Deduction Flashcards
Categorical Arguments (groups/classes/sets)
Example 1:
(1) All dogs are mammals.
(2) All Chihuahuas are dogs.
(3) Thus, all Chihuahuas are dogs.
Example 2:
(1) All soccer players are rich.
(2) Some Professors are soccer players.
(3) Thus, Some Professors are rich.
Example 3:
(1) Some pirates are murderers.
(2) Some sailors are pirates.
(3) Thus, some sailors are murderers.
There is an entire branch of logic, Categorical Logic, developed by Aristotle and enhanced by various others since then, which shows which studies Categorical Arguments and their various forms. We do not cover all these arguments in this course but we will examine some basic forms.
Sentential Arguments (sentences) 6 EXAMPLES
Good argument form because if the premises are true then the conclusion will be true.
What makes these arguments good or bad we will discuss later in this module. But it might make some sense to you at this stage that some of these arguments are better than others.
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Example 1: GOOD ARGUMENT FORM - Modus Ponens
(1) If the car is red, then the car is colored.
(2) The car is red.
(3) Thus, the car is colored.
1 is a conditional sentece. First condition is “if the car is red” the second part is “the car is colored” mini sentences inside of a big sentece. Anticedent is the first part. Consequent is the second.
FORM: where A and B are sentences or propositions
If A, then B.
A.
Thus, B.
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Example 2: GOOD ARGUMENT FORM - Modus Tollens
(b) MT, Modus Tollens
(1) If the car is red, then the car is colored.
(2) The car is not colored. (Say, it is invisible)
(3) Thus, the car is not red.
FORM:
If A, then B.
~B.
Thus, ~A.
1) If I’m in San Fransisco then I’m in California
2) I am not in California
3) So I am not in San Fransisco
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Example 3: GOOD ARGUMENT FORM - Disjunctive Syllogism
(1) There are only two options: Clean is either first in the race or second in the race.
(2) Clean is not first in the race.
(3) Thus, Clean is second in the race.
FORM:
Either A or B. (Only two options)
~ A.
Thus, B.
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Example 4: GOOD ARGUMENT FORM Constructive Dilemma
(1) If it is a cat, then it has worms and if it is a dog, then it has fleas.
(2) It is a cat or a dog.
(3) Thus, it has worms or fleas.
FORM
If A then T and If B then S.
A or B.
So, T or S.
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Example 5: BAD ARGUMENT FORM Denying the Antecedent
(1) If I am in Los Angeles, then I am in California.
(2)I am not in Los Angeles.
(3) Thus I am not in California.
FORM:
If A, then B.
~A.
Thus, ~B.
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Example 6: BAD ARGUMENT FORM Affirming the Consequent
(1) If I am in Los Angeles, then I am in California.
(2) I am in California.
(3) Thus, I am in Los Angeles.
If A, then B.
B.
Thus, A.
These arguments do not take place in a vacuum. An important factor for thinkers not familiar with the tools we will develop in this class whether or not the conclusion is believable. The more believable the conclusion is, the higher the chance that a subject will mistake a fallacy for a valid argument
If the conclusion is believable, then they’re likely to conclude that the arguemnt is good
Instead of thinking “Yeah I kinda believe the conlcusion, ask yourself how close is the conlcusion to the reasons given to thinking the conclusion is true. O
Arguments from Definition (meanings of words)
(1) Hypatia is a bachelorette.
(2) Thus, Hypatia is an unmarried female.
Certain legal arguments rest on how certain words are defined. Economic arguments also. Just be aware that definition are deductive arguments.
Mathematical Arguments (mathmatical models)
(1) The length of a square is 5 feet.
(2) Thus, the area of the square is 25 square feet.
