Syllogisms

Basics

The syllogism comes in 3 propositions and has 3 terms

Terms

Major term: Term taken in the major premise

Minor term: Term taking in the minor premise

Middle term: Term that links the aforementioned terms together

Premises

Major premise: Premise that asserts a relationship between the major term and the middle term

Major premise: Premise that asserts a relationship between the minor term and the middle term

Conclusion: Assuming the premises are true, it is then proved the major and minor terms are linked.

Figures

The figures are the arrangements of the premises.

Figure 1

The middle term is a subject in one premise and a predicate in the other

Example

1. All mammals are creatures that have hair.
2. All dogs are mammals.
3. Therefore, all dogs are creatures that have hair.

Figure 2

1. The middle term is the predicate of both premises.

Example

1. No states with coastlines are states that are landlocked.
2. Some U.S. states are states that are landlocked.
3. Therefore, some U.S. states are not states with coastlines.

Figure 3

The middle term is the subject of both premises.

Example

1. All humans are mortal.
2. All humans are mammals.
3. Some mortals are mammals.

Categorical Forms

The quantitative and qualitative forms of each premise.

The qualitative is the affirmative (+) or negative (-).

The quantitative is the universal (∞) or the particular (finite)

1. A) Affirmatively Universal
2. E) Negatively Unviersal
3. I) Affirmatively Particular
4. O) Negatively Particular

Moods

These are all the combinations of both the Figures and Categorical Forms. While this gives us 64 total moods, only 19 valid direct moods and 5 sub-alternate moods, leading to 24 total valid moods.

Each of these moods has a corresponding name.

Hegel's use

While this definitely will be revamped in further review - both as I review this currently and when I get into this in depth in my science of Logic to determine how this is proven - I wanted to log my insights as is at the moment.

The Singular (S), Particular (P), and the Universal (U) are utilized in all 3 positions with different focus on the middle-term type. This is definitely a more formulaic description at this moment, and as such will be resolved more appropriately later.

Qualitative [S → P → U]

The Particular is the middle term here in its finity.

Figure 1: $S\rightarrow P\rightarrow U$

Figure 2: $U\rightarrow S\rightarrow P$

Figure 3: $P\rightarrow U\rightarrow S$

Quantitative: $U\rightarrow U\rightarrow U$

Reflection [U → S → P]

All singular objects taken together. This is a long string of infinity, so ends up being the spurious or bad infinity.

Allness: $S\rightarrow P^{\infty }\rightarrow U$

Induction: $U\rightarrow S^{\infty }\rightarrow P$

Analogy: $P\rightarrow U^{\infty }\rightarrow S$

Necessity [P → U → S]

The universal - in its self-referentialness - references back to itself, as true infinity.

Categorical: $S\rightarrow P^{\circ }\rightarrow U$

Hypothetical: $U\rightarrow S^{\circ }\rightarrow P$

Disjunctive: $P\rightarrow U^{\circ }\rightarrow S$

Modern Interpretation and Figure 4

Info on Figure 4 and how ordering of the terms was deemed to be of concern. New definitions of the terms (major term is the predicate of the conclusion specifically)

This is important has Hegel does call this out but does not use it in his logic. I have not read this part of the SoL yet - although I have of the EL1 - but I assume he takes like others have the ordering per Figure 1 doesn't matter and the reflections in this "Figure 4" are just Figure 1 with the Conclusion ordering reversed. While this may have some importance disntiction in certain views, I can see that the end result likely has no relevancy for the investigation of the logic.

Later review is needed to see if this is mistaken.

External Links

Syllogism on The Logic Museum

Syllogism on Wikipedia