Abstract

Do you want to know a logic that solves all problems of old classical and nonclassical logics? Have you wondered why all previously invented logics are so inept at solving everyday problems for mathematicians? Are you fed up with the fact that these logics can't do the simplest things, e.g.: speak about themselves, define truth decently, solve paradoxes conclusively and reliably, easily solve implications based on the meaning of natural language sentences that are so obvious to us, distinguish a statement from a sentence, give legitimacy to material implication and finally solve the problem of material implication, and lend themselves to subjective sentences such as "This is a beautiful day", etc.? I have been working on this logic for 10 years and it solves all these problems. The fundamental rules of rational thinking are given in this book.

Enjoy!

Preface

I marked some dependent clauses using commas to make clearer their structural situation in sentences. For example: "The truth, that she comes to know, nourishes her soul" means the same as "The truth that she comes to know nourishes her soul", "He used to say, that thinking can be an art" means the same as "He used to say that thinking can be an art". Simply, the word "that" preceded by a comma is always a relative pronoun or a conjunction.

The mix of two coordinating conjugations "and/or" have exactly the same meaning as "or", so I will use coordinator "or" in the meaning, that includes the fact, that the statement of an outer sentence can concern all its arguments at the same time. For example: red or sweet = exactly one of three possibilities: red and sweet, red and not sweet, not red and sweet.

A text in square brackets used in citations is a complement information or an additional explanation or my commentary to the information contained in the citation.In this book, the convention of omitting articles before the names of variables has been adopted to enhance readability.

As you will see, some small fragments of this book are repeated in different places. This is done so that you don't have to leaf through the pages of the book looking for things that are very important in a particular place. This will also be helpful for readers who will be coming back to read after some time or who will not read the book in the traditional linear way.

To minimize redundant text, some sections in this book have little text, so read mathematical expressions in those sections as sentences, the meaning of which is the content of those sections.

In this book, for example, the sentence "For any statements or attributes x,y,.:P(x,y,.)" means the same as the sentence "P(x,y,.) holds for all x,y,. such that all of them are statements or all of them are attributes", which has the same meaning as the sentence "P(x,y,.) holds for any statements x,y,. and P(x,y,.) holds for any attributes x,y,.".

The main idea that guided me in creating this logic was to create a logic that would solve all the problems of previous logics. I noticed that previous logics used sentences leaving out their meaning, which is information. I wanted to create a logic along the lines of arithmetic, which would literally be the "arithmetic" of information and would talk about information instead of sentences. I noticed that a piece of information implicated by another piece of information is literally a part of that piece of information and I discovered new mereology (which is the study of part-whole relationships) to solve that problem, and then I drew all the consequences from that. And that is exactly what I have accomplished in this book. I discovered this new type of approach that allows to develop the complete and the revolutionary-way formal system of information oriented logic.

The following citations show us that some great logicians had some faint glimmerings of this idea, which they unfortunately were not able to develop back then:

The two . logical inferences . from the original [set of] propositions . give us all the information which it contains respecting the class ([6] George Boole, 1847, p. 75).

it is the office of a conclusion not to present us new truth, but only to bring into explicit form some portion of that truth which was implicitly involved in the premises . [some portion of] the particular information conveyed in the premises ([6] George Boole 1856?, p. 239).

Every collective set of premises contains all its valid conclusions; . speaking objectively, the assumption of them [the premises] is the assumption of the conclusion; though, ideally speaking, the presence of the premises in the mind is not necessarily the presence of the conclusion ([7] Augustus De Morgan, 1847, p. 254).

All the propositions of pure geometry, which multiply so fast that only a small . class . among mathematicians . know all that has been done ., are certainly contained in a very few notions . . [The] consequences are virtually contained in the premises ([7] Augustus De Morgan, 1847, p. 45).

The very purpose of syllogism is to deduce a conclusion which will be true when the premises are true. The syllogism enables us to restate in a new form the information . contained in the premises, just as a machine may deliver to us in a new form the material . put into it ([8] W. Stanley Jevons, 1870, p. 149).

We extract out of the premises all the information . useful for the purpose in view - and this is the whole which reasoning accomplishes ([8] W. Stanley Jevons 1870, p. 15).

[To deduce is] . to draw . propositions as will necessarily be true when the premises are true. By deduction we investigate and unfold the information contained in the premises ([8] W. Stanley Jevons, 1879, p. 49).

These . [consequences] . contain every particle of information yielded by the original [premise] ., or in any way deducible from it ([9] John Venn, 1881, p. 296).

That is, [in making this inference] we have had to let slip a part of the information contained in the data ([9] John Venn, 1881, p. 362).

logicians in overwhelming majority maintain that every conclusion is implicitly contained in the premises ([9] John Venn, 1889, p. 42).

The most striking and the most important competitive advantage over previous logics is, that this logic solves entirely all elementary problems of previous logics and it is not bragging, because it is the honest truth indeed. First of all, the notion of decidability of a statement solves all logical paradoxes and many other elementary problems. Secondly, new set theory allows to solve all elementary problems in set theory. Additionally, this logic fits into opinions and objective sentences as well. And for dessert, it introduces probabilistic logic for contextual sentences. To see solutions of logical paradoxes and most elementary problems, see Chapter 15.

Ask yourself the following questions:

Do you want to know the logic that solves all the problems of old classical and nonclassical logics?

Have you wondered why all previously invented logics are so inept at solving everyday problems for mathematicians?

Are you fed up with the fact that these logics can't do the simplest things, e.g.:

• speak about themselves,

• define truth decently,

• solve paradoxes conclusively and reliably,

• easily solve implications based on the meaning of natural language sentences that are so obvious to us,

• distinguish a statement from a sentence,

• give legitimacy to material implication and finally solve the problem of material implication,

• lend themselves to subjective sentences such as "This is a beautiful day",...