Immediate Inference

The square of opposition expresses the relationships between the four standard forms of categorical propositions. These are relationships of compatibility or incompatibility.

However, there are also relationships of logical equivalence among categorical propositions. If two propositions are related in such a way that the truth of one implies the truth of the other, they are equivalent from a logical standpoint.

In the traditional analysis of categorical reasoning, three particular operations were identified. These operations were called immediate inferences. Let us examine each of these in turn.

Conversion

Obversion

Contraposition


Comprehension Questions

1 What is the convert of "Everybody loves a circus."
a) Circuses love everybody.
b) Anyone who loves a circus is everyone.
c) It is not legitimate.
2 What is the convert of "No animal is an autotroph."
a) No autotroph is an animal.
b) All animals are autotrophs.
c) It is not legitimate.
3 What is the convert of "Some spiders are poisonous."
a) Some spiders are not poisonous.
b) Some poisonous things are spiders.
c) It is not legitimate.
4 What is the convert of "Some animals are not land-dwellers."
a) Some land-dwellers are not animals
b) Some animals are land-dwellers
c) It is not legitimate.
5 What is the obvert of "No non-human is rational."
a) No human is non-rational
b) No human is rational
c) Every human is non-rational
d) Every non-human is non-rational
6 What is the obvert of "Every animal is non-autotrophic."
a) Every non-animal is non-autotrophic
b) Every animal is not autotrophic
c) No animal is autotrophic
d) No non-animal is autotrophic
7 What is the obvert of "Some sunsets are beautiful."
a) Some sunsets are not non-beautiful
b) Some sunsets are not beautiful
c) Some non-sunsets are non-beautiful
d) Some sunsets are non-beautiful
8 What is the obvert of "Some pranks are not funny."
a) Some pranks are not non-funny
b) Some pranks are non-funny
c) Some pranks are funny
d) Some non-pranks are not non-funny
9 What is the contraposition of "Every machine is non-conscious."
a) No machine is conscious
b) Anything that is conscious is a non-machine
c) Anything that is non-conscious is a machine
d) It is not legitimate.
10 What is the contrapositive of "No civilization lasts forever."
a) Nothing that lasts forever is a civilization
b) No civilization is something that does not last forever
c) Nothing that does not last forever is a non-civilization
d) It is not legitimate.
11 What is the contrapositive of "Some liars prosper."
a) Some who prosper are liars
b) Some who do not prosper are non-liars
c) Some liars are ones who do not prosper
d) It is not legitimate.
12 What is the contrapositive of "Some animals are not able to adapt to a changing environment."
a) Some who are not able to adapt to a changing environment are not non-animals
b) Some non-animals are able to adapt to a changing environment
c) Some who are able to adapt to a changing environment are not animals
d) It is not legitimate.


Venn Diagrams

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