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• CommentRowNumber1.
• CommentAuthortomr
• CommentTimeOct 16th 2019

Reasoning in mathematics is simple and subject to automation and discipline/system, because every concept (e.g. integer number, real number, derivative, integral, differential equation and its solution, etc.) can be expressed using some very small set of simple notions. If one considers the type theory approach to the fundamentals of mathematics, then there are only two basic types (entity and Boolean-truth) and all the other types, all the other notions and concepts are formed from those two simple types. Reasoning in mathematics is systematic because we completely know the content of the every concept. Yes, sometimes we imagine some new concepts (poetics of math) but even in such cases we manage to write down those concepts (or approximations of them) into the other concepts that can be traced to the first principles. Concepts in the mathematics are formed (or at least - can be expressed) in the bottom-up manner.

Reasoning about physics, about real world (ontology, metaphysics, nature, social world, humanities, emotions, mind, etc.) is very hard, because we can only make guesses about the eventual concepts, about the connections with other concepts and we don’t know the full content of the concept, every research discover new shades of some concept, concepts are created, merged etc. And all this happens in non-rigorous manner, because we don’t know the complete content of the concepts expressed in the first principles. We even don’t know the first principles that can be used for the real world.

Semantics of the natural language is perfect example for efforts to discover such first principles. E.g. reading from https://edinburghuniversitypress.com/book-elements-of-formal-semantics.html one can see the table that expresses each grammatical category as the derived type that is made from just two basic types:

Abstract type F-type S-type NP→S intransitive verb ff et NP→(NP→S) transitive verb f(f f ) e(et) A→(NP→S) be copula f(f f ) (et)(et) A→A adjective modifier f f (et)(et) S→(S→S) sentence coordinator f(f f ) t(tt) A→(A→A) adjective coordinator f(f f ) (et)((et)(et)) (NP→S)→S quantified noun phrase (f f )f (et)t N→((NP→S)→S) determiner f((f f )f ) (et)((et)t) (NP→S)→(N→N) relative pronoun (f f )(f f ) (et)((et)(et))

One can guess - if mathematics is the model of the real world, then we already have all the first principles, we just need more efforts to express such concepts as ’happines according to Aristotle’, ’ontology according to Hegel’, ’ontology according to British encyclopedia’, ’ontology according to some famous philosopher N.’ (we should always take into account that well defined concepts are connected to some personality in whose inner semantic we they can be found and only from such personal concepts the conventional concepts can emerge by convention in some scientific community, legal system, etc.) using the basic notions of math.

OK, I know that my thoughts are very childish. That is why my real question is this - is there some discipline in philosophy that tries to express the content of the each concept in some basic notions, is there discipline of the philosophy that tries to uncover such basic notions and types (be they the already known mathematical notions and types or something other)? What are the names of such disciplines of philosophy? What are common terms and research themes in such disciplines? Just keywords and names? Everything other I can find further myself.

I know, that there is metaphysical ontology (as opposite to applied ontology) but I don’t know the efforts to find the content of concepts and the first principles. I know that there is mereology, but it is about parts, about structures and systems, but the essence of the concept is something more that just its structural build-up. So, I am completely lost and I don’t know where to search further.

p.s. Why I am asking this? Well, I have zero internal/personal drive to understand world in such basic terms. I am just trying to automate thinking/reasoning (artificial general intelligence) for applied purposes and that is why I need systematic, disciplined, extensible and automatable way of handling concepts and I am just seeking for theories that are already created for such handling of concepts. Of course, they can not give the final answers, but they can be good starting point and the system can discover further horizons itself.

• CommentRowNumber2.
• CommentAuthoratmacen
• CommentTimeOct 16th 2019

It’s not clear to me from your message what your problem is with existing scientific models and their mathematical definitions. For example, quantum mechanics is ’the universe, according to quantum mechanics’. (Maybe that’s a bad example, since I don’t know it.)

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeOct 17th 2019

Some Leibnizian moments there in #1: mathematics as finite construction of proof from identity statements, science as discovering approximations to the full story (the latter involving infinite proofs). All empirical facts are deducible, but requiring infinitary analysis, which only God can achieve.

But we can develop a calculus, a Characteristica universalis:

Algebra, which we rightly hold in such esteem, is only a part of this general device. Yet algebra accomplished this much—that we cannot err even if we wish and that truth can be grasped as if pictured on paper with the aid of a machine. I have come to understand that everything of this kind which algebra proves is only due to a higher science, which I now usually call a combinatorial characteristic, though it is far different from what may first occur to someone hearing these words. I hope sometime, given health and leisure, to explain its remarkable force and power by rules and examples. I cannot encompass the nature of the method in a few words. Yet I should venture to say that nothing more effective can well be conceived for perfecting the human mind and that if this basis for philosophizing is accepted, there will come a time, and it will be soon, when we shall have as certain knowledge of God and the mind as we now have of figures and numbers and when the invention of machines will be no more difficult than the construction of geometric problems. And when these studies have been completed— though there will always remain to be studied the choicest harmonies of an infinity of theorems, but by observation from day to day rather than by toil—men will return to the investigation of nature alone, which will never be entirely completed. For in experiments good luck is mixed with genius and industry.

Of those looking for a language of basic kinds of entity, you might try Building Ontologies with Basic Formal Ontology. I mean to look at this at some point suspecting that type theory will do a better job.

• CommentRowNumber4.
• CommentAuthorphilophronesis
• CommentTimeMay 19th 2022
Has anymore work been done on this subject? I have my own ideas about philosophy of concepts, and have heard of about the Characteristica universalis before. I think a type theoretical, and ontological approach are both bound to fail. I think something like this is much more likely to succeed in the long run https://www.cortical.io/wp-content/uploads/Semantic-Folding-Arguments_V01.pdf.