LOGIC
ARGUMENTS

Note well: Neither argument type is true or false (only propositions are T/F). Deductive arguments are logically evaluated as valid/invalid and sound/unsound; inductive arguments are logically evaluated as strong/weak and cogent/uncogent (cf. Hurley, p. 51).

2. Types of Deductive and Inductive Arguments

a) Deductive arguments

• argument based on mathematics
• argument from definition
• categorical syllogism
• hypothetical syllogism
• disjunctive syllogism

 
Examples

1. X = 5 because 2 + X = 7. (mathematics)

2. Since Peter is a bachelor, he is an unmarried male. (definition)

3. All humans are mortal.
     Socrates is a human.
     Therefore, Socrates is mortal. (categorical syllogism)

4. If it’s Monday, then I have logic class tonight.
    It is Monday.
    So I have logic class tonight. (mixed hypothetical syllogism)

5. Either New England or St. Louis will win the Super Bowl.
    But St. Louis will not win the Super Bowl.
    Therefore, New England will win the Super Bowl. (disjunctive syllogism)

Types of Deductive Syllogism

1. Categorical syllogism:

All M is P
All S is M
Therefore, all S is P

2. Disjunctive syllogism:

Either P is true or Q is true
P is not true
Therefore, Q is true

3. Hypothetical syllogism:

If P is true then Q is true
P is true
Therefore, Q is true (mixed hypothetical syllogism)

If P is true then Q is true
If Q is true then R is true
Therefore, if P is true then R is true (pure hypothetical syllogism)

b) Inductive arguments

• prediction
• argument from analogy
• inductive generalization
• argument from authority
• argument based on signs
• causal inference
• statistical syllogism
• simple enumeration

 
Examples

1. David will probably excel in his current logic course because he’s always excelled academically. (prediction)

2. Gloria-Jean has demonstrated her ability to apply CPR (cardiopulmonary resuscitation) to a dummy in simulated cases of cardiac arrest. Therefore, she can be expected to apply CPR to actual cardiac patients effectively as well. (argument from analogy)

3. Western religions (Judaism, Christianity, Islam) are monotheistic. Therefore, all the major world religions are monotheistic. (inductive generalization)

4. Alan Greenspan, the chairman of the Federal Reserve, recently stated that the economy should improve in the fall. Given Mr. Greenspan’s wisdom in such matters, the economy probably will improve in the fall. (argument from authority)

5. The sign we just passed said there’s an accident up ahead, so it probably is the case. (argument based on signs)

6. My roommate woke up this morning feeling nauseous and with a terrible headache. He must have been downing mudslides at Babylon last night. (causal inference)

7. Most CCRI students are interested in improving their critical-thinking skills. Daniel is a student at CCRI. Therefore, Daniel is probably interested in improving his critical-thinking skills. (statistical syllogism)

8. Observant toddler: The cardinal I saw last month was red, and the one I saw last week was red, and the one I saw yesterday was red. So the next cardinal I see will be red. (simple enumeration)

Inductive Argument Forms

1. Inductive Generalization: A form of inductive reasoning that proceeds from particular premises (a sampling of X, a statistical percentage of X) to a general conclusion (universal, statistical).

a) Terminology:

• population: all members of a group, class, or category (referred to in the conclusion)
• sample: a subset of the population (referred to in the premise)
• target characteristic: that characteristic observed in the sample and concluded to be true of the population.

b) Types of Inductive Generalization:

• Universal generalization (UG)
• Statistical generalization (SG)

Universal Generalization: Concludes that something is true about all members of X (population) on the basis of what is observed (target characteristic) about some of them (sample). Hence, universal inductive generalizations reason from a sample of X (class or category) to a generalization about all members of X.

         General form:    X¹ is p.
                                   X² is p.
                                   X³ is p.
                                  All X’s are p.

Example: The students I’ve met in my logic class are personable and interesting (X¹, X², X³ are p.). So, probably all the students in my logic class are personable and interesting (All X’s are p.).

Statistical Generalization: Concludes that something is true about a statistical percentage of X (population) on the basis of what is observed (target characteristic) about a statistical percentage of them (sample). Hence, statistical inductive generalizations reasons from a statistical percentage of observed members of X (class or category) to a statistical percentage of X itself (entire class or category).

General form: X percent of observed As are F.
                       Thus, probably X percent of all As are F.

Example: 75 % of the professional wrestlers we interviewed admitted taking anabolic steroids. Consequently, probably 75 % of all professional wrestlers are taking anabolic steroids.

d) Assessing the Inductive Strength of Inductive Generalizations:

• representative sample: a sample is representative of a population if it reflects the variety internal to the population; and if the target characteristic(s) observed in the sample occurs with the same frequency or in the same proportion as they occur in the population. The size and diversity of the sample must be adequate.

2. Causal Inference/Argument

a) Causal concepts:

• causal relationship: any cause-effect relationship. Example: turning a key in a locked door/unlocked door allows entry

• causal proposition/statement: any proposition that asserts or denies that “A causes B” (causal relationship) in which A and B refer to specific things, objects, people, events, states of affairs, or their types (A causes B).
  Example: Increased stress causes increased risk of heart attack.
• causal generalization: asserts or denies a causal relationship between types of things or events (As cause Bs).
  Example: Power failures cause loss of unsaved data in a computer’s memory.
• causal argument/inference: An argument in which at least one causal proposition occurs either as a premise or as a conclusion.
• sufficient condition: A is a sufficient condition for B if and only if (iff) given that A occurs, B occurs. If B does not occur (~B), then A has not occurred (~A). Example: A dead battery (A) causes (sufficient condition) the engine to not start (B).

• necessary condition: A is a necessary condition for B if and only if (iff) given that B occurs, A occurs. If A does not occur (~A), then B does not occur (~B).
  Example:  If there is a fire (B), then oxygen is present (A). Oxygen is a necessary condition (in its absence, or without it, a fire cannot occur) but not a sufficient condition (which always causes the effect).
• partial cause: A is a partial cause, or contributing factor, of B if and only if (iff) given factors f, g, h, the occurrence of A increases the likelihood of B, and A is neither sufficient nor necessary for B to occur.
  Example: Smoking is a partial cause, or contributing factor, of cancer. Smoking, however, is neither a sufficient (since some people who smoke do not get cancer) nor a necessary (since some people with cancer never smoked) condition for cancer to occur.
• causal chain: a sequence of events that lead to a causal effect.
  Example: I have a long-standing habit of being easily distracted and lacking concentration (remote cause), so I forget my course textbook at school even though I have an exam tomorrow (intermediate cause), so I’m unable to study for the exam (proximate cause), so I perform poorly on the exam (causal effect).
• converging circumstances: independently occurring events or circumstances that converge at different points in a causal chain and thereby bear upon the occurrence of the event.
  Example: In the causal chain above, I can’t return to school to retrieve my book because my car won’t start, because my spark plug wires are wet, because I drove through large pools of water resulting from a heavy downpour of rain, which was caused by….

b) Types of Causal Inference/Argument:

• causal prediction: drawing a causal inference about an anticipated effect based on an actual cause; reasoning from cause to effect.
  Example: I left the cake in the oven. It will probably be burned by the time we get home.
• causal explanation: drawing a causal inference about a hypothesized cause based on an actual effect; reasoning from effect to cause. This is an argument because you are claiming that X is the cause, rather than ~X. If the alleged cause is disputable one must argue for it. If the cause is a known fact, then there is no argument, only an explanation.
  Example: Carl is not himself lately. He probably caught his wife cheating on him again.
• causal prescription: drawing a causal inference about a hypothetical situation. If A is (is not) desired, then do (do not) B.
  Example: An adequate amount of water intake is essential to human life. Therefore, if continued life is desired, take in an adequate amount of water.
   

3. Argument from Analogy

a) General Form

A and B are similar in that both possess features f, g, and h. (similarity, resemblance, analogous)
A also possesses feature j.
Thus, B probably possesses feature j also.

Example

Professor Leclerc and Minuto are in the CCRI Department of Social Sciences, are males, drive automobiles, are critical of contemporary culture, and enjoy intellectual discussion.
Professor Leclerc also likes cats.
Therefore, Professor Minuto probably likes cats.

b) Terminology: utilizing the above example, we may distinguish the following terms.

• subject: the event, thing, or practice at issue in the argument (Prof. Minuto’s attitude toward cats).
• analogue: what the subject is allegedly analogous to, that to which the analogy is drawn (Prof. Leclerc liking cats).
• common features: the claimed similarities between A and B (department, male, driving, critical, discussions)
• inferred feature: the feature (j) possessed by A (Prof. Leclerc liking cats) and concluded to be possessed by B (Prof. Minuto liking cats).
   

c) Assessing the Inductive Strength of Arguments from Analogy:

• relevance: Are the common features relevant to the inferred feature?
• dissimilarities: Are there relevant dissimilarities between A and B?
• extent of similarity: Are the similarities between A and B extensive?

 
4. Argument from Authority

a) General Form

Expert X argues that p
Accordingly, P is probably the case

Example

My primary care physician claims that poison ivy is contagious when it is oozing.
Therefore, poison ivy is probably contagious when it is oozing.

b) Assessing the Inductive Strength of Arguments from Authority:

• relevant expertise (field-specific competence): Is the person cited an expert in the relevant field?
• prerequisite ability to perceive or recall: Is the witness in a court proceeding reliable?
• impartiality and truthfulness of expert: Is the expert prejudicial, biased, or motivated to lie?