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"Famous" Forms in Logic - Coggle Diagram
"Famous" Forms in Logic
Modus Tollens
- The way of removing
The Outline:
1. If A, then B. 2. Not B. So, 3. Not A.
"Not B" stands for the
negation
or denial of B
E.g., negations of "Nadal is a scientist":
Nadal is not a scientist
It is not the case that Nadal is a scientist
It is not true that Nadal is a scientist
It's false that Nadal is a scientist
If Nadal is a physicist, then he's a scientist
Nadal is not a scientist
So, 3. Nadal is not a physicist
Take Care: Related Fallacies
Outline:
1. If A, then B. 2. Not A. So, 3. Not B
Ex: 1. If Marie is not a biologist, she is a scientist. 2. Marie is not a biologist. So, 3. Marie is not a scientist (Denying the Antecedent)
Other Outline:
1. If A, then B. 2. B. So, 3. A.
Ex: 1. If Marie is a biologist, she is a scientist. 2. Marie is a scientist. So, 3. Marie is a biologist. (Affirming the Consequent)
A form involving ONLY Conditionals:
Hypothetical Syllogism:
1. A, then B. 2. B, then C. So, 3. If A, then C.
If China attacks Taiwan, Taiwan will counterattack. 2. If Taiwan counterattacks, a major war will occur. So, 3. If China attacks Taiwan, a major war will occur.
The order of the premises doesn't affect the validity, but it may confuse you
Forms Involving Disjunctions:
Disjunctive Syllogism:
Disjunctions: either or statements
There are two forms:
1. Either A or B. 2. Not A. So, 3. B. & 1. Either A or B. 2. Not B. So, 3. A
Ex.
1. Either Mary shot Al or Bob shot Al. 2. Mary did not shoot Al. So, 3. Bob shot Al.
Constructive Dilemma:
Combines disjunctions and conditionals
Either A or B. 2. A, then C. 3. If B, then D. So, 4. Either C or D.
Ex:
1. Either human acts are determined or they are not. 2. If human acts are determined, the our actions are not fully controlled by preceding events. 3. If human acts are determined, then our actions occur at random. So, 4. Either our actions are fully controlled by preceding events or our actions occur at random.