Syllogisms

01 Jun 2021 | philosophy

Thesis: The final conclusion and ultimate point proven by the premises.
Valid Argument: An argument that contains no logical fallacies.
Sound Argument: An argument that is valid and whose premises are true, therefore it is necessary that the conclusion is true.
Conversion: Switch S and P to get an equivalent meaning
Syllogism: The formal structure of a logical argument where two premises lead to a conclusion.
Premise: A proposition that is used as evidence in an argument.
Conclusion: Asserted by the logical result of an argument based on the relationship of the stated premises.

Example:

All M are P. (major premise)
All S are M. (minor premise)
All S are P. (conclusion)

M: Middle term
S: Subject of the conclusion
P: Predicate of the conclusion
Major premise: Links M with P
Minor premise: Links M with S

Categorical Propositions or Forms

Proposition: A spoken assertion.
Categorical Proposition: A proposition containing 2 terms, subject and predicate, in which the predicate is either asserted or denied of the subject.

The Four Proposition:

code	quantifier	subject	copula	predicate	type
`A`	All	S	are	P	universal affirmative
`E`	No	S	are	P	universal negative
`I`	Some	S	are	P	particular affirmative
`O`	Some	S	are not	P	particular negative

Example A: All dogs are white
Example E: No dogs are white
Example I: Some dogs are white
Example O: Some dogs are not white

Syllogistic Figures

Figure: in logic a figure is the classification of syllogisms according to the arrangement of the middle term.

	Fig1	Fig2	Fig3	Fig4
Major	M-P	P-M	M-P	P-M
Minor	S-M	S-M	M-S	M-S
Conc.	S-P	S-P	S-P	S-P
	AAA	EAE	AII	AEE
	EAE	AEE	IAI	IAI
	AII	EIO	EIO	EIO
	EIO	AOO	OAO	AEO
	AAI	EAO	EAO	EAO
	EAO	AEO	AAI	AAI

Examples:

AAA: All dogs are animals. All animals are living beings. Therefore, all dogs are living beings.

Modern Square of Opposition

Contradictory: The truth of one proposition implies the falsity of the other, and conversely(e.g. “all dogs are white” and “not every dog is white”)
Contrary: Propositions that cannot both be true (e.g. “every dog is white” and “no dog is white”)

A ----contrary----- E
| \                 |
|   \               |
|     \             |
|   contradictory   |
|                   |
|                   |
|                   |
I ---subcontrary--- O

AO/OA: Contradictory (All dogs are white. Some dogs are not white.)
EI/IE: Contradictory (No dogs are white. Some dogs are white.)
AE/EA: Contrary (All dogs are white. No dogs are white.)
IO/OI: Subcontrary (Some dogs are white. Some dogs are not white.)
EO/OE: Subalternation (No dogs are white. Some dogs are not white.)
AI/IA: Subalternation (All dogs are white. Some dogs are white.)

Argument

Father Deacon Ananias Sorem

A All physical things are particulars (E.G. This pen is a particular pen.  It does not represent the class of all markers.  It's one marker.)
E No universals are particulars
E No universals are physical things
Conversion: No physical things are universals

E No physical things are universals
I Some concepts are universals
O Some concepts are not physical things

O Some concepts are not physical things
A All concepts are in the mind
O Some (things) in the mind are not physical things
Translated: Some things in the mind are not physical

O Some things in the mind are not physical
A All things in the mind are part of the mind
O Some part of the mind is not physical
Translated to I** Some part of the mind is immaterial

**Contradiction** 
- **I** Some part of the mind is not physical
- **E** No part of the mind is immaterial (materialism thesis)

References

A Refutation of Materialism via Immateriality of the Intellect