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Chapter 3: Deduction: Argument Forms - Critical Thinking
Terms in this set (42)
the process of finding truth by making observations; these observations may be from statistical polling, controlled experiments, or relevant examples and analogies
the process of inferring a conclusion by putting forth true premises in a valid format
an argument that follows formal patterns of reasoning and is aimed at establishing the certainty of a conclusion through presenting true premises in valid form
these patterns give us "quality control"
an argument structured in a correct deductive format; an argument structured in such a way that if its premises are true, then its conclusion must be true
a valid deductive argument whose premises are true
a deductive argument usually consisting of two premises and a conclusion
the statement in a syllogism that sets forth a general principle. (the major premise contains the term that is the predicate of the conclusion.)
the statement in a syllogism that expresses an instance of the principle set out in the major premise. (The minor premise contains the term that is the subject of the conclusion.)
in deductive reasoning, the inference drawn from the major and minor premises of a syllogism
My Notes: Correct form....sound argument
correct form makes an argument valid, which is a formal term for "logical"; accurate content makes it true. when the form is valid and the content is true, the argument is called "sound."
a statement in which members of one class are said to be included in another class. this statement may be used as the major premise of a syllogism
in deductive reasoning, a syllogism whose major premise asserts that if the condition cited in the first part of a statement is true, then the claim cited in the second part of the statement will follow
Forms of conditional/hypothetical syllogisms: 1) modus ponens; 2) modus tollens; 3) chain argument
modus ponens (or Affirming the Antecedent)
a valid conditional/hypothetical syllogism in which the antecedent is affirmed
means "the way of affirmation"; or, affirming the antecedent
* modus ponens
If A, then B. (major premise; we are stating that the antecedent (A) leads to the consequence (B)
A (minor premise; we are affirming that the antecedent is true)
Therefore, B. (conclusion; if the antecedent is true, the consequence is also true)
If our team wins the playoff game, it will be in the championship game.
Our team did win the playoff game.
Therefore, our team will be in the championship game.
SEE CONDITIONAL SYLLOGISM
a syllogism in which the major premise presents a condition (if A, then B) or a possibility (either A or B) that is resolved in the minor premise so that a valid conclusion can follow. The condition or possibility is resolved in the minor premise in the form of affirmation or denial. Conditional and disjunctive syllogisms are forms of hypothetical syllogisms
modus tollens (or Denying the Consequent)
a valid conditional/hyothetical syllogism in which the consequence is denied
means "denying the consequent"
* modus tollens
If A, then B.
Not B. (here the consequent is denied)
Therefore, not A. (since the consequent is denied, the antecedent must also be denied in the conclusion)
If I have strep throat, then the culture will be positive.
But the culture is not positive.
So, I don't have strep throat.
If I have to get up now, my alarm will go off again.
But my alarm hasn't gone off again.
Therefore, I don't have to get up now.
a third form of the conditional argument that builds and depends on a series of conditions being met
If A, then B.
If B, then C.
Therefore, if A, then C.
If you lower the fat in your diet, you will lower your cholesterol.
If you lower your cholesterol, you will reduce the risk of heart disease.
Therefore, if you lower the fat in your diet, you will reduce your risk of heart disease.
a hypothetical syllogism in which two possibilities are give in the major premise and one is assumed to be necessarily true. In the minor premise, one of the possible alternatives is negated, and the remaining alternative is then affirmed in the conclusion.
a disjunction is an "or" statement
Either A or B.
Either A or B.
Either Ramon took the car to work or he took the bus.
But Ramon didn't take the bus to work.
Therefore, Ramon took the car.
If Bill goes to the doctor, he will have to get physical therapy.
Therefore, if Bill doesn't have to get physical therapy, he hasn't gone to the doctor.
argument by elimination
(closely related to the disjunctive syllogism) a valid syllogism that seeks to logically rule out various possibilities until only a single possibility remains
Either A, or B, or C.
Not B or C.
The car's problem is the alternator, the generator, or the battery.
It's not the alternator or the generator.
Therefore, it's the battery.
Either A, or B, or C.
If B or C, then D.
Either Rachel bought dinner, Roy bought dinner, or Sammy bought dinner.
If Roy or Sammy bought dinner, then they skipped baseball practice.
But Roy and Sammy did not skip baseball practice.
Therefore, Rachel bought dinner.
a syllogism with a key part or parts implied rather than directly stated
evidence offered to prove a claim. grounds can consist of statistics, examples, research, physical evidence, logical reasoning, and expert opinion
british philosopher stephen toulmin. developed method of dissecting arguments that helps us isolate the implied premises.
his method id's claims (conclusions), reasons, those supports for the claims that are directly state, and warrants, those connections between reasons and claims that are taken for granted (the reality assumptions). the warrants are the implied premises; they are the "glue" that attaches the reasons to the claims.
Why use deductive reasoning
1) illuminate and clarify our beliefs (reality assumptions) and help us consider whether those beliefs are rational. If we find that our beliefs are rational and logical, we may act on them. If they are irrational, we can challenge and revise them.
2) help us discover truth, particularly in situations in which there is a right and wrong answer
3) help us make decisions, particularly when there are established rules, laws, and guidelines to follow.
4) help us recognize and challenge stereotypes and prejudicial statements.
5) help us understand argument
classifying people, places, or things solely on common traits while ignoring individual differences that make these comparisons invalid
premise of contention / contentious premise
the premise of a deductive argument that is under dispute. this is also often called the contentious premise
1) reality assumptions are beliefs about what is true and false; these beliefs are often taken for granted, and they are part of the foundation of a person's argument
2) reality assumptions need to be brought to light and examined so that those who make them do not build arguments on faulty foundations
3) reality assumptions can be discovered and examined through deductive reasoning and through the Toulmin model of argumentation
4) in deductive reasoning, the conclustion is inferred from the premises. when the premises follow correct syllogistic patterns, the argument is considered valid
5) a conclusion derived from true premises that are expressed in a valid form creates a sound argument
6) deductive reasoning helps us discover and examine our underlying reality assumptions, find both logic and truth in an argument, make clear decisions, combat prejudice and stereotyping, understand argument, and argue constructively
to be persuasive, arguments must be valid in addition to containing truth
validity refers to the FORM of an argument. rather than content, form is the logical configuration between the premises and the conclusion that makes an argument valid or invalid.
Valid Argument Forms
all puppies (A) are cute critters (B).
all cute critters (B) are cuddly (C).
therefore, all puppies (A) are cuddly (C).
no birds (A) are quadrupeds (B).
all crows (C) are birds (A).
therefore, no crows (C) are quadrupeds (B).
all musicians (A) are creative types (B).
some poets (C) are musicians (A).
some poets (C) are creative types (B).
no logic classes (A) are pointless classes (B).
some fun classes (C) are logic classes (A).
therefore, some pointless classes (B) are not fun classes (C).
all excellent things (A) are rare (B).
some difficult things (C) are not rare (B).
therefore, some difficult things (C) are not excellent things (A).
some dogs (A) are not long-haired animals (B).
all dogs (A) are quadrupeds (C).
some quadrupeds (C) are not long-haired animals (B).
all mothers (A) are women (B).
all grandmothers (C) are mothers (A).
some grandmothers (C) are women (B).
no mammals (A) are cold-blooded animals (B).
all marmots (C) are mammals (A).
therefore, some marmots (C) are not cold-blooded (B).
all britons (A) are europeans (B).
no americans (C) are europeans (B).
some americans (C) are not britons (A).
no men (A) are mothers (B).
all men (A) are sons (C).
therefore, some sons (C) are not mothers (B).
all pennies (A) are coins (B).
all pennies (A) are made of copper (C).
some copper items (C) are coins (B).
Symbolizing Logical Words
- when symbolizing an argument, its form will make it valid or invalid, rather than what's included in the content of the statements or premises
- letters are used to represent the non logical words of an argument
- symbols will often represent logical words in an argument
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