Definitions for a Demonstrative Science

Chapter 1

What is demonstration and demonstrative science?

What is a:

• premise
• term
• syllogism
• the nature of a perfect and of an imperfect syllogism
• the inclusion or noninclusion of one term in another as in a whole
• predicating one term of all, or none, of another.

A premise is a sentence affirming or denying one thing of another.

This is either:

1. Universal

This is a statement that something belongs to all or none of something else.

2. Particular

This is a statement that belongs to some or not to some or not to all.

3. Indefinite

This is a statement that belongs or does not belong, without any mark to show whether it is universal or particular. For example, ‘contraries are subjects of the same science’, or ‘pleasure is not good’.

A premise can also be:

1. Demonstrative

This is the assertion of one of two contradictory statements.

2. Dialectical

This depends on the adversary’s choice between two contradictories.

• The demonstrator does not ask for his premise, but lays it down.

But this will make no difference to the production of a syllogism in either case.

This is because both the demonstrator and the dialectician argue syllogistically after stating that something does or does not belong to something else.

Therefore a syllogistic premise without qualification will be an affirmation or denial of something concerning something else in the way we have described.

It will be demonstrative, if it is true and obtained through the first principles of its science.

A dialectical premise is the giving of a choice between 2 contradictories, when a man is proceeding by question.

But syllogizing is the assertion of that which is apparent and generally admitted, as has been said in the Topics.

I will discuss:

• the nature of a premise
• the difference between syllogistic, demonstrative, and dialectical premises

I call that a term into which the premise is resolved, i.e. both the predicate and that of which it is predicated, ‘being’ being added and ’not being’ removed, or vice versa.

A syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so.

• This produces the consequence.
• By this, no further term is required from outside in order to make the consequence necessary.

A “perfect syllogism” needs nothing other than what has been stated to make plain what necessarily follows.

An “imperfect” syllogism is one that needs either one or more propositions, which are the necessary consequences of the terms set down, but have not been expressly stated as premises.

That one term should be included in another as in a whole is the same as for the other to be predicated of all of the first.

One term is predicated of all of another, whenever no instance of the subject can be found of which the other term cannot be asserted: ’to be predicated of none’ must be understood in the same way.