Syllogism

In order for the conclusion of reasoning should become credible, the reasoning must be logically correct, and, in addition, its premises must be credible

An example of correct argument is seen by the syllogism.

When the premises are assumed to be credible the syllogism may also be called a demonstration.

As in every other correct reasoning, the conclusion of the syllogism follows the epistemological status of the premises.

This is illustrated using two syllogisms below:

In the syllogism above the premises A1 and A2 consist of credible probability arguments. Therefore the conclusion A also becomes a trustworthy probability argument.

Du to the high credibility of the premises, this and similar examples are used to claim "absolutely credible" conclusions from logical arguments. Such claims are deceptive and erroneous.

/premise B1/ Every metal can hover
and
/premise B2/ Gold is a metal.
Hence:
/conclusion B/ Gold can hover.

This syllogism illustrates that the credibility of the premises, and not only that the argument is logically correct, determine the credibility of the conclusion.

According to what we may perceive premise B1 is obviously improbable and the conclusion B, which follows logically from the premises, therefore also becomes improbable.

Rationalistic philosophers have claimed that premises that are "definitions", "axioms", "a priori", "transcendentally known", "given", and so forth are "absolutely certain". Logically correct syllogisms with such premises should then result in conclusions with the same epistemological status.

The unspoken problem for such philosophers is that every until now known premises consist of probability arguments.

A correct syllogism implies a synthesis of two premises, which is not the traditional view. Therefore the classic syllogism about Socrates again.

/premise 1/ Every human is mortal.
TOGETHER WITH
/premise 2/ Socrates is a human.
HENCE:
/conclusion/ Socrates is mortal.

We are able to create the conclusion "Socrates is mortal" because premise 1 and premise 2 contain something that makes them related. Both contain the term "human". We create a synthesis between the two premises through similarity of these two concepts

The premises of the syllogism imply analyses, and also the conclusion consists of a newly formed analysis. But the actual reasoning, the syllogism, implies a synthesis.

Rewriting the syllogism clarifies the analyses.

Every human is included in the concept mortal.
TOGETHER WITH
Socrates is included in the concept every human.
HENCE:
Socrates is included in the concept mortal.

The conclusion is hence created through a synthesis of the two premises.

It has been claimed that very credible probability arguments are "absolutely certain". Therefore the premises, and hence the conclusion, of the commonly used syllogism is discussed below:

Premise 1 "Every human is mortal"

The premise is ultimately created by synthesis from perceptions similar to "Anna was a human and Anna was mortal", "Bertil was a human and Bertil was mortal", Carl was a human and Carl was mortal" and so forth.

Because the perceptions are virtually innumerable and as so far no exception has been credibly observed, premise 1 is a very reliable probability argument.

Premise 2 "Socrates is a human"

Our concept "human" is ultimately synthesized from perceptions of many phenomena that we have learnt are called "human". They may be coloured differently, but as no other phenomenon is closely related, our concept "human" becomes quite distinct.

The phenomenon called Socrates show many properties that are included in our concept "human". It is hence credible that Socrates "is a human" and not the he e.g. "is a horse".

Probability argument

Because the premises are probability arguments also the syntheses of them, the conclusion, becomes a probability argument.