### [ΛΟΓΟΣ] De Ratiocinatione Logica

Posted:

**Sun Jun 18, 2017 2:53 am**Salvete, philosophi!

This thread will be the first of a series about logic.

Logic is one of the three principal branches of Stoic philosophy, the others being natural philosophy and ethics. Like for no other philosophic school, maybe more even than for the peripatetic school of Aristotle, they gave utmost importance to this subject.

For me personally it is so important, because I believe that logic shows us the way to overcome conflicts between humans. I see more and more unnecessary conflicts and aggression, especially in anonymous Internet communication that could have been avoided. If people abstained from personal attacks and followed the methodology of valid arguments, we would not see this kind of reactions. In fact we have already seen too many of these conflicts here in our Republic.

Logic is a set of laws just as precise as mathematics. It is impossible to quarrel over mathematics. Its rules are clear and undeniable. The same is true for logic, of which mathematics is only a subcategory. The principles of logic are objective, they are the same for every human being, even for non-humans like A.I. Nature has to obey them, because otherwise it could not form a consistent and stable universe. This means that logic is valid a priori, before any empirical observation (although Epicurus and probably Aristotle would probably disagree here).

This makes logic a set of rules, which is universally agreeable. And this is the first step to overcome conflicts among people.

It has been argued that faith is essential for the conditio humana, but faith can never be universally agreeable, since everyone can have a different one. The same is true for emotions or conscience. They depend on the individual, i.e. they are subjective and therefore not necessarily agreeable. If we argue with our conscience or based on our faith, we are predestined to get into a conflict with others who will not agree with us.

All threads in this series will start with [ΛΟΓΟΣ], which means "logic" (= logos) in Greek. They are based on a book that I wrote. I will add the corresponding part of the book as attachment to the first post in each thread. Although the book is in Latin, it is easy understandable due to the use of tables, formulas and technical terms. Furthermore the Latin text contains nothing that would not be explained in the English text of the introductory post.

I would appreciate comments, corrections or doubts. If someone can point out inconsistencies in my approach, I would be grateful, as long as proper logical methodology is used.

After this introduction I would like to get started with the most basic principles of classical logic, upon which all that follows is based.

Aristotle, the "father of logic", established the three Axioms of Classical Logic:

1. The Principle of Identity

Short: A is A.

Everything is itself. If something is true, then it is true.

2. The Principle of the Excluded Middle

Anything is either A or not A.

Anything is either true or false.

3. The Principle of Non-Contradiction

Nothing is at the same time A and not A.

No statement is at the same time true and false.

Aristotle provided the following proof for his axioms:

1. All syllogisms are based on them.

2. They can be defended by retortion, i.e, their refutation would depend on the same axioms, which would lead to self-refutation.

The three Axioms of Classical Logic are therefore necessary propositions, i.e. their negation implies necessarily a contradiction. This means they are tautologies, formulas whose negation is impossible. They are to distinguish from contingent propositions, which can either be true or false.

Keywords: Axioms of Classical Logic, retortion, tautology, necessary proposition, contingent proposition

I hope this introduction was somehow helpful and the subject is of some interest. Everybody should understand these three axioms and why they are necessary and irrefutable. Philosophy is not possible without them.

Valete!

C. Florius Lupus

This thread will be the first of a series about logic.

Logic is one of the three principal branches of Stoic philosophy, the others being natural philosophy and ethics. Like for no other philosophic school, maybe more even than for the peripatetic school of Aristotle, they gave utmost importance to this subject.

For me personally it is so important, because I believe that logic shows us the way to overcome conflicts between humans. I see more and more unnecessary conflicts and aggression, especially in anonymous Internet communication that could have been avoided. If people abstained from personal attacks and followed the methodology of valid arguments, we would not see this kind of reactions. In fact we have already seen too many of these conflicts here in our Republic.

Logic is a set of laws just as precise as mathematics. It is impossible to quarrel over mathematics. Its rules are clear and undeniable. The same is true for logic, of which mathematics is only a subcategory. The principles of logic are objective, they are the same for every human being, even for non-humans like A.I. Nature has to obey them, because otherwise it could not form a consistent and stable universe. This means that logic is valid a priori, before any empirical observation (although Epicurus and probably Aristotle would probably disagree here).

This makes logic a set of rules, which is universally agreeable. And this is the first step to overcome conflicts among people.

It has been argued that faith is essential for the conditio humana, but faith can never be universally agreeable, since everyone can have a different one. The same is true for emotions or conscience. They depend on the individual, i.e. they are subjective and therefore not necessarily agreeable. If we argue with our conscience or based on our faith, we are predestined to get into a conflict with others who will not agree with us.

All threads in this series will start with [ΛΟΓΟΣ], which means "logic" (= logos) in Greek. They are based on a book that I wrote. I will add the corresponding part of the book as attachment to the first post in each thread. Although the book is in Latin, it is easy understandable due to the use of tables, formulas and technical terms. Furthermore the Latin text contains nothing that would not be explained in the English text of the introductory post.

I would appreciate comments, corrections or doubts. If someone can point out inconsistencies in my approach, I would be grateful, as long as proper logical methodology is used.

After this introduction I would like to get started with the most basic principles of classical logic, upon which all that follows is based.

Aristotle, the "father of logic", established the three Axioms of Classical Logic:

1. The Principle of Identity

Short: A is A.

Everything is itself. If something is true, then it is true.

2. The Principle of the Excluded Middle

Anything is either A or not A.

Anything is either true or false.

3. The Principle of Non-Contradiction

Nothing is at the same time A and not A.

No statement is at the same time true and false.

Aristotle provided the following proof for his axioms:

1. All syllogisms are based on them.

2. They can be defended by retortion, i.e, their refutation would depend on the same axioms, which would lead to self-refutation.

The three Axioms of Classical Logic are therefore necessary propositions, i.e. their negation implies necessarily a contradiction. This means they are tautologies, formulas whose negation is impossible. They are to distinguish from contingent propositions, which can either be true or false.

Keywords: Axioms of Classical Logic, retortion, tautology, necessary proposition, contingent proposition

I hope this introduction was somehow helpful and the subject is of some interest. Everybody should understand these three axioms and why they are necessary and irrefutable. Philosophy is not possible without them.

Valete!

C. Florius Lupus