No logical/mathematical “truths”, no physical “laws”

Content

Introduction

1. There are no “truths” in logic and mathematics; there are no “truths” in any language at all; logic and mathematics cannot have any kind of ontology
2. Physical laws cannot have any ontological status
3. Color vision and the EDWs perspective

Conclusion

Introduction

Following mainly Odifreddi’s book about Gӧdel, “The God of Logic”, in this short article, I will indicate, within the EDWs perspective, that there are no logical truths, mathematical truths and physical laws at all, i.e., these truths and physical laws

• do not have any ontological status
• are just certain mental states/thoughts in each mind-EW, nothing else.

More exactly, logic and mathematics are nothing else than an old “chat-GPT”, just an “old game in an old town”. Obviously, logic and mathematics are related to language (signs), therefore, we have also to deal with language. From my viewpoint, we have to related logic, mathematics and language with perception and thinking. From my viewpoint, all the mental perceptual states and the mental thoughts are the mind-EW. This is the reason, the third part of this work is on colors. More exactly, we have to use the very important distinction between the explicit/declarative/conscious knowledge and the implicit/procedural/unconscious knowledge which it is strong related to the syntax and the semantics of language. (see my works 2007, 2008) Finally, if we talk about the logical statements and language, we have to find an answer to the main problem: “truths”. I will make a clear distinction between “truths” and “real things”. Truths involves, with necessity, logical propositions (formal systems) or sentences from language. A word cannot express the “truth”. For instance, “tree” cannot express a “truth”.[1] However, I want to emphasize, the main distinction between “truth” and “a real thing”: a statement/sentence is true or false; a real thing exists independent of our thinking/perception and logic/language. Surely, the Earth have existed before the human beings have appeared on it. (see my previous works) The last statement indicates a macro-entity (a planet, the Earth) which have existed independent of the existences of the human beings (perception/thinking/logic/language). We can extend the notion of “truth” to our “internal/implicit thoughts”: for instance, I think, without pronouncing something, that 2 + 2 = 4. I use an “internal language”/numbers to have this thought. Can this statement be truth or false? It depends on what I have been learning, nothing else. In the first years of school, I learned that 2 + 2 = 4, but this is not a “true statement” in itself. (truth cannot even exist – see below) Moreover, this statement does not even exist in itself, it is in my mind (more exactly, it is my mind). Also, I can see a tree in my garden and think: “There is a green tree in my garden”.  This thought refers to the existence of a green tree in the garden. I can remark, not being aware, a dog in my garden, I have a perceptual visual state about that dog, and later, maybe I could remember (I can have a thought or express a statement to somebody) that I saw that dog.[2] These thoughts/statements refer to something which really exist (the tree, the garden), but according to my EDWs perspective, I perceive these entities indirectly. Therefore, I cannot claim there are true statements (see my previous works or below).

In the Part 1, I will introduce, from Odifreddi’s book, very few notions regarding a logical system[3]: “correctitude” or “consistence” means there are no contradictions in the system; “completeness” means that if a statement is true, there has to be a proof following the axioms and the rules of the system. (Odifereddi 2020, p. 20)[4] I will investigate all these notions from my EDWs perspective and following the difference between truths and real things. I will move from one topic to another without specifying this process. However, later I will try to relate some of these topics. In Part 2, I will related mathematics with physics and physical laws. I will argue that there are no physical laws at all, i.e., the physical or natural laws have no ontology. In the Part 3 I will introduce very few aspects about perception just because in Part 1 I indicated that the mathematical concepts are just abstractions created by the human mind exactly as are the colors. However, there is an important difference: the colors in the mind-EW correspond to certain macro-entities (the macro-EW) which correspond to an amalgam of electromagnetic waves (the field-EW) and an amalgam of microparticles (the micro-EW). The mathematical numbers correspond to nothing in reality since these notions are just simple abstractions (at the beginning of evolution species) and later these abstractions have become more and more complex mathematical functions/operations.

[1] Obviously, if a person asks another person: “What do you have in your garden?” the second person can answer: “Trees”, but this answer has the explicit word, “trees” and other implicit words: “In my garden, I have tress”.

[2] My EDWs perspective is beyond nominalism-realism distinction; however, my approach is much closer to nominalism…

[3] I mention again that, during my career, I have not worked on logic and mathematics at all. Therefore, almost sure, there are some mistakes in this article. However, I will analyze only very general concepts of these domains, more exactly, I am interested in investigating their foundations. This is the reason, I quoted many paragraphs from different books/articles in my work: I am not specialist in logic or/and mathematics and I have not time to translate the ideas from those paragraphs in my words. The reader can imagine I talk with the great thinkers mentioned in so many quoted paragraphs… The notions from logic are from Odifreddi’s book (in Romanian), so, certain notions and statements from this book are just my translation (very possible, some of them I translated incorrectly).

[4] Odifreddi’s book has been published in Italian in 2018. Rosser dialed with the theorem of incompleteness for consistent systems (there cannot be demonstrated contradictions; the theorem of incompleteness for correct system (there cannot be demonstrated the false) was elaborated by Gӧdel. (p. 17)