P terms are fully distributed
I= No term is distributed
O= Only the P term is fully distributed

Logic 1.4

Evaluation of every argument consists in evaluating either the factual claim or the inferential claim of an argument, or sometimes both. Succeeding in proving the inferential claim makes an argument valid, but the conclusion may still be false, or the argument may not be sound.

Valid Deductive Arguments: an argument in which it is impossible for the conclusion to be false given that the premises are true and the conclusion follows from the premises.

Invalid Deductive Arguments: an argument in which it is possible for the conclusion to be false given that the premises are true.

How to test validity: Assume the premises are true. If it is possible to deny the conclusion given the premises, then the argument is invalid.
Ex: All teachers are lunatics.
Mr. Nicholson is a lunatic.
Therefore, Mr. Nicholson is a teacher.

* Validity is not determined by the truth or falsity of premises and conclusions, but by the relationship between premises and conclusion.

* An argument with true premises, but a false conclusion is obviously invalid. This is the foundation of logic.

Sound Argument: A deductive argument that is valid and has all true premises.

Unsound Argument: A deductive argument that is invalid, has one or more false premise, or both.

*The addition of a false premise to an already sound argument does not make it unsound. For an argument to be unsound, it must have a false premise as needed by the argument, or be invalid.

Inductive Arguments: It is improbably that the conclusion be false and the premises be true.

Strong Inductive Arguments: it is improbable that the conclusion be false given that the premises are true.

Weak Inductive Arguments: it is not improbable that the conclusion be false given that the premises are true, but it is claimed to be probable.

Testing Inductive Validity: Assume the premises are true, then consider whether the conclusion is probably true.
E.g., All emeralds examined up to this point have been green, therefore, the next emerald we examine will be green.

E.g., During the last 2000 years, Christianity has been a dominant force in Western Civilization. Therefore, the American presidency will probably continue to be a secular office.

A Cogent Argument is an inductive argument that is strong and has all true premises. It is the inductive analog of a sound deductive argument.
An Uncogent Argument is an inductive argument that is weak, has one or more false premises, or both.

The most an inductive argument can prove is probability.

Total Evidence Requirement: unlike deductive arguments, the premises of an inductive argument must not only be true, but they must not ignore evidence to the contrary.

Statements: true or false;
Groups of Statements: arguments or non-arguments;
Arguments: Inductive or Deductive;
Deductive Arguments: Valid or Invalid;
Valid Deductive Arguments: Sound or Unsound;
Inductive Arguments: Strong or Weak;
Strong Inductive Arguments: Cogent or Uncogent.

Logic 1.3

Deduction and Induction

•Deductive Arguments: it is impossible for the conclusion to follow from the premises, be false and the premises to be true. The conclusion follows necessarily from the premises. (Possible worlds and counter-examples)

•Inductive Arguments: it is improbable that the conclusion be false given that the premises are true. The conclusion follows probably from the premises. (What is the nature of, and problems with, probability?)
Exs.

The difference lies in the strength of the inferential claim. Interpretation is required.
•Special indicators (probably, necessarily, etc.)
•The actual strength of the inferential link (possible worlds, counter-examples)
•The form or style of argument

Deductive Forms (analyticity)
• Mathematics
• Definitions
• Categorical Syllogisms (all, no, some)
• Hypothetical Syllogisms (if…then)
• Disjunctive Syllogisms (either…or)

Inductive Forms (goes beyond available content)
• Predictions
• Analogy
• Generalization
• Authority
• Signs
• Causal Inference (from cause to effect, Hume or Kant)


Generally, deductive arguments move from a position greater to or equal to their conclusions. Inductive arguments move from a position inferior to their conclusions. Exceptions occur, and these generally reveal problems for logic, most particularly induction. (Grue)

Logic 1.1

Logic is the organized body of knowledge or science that evaluates arguments.

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

Effect: Gain confidence in making and criticizing arguments.

Arguments: Claims that support a conclusion.

Two Types: Those that do support a conclusion, and those that do not do so.

Exs:

Statements: A sentence that is either true or false

What are some T/F statements?

Why are they T/F?

Truth-Value: The truth or falsity of a statement.

Questions, Proposals, Commands, Suggestions, Exclamations have no truth-value. Why not?

The statements that make up an argument fall into two classes:

The conclusion is supposed to follow, be supported by (the evidence) premises. Consider the application to science: evidence stands as the premises of a scientific conclusion.

What kind of entailment (“following through”) is involved? Induction? Deduction? Which is stronger? Why? How has this distinction been important in the history of philosophy?

Exs of good and bad arguments:

Conclusion Indicators: therefore, hence, so, etc.

Premise Indicators: since, because, for, etc.

Not all statements will have clear indicators. You must carefully and critically read for sense.

E.g.,

Often the first or last statement in a paragraph is the conclusion, but not always.

Demonstration of an argument:

“Since {P1} the secondary light [from the moon] does not inherently belong to the moon and {P2} is not received from any star or {P3} from the sun, and {P4} since in the whole universe there is no other body left but the earth, what must we conclude? Surely we must assert that {C} the lunar body (or any other dark and sunless orb) is illuminated by the earth. G. Galilei, The Starry Messenger)

Try to retain as much of the original as possible.

Exclude whatever is unnecessary in the statement.

Inference: The reasoning process expressed by an argument (for our purposes, synonymous with argument).

Proposition: The meaning, or information content, of a statement (for our purposes, synonymous).