2. Give Me that Second Half One More Time - Critical Thinking Outline

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Good Argument
A good argument justifies acceptance of the conclusion.

Valid/Sound Argument (Deductive)
A valid argument has this defining characteristic: It is necessary, on the assumption that the premises are true, that the conclusion be true.

Strong Arguments (Inductive)
A strong argument has the distinguishing characteristic: It is unlikely, on the assumption that the premises are true, that the conclusion is false.

Categorical Logic
The relations of inclusion and exclusion among classes (“categories”)

Terms
The S and P are terms.

Subject (“The Only”)
The noun or pronoun phrase that refers to the first class mentioned in a standard-form categorical claim.

Predicate (“Only”)
The noun or noun phrase that refers to the second class mentioned in a standard-form categorical claim.

 
Square of Opposition

 
Standard-form Categorical Claims
All distributed terms are in bold: 
  A: All S are P
  E: No S are P
  I: Some S are P
  O: Some S are not P

Conversion:
 
E: No P are S
I: Some P are S

Obversion:
 
A: No S are ~P
E: All S are ~P
I: Some S are not ~P
O: Some S are ~P
 
Contrapositive: 
 
A: All ~P are ~S
 
O: Some ~P are not ~S  


Syllogisms: 
   
Rules of Validity Testing
1. The number of negative claims in the premises must be the same as the number of negative claims in the conclusion.
2. At least one premise must distribute the middle term.
3. Any term that is distributed in the conclusion of the syllogism must be distributed in its premises.

Major Term
Occurs as a predicate of the syllogism’s conclusion.

Minor Term
Occurs as a subject of the syllogism’s conclusion.

Middle Term
Occurs in both the premises but not in the conclusion.
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Truth Tables
 

Antecedent (Is Nessasary)
The P in the Truth Table

Consequent (Is Sufficent)
The Q in the truth table.

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Rule 1: Modus ponens
Also known as affirming the antecedent
P → Q (P v R) → Q
P . P v R .
Q Q

Rule 2: Modus tollens
Also known as denying the consequent
P → Q
~Q .
~P

Rule 3: Chain argument
P → Q
Q → R.
P → R

Rule 4: Disjunctive argument
P v Q P v Q
~P . ~Q .
Q P

Rule 6: Conjunction
P
Q .
P & Q

Rule 10: Double negation
P ↔ ~~ P P → ~~(Q v R)

Rule 13: Contraposition
(P → Q) ↔ (~Q → ~P)

Rule 16:Association
[P & (Q & R)] ↔ [(P & Q) & R] [P v (Q v R)] ↔ [(P v Q) v R]

Rule 18: Tautology
(P v P) ↔ P (P & P) ↔ P

Sample
An item or items we believe something about. (How many of the set is being viewed.)

Target/Class
An item or group of items to which we wish to extend our belief. (The whole number of the set.)

Feature/Property in Question
The feature we know about in the sample and we extend to the target object.

National Sample
1500

State Sample
500

Analogical Argument
Comes to a conclusion by comparing one thing to another. (Have one thing or event for a target)

Terms
The items being compared.

Feature in Question / Property in Question
What feature every member of a set possessives.

Target Class
The whole group of members for a specific set.

Inductive Generalization
Generalizations have their samples drawn from the target class.

Representative
The measure of how accurately the members represent the whole target.

Biased Sample
A sample that is significantly different from the target in one or more aspects. (the more alike the target and sample are, the stronger the argument is.) (The larger the sample the better – the stronger the argument)

Random Selection
Gives every member of the target class an equal chance of becoming a member of the sample or lottery. (More representative of the target.)

Error Margin
A range of percentage points within which an answer is claimed to fall.
↑ Sample = ↓ Error Margin = ↑ Confidence Level.

Confidence Level
A measure of the argument’s strength; the higher the confidence level, the more likely the argument’s conclusion is to be true.

Hasty Conclusion/Generalization
A fallacy of inductive arguments that occurs when conclusions are drawn from a sample that is too small. (Jumping to a conclusion based on information from a sample that is too small.)

Anecdotal Evidence
Always consists in taking a story about one case (or more than one) and drawing an unwarranted conclusion (usually from a personal story). [Too small of a sample]

Weak Analogy
The two or more objects, events, or other phenomena being compared in a story or dialog, which have little or nothing in common – [See - A hasty comparison.]

Slanted Question
A question which contains bias.

Larger Number Rule/ Law of Large Numbers
The larger the number of chance repetitious events, the closer the events will approach a predictable ratio.

Gambler’s Fallacy
The belief that recent past events in a series can influence the outcome of the next event in the series. This reasoning is fallacious when the events have a predictable ratio of results, as is the case in flipping a coin, where the predictable ratio of heads to tails is 50-50.
(Assumption that the previous random events will effect future random events and the odds of these events.)

Causal Reasoning
One event necessarily leads to another event.

Non-Sequitur
The fallacy of irrelevant conclusion; an inference that does not follow from the premises.
 

Post Hoc Fallacy
Post hoc, ergo propter hoc
Reasoning that X caused Y simply because Y occurred after X.
(Just because one thing happened before the other does not mean that the first caused the second.)

Causal Claim / Cause-and-effect Claim
A statement that says or implies that the presence or absence of one thing caused or causes another.

Relevant Difference
A relevant difference is one that is not unreasonable to suppose caused the feature in question.
(An effect present is not present in another similar situation. The attempt is to find the difference between the situations where the effect was seen and where it was not.)

Common Thread
In common thread reasoning, multiple occurrences of a feature are said to be united by a single relevant common thread.
(The same effect is common in multiple situations and the cause links them.)

Experimental Group
The members of a group who are exposed to the suspected causal factor.
(The sample of the target population whose members are all exposed to the suspected causal agent.)

Control Group
The members of a group who are not exposed to the suspected causal factor.
(The sample of the target population whose members are treated exactly as the members of the experimental group are except that thy are not exposed to the suspected causal agent.)

Hypothesis
Supposition offered as a starting point for further investigation.

Statistically Significant
To say that some finding is statistically significant at a given confidence level – say, .05 – is essentially to say that the finding could have arisen by chance in only about five cases out of one hundred.
(The idea that it would be unreasonable to attribute this difference in frequency to chance.)

Controlled Cause-to-Effect
An experiment designed to test whether something is a causal factor for a given effect. A causal agent is introduced into the experimental group but not the control group. If the effect is then found to occur with significantly more frequency in the experimental group, the suspected causal agent is considered a causal factor for the effect.
(A causal agent is introduced into the experimental group but not the control group.)

Non-Experimental Cause-to-Effect
To test whether something is a causal facto for a given effect.
(No introduction of causal agent occurs. Instead a study is conducted on a group of individuals in which exposure has resulted from their own actions or circumstances.)

Non-Experimental Effect-to-Cause
To test whether something is a causal factor for a given effect.
(No introduction of causal agent occurs. The members of the experimental group display the effect as compared with the control group. Showing that the suspected causal agent is a causal factor in the population involved.)

Circularity
The property of a “causal” claim where the “cause” merely restates the effect. (The “cause” restarts the effect.)

Non-testability
The inability to test if something is true or false (“There are aliens in the universe.” For now, this is non-testable.)

Excessive Vagueness
A statement that is too vague to pinpoint a meaning and thus is non-testable.

Unnecessary Assumptions
The denial of apparent truth in order to accept an unreliable alternative.

Conflict-with well established Theory
A claim that conflicts with well-established theory. This claim does not support the burden of proof placed on it. There is good reason to reject this claim without powerful evidence of its truth (High Burdon of Proof).

Inductive Generalization
A claim who attempts to have a statement true about every member of a set.

Conclusion Indicators
Therefore
It follows that…
We may conclude that…
This serves to show that…
Thus
Hence
Accordingly
Consequently
So

Premise Indicators
Since
For
Because
In view of…
This is implied by…
Given