Primitive notion

In mathematics, logic, and formal systems, a primitive notion is an undefined concept. In particular, a primitive notion is not defined in terms of previously defined concepts, but is only motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory or other formal system, the role of a primitive notion is analogous to that of axiom. In axiomatic theories, the primitive notions are sometimes said to be "defined" by one or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of infinite regress.

for all those who have called me to question you seem to think my math was a game a simple paly on words id like to defend my self but first its time for you to wake up look around because I was having such a hard time explaining such simple math to you when in fact any one with eyes can see the math is absolute indeed should you want a simplified verson of my theory of string and what not look at blockchain where i solved all questions you could answer all prover the set and existance yadada basically just like the most simple system found at work with in us around us everywhere lets look at the two thing though when im done you will factually understand why God does exist and i created so many thing modeling the example and system created in explained with in the bible yes plain in simple ill now explain between my mathematical proof i created as satoshi called blockchain. the reproductive system and the bible 

one to understand the trinity and the bible the lets first look at some facts all around us we see reproduction system with in the tinyest cell and organism you will find dna encoded in dna both the code and instruction of both the cell system and organism each a closed set or system with in it self having both evidence of it self and the system it blongs or X=×. X=×B B=b B=×xbC. C=c C=×xbcG G=xbcG G=GG=GGG now lets look at the world and existence just like us we contain dna and living systems in our body we are also part of a living system call the world the world is part of the living universe and we are all part of the creator and yet we are not an example of this is take male and female x and y cells the same for goes for planets if you pay close attention you will see this same reproductive system at work on just a larger scale stars and planets the go super nova a male planets stars and planets that do not are the female species in which at the end of its cycle the male planet destructs sending bits of its data and matter germinating the galaxy while female planets become black holes worth they gather all this data and continue to until they eventually become pregnant and collapse sending bits and peices of data germinating the galaxy just like fish and humans just like cells reproducing though they have difference of scale and size its the same thing now lets look at my creation as aka satoshi other wise darrin edward mcduffey and founder craetor of blockchain which in fact is a direct replica of this process with in signiture in block chain there are bits to simplify it we will call it what it looks like numbers and letters these with in this numbers like cells in our body the bits and code underlying them are the double helix and instruction the make up these letters that in turn make up the signiture every living thing on earth is a letter or numvlber our minds like the bits and underlying language having with in us all info we need and where and what system we belong now the bitcoin address in blockchain is like the planets or the stars all containing their individual system now each address belongs to a block this blocks is the universe or galaxy and each block or solar system is part of blockchain which is like existance everything with in it both verifies its self and what it belongs where it was created when it existed when i didnt and having doing so it verifies it self or G=G <>G=×XbBcC now this where it the big mystery is solve for i created blockchain to mirror the bible. exactly and creation and just like you understand and see why or how now lets look at the bible now being that the system is closed GG and us being with in it there is no way we can percieve entirety of existence but yet with in us we carry all an extension and piece linking us all the back to its origin for everything that is or every will be has a beging and end or G----G but having all. information of both G & G we know that even that this system came from some Hence GGG because the existence of a God we have are now able to comprehend this existence now if we look at. darrin e mcduffey aka satoshi im like the origin or god if you will of bitcoin hence im the S in BBS or Bitcoin blockchain having being its creator i alone have the full scope and verify my system and since the system was litterally based of me and well everything we can now go back and look at scripture well this process is explain word for word since God being G in GGG and the only one who know the scope of existence well start there in the bible God is the Alpha and Omega or G----G or mentions being both here before the world and its creator or G---G G now you will see this patern explaining the trinity for G H JC or God The Son The Holy Ghost. God being the creator of the world yet not being apart of explains why when he was here he was not bound by the laws and rules of this reproductive system in which we see everywhere yet being also the one who set this rule we see it explained in the begining of the bible genesis after God created this world and created life he commanded them to multiply for just like cell with in us and all living things if you look around and including to space you a continues multiple of species for all life has been given this command in which God claimed to have created not only this planet but the entire galaxy and existence so its understandable should he speak a command the all life reproduce and planets being amongst the living having both begining and end and also under his rule of reproduction you begin to understand why i said male planets and female planets and just like Me darrin being the creator of blockchain having been at its begining and just like God being able to enter this systen yet remain seperate and both for if you look closely you now understand why indeed i named it the genisis block and just like Jesus im able to enter this system and partake in it yet im am not a part of it and yet i am and just like Jesus and the Holy Ghost the bitcoin community await my return please excuse my reference for being like G for I am but man and give all glory to God for everything about my system was modeled directly from him all events in existence has a date a location a time and in reference to all existance the simple and plain core technology of blockchain and bitcoin that any who paid attention with no knowledge of computer can umderstand and for all who asked me to or talked down on me go and buy and bitcoin and if you pay close attention you would soon see that while you mock and insulted me ive been changing the world around you millions and millions all based of. a well known book called the bible and Jesus Christ for with in it just like dna and bits of data contain all the information and instruction to life but lord forgive for as i spoke your word reminded least any man boast so i shall humble myself before you almight and hope that those who seek truth actually beging to know you and start open that book of your so many have rejected just like me and my math or my ideas failing to realize that I could not have done it with out you and that they are changing peoples lives every

Details

Alfred Tarski explained the role of primitive notions as follows:

When we set out to construct a given discipline, we distinguish, first of all, a certain small group of expressions of this discipline that seem to us to be immediately understandable; the expressions in this group we call PRIMITIVE TERMS or UNDEFINED TERMS, and we employ them without explaining their meanings. At the same time we adopt the principle: not to employ any of the other expressions of the discipline under consideration, unless its meaning has first been determined with the help of primitive terms and of such expressions of the discipline whose meanings have been explained previously. The sentence which determines the meaning of a term in this way is called a DEFINITION,...

An inevitable regress to primitive notions in the theory of knowledge was explained by Gilbert de B. Robinson:

To a non-mathematician it often comes as a surprise that it is impossible to define explicitly all the terms which are used. This is not a superficial problem but lies at the root of all knowledge; it is necessary to begin somewhere, and to make progress one must clearly state those elements and relations which are undefined and those properties which are taken for granted.

Examples

The necessity for primitive notions is illustrated in several axiomatic foundations in mathematics:

• Set theory: The concept of the set is an example of a primitive notion. As Mary Tiles writes: [The] 'definition' of 'set' is less a definition than an attempt at explication of something which is being given the status of a primitive, undefined, term. As evidence, she quotes Felix Hausdorff: "A set is formed by the grouping together of single objects into a whole. A set is a plurality thought of as a unit."
• Naive set theory:The empty set is a primitive notion. To assert that it exists would be an implicit axiom.
• Peano arithmetic: The successor function and the number zero are primitive notions. Since Peano arithmetic is useful in regards to properties of the numbers, the objects that the primitive notions represent may not strictly matter.
• Axiomatic systems: The primitive notions will depend upon the set of axioms chosen for the system. Alessandro Padoa discussed this selection at the International Congress of Philosophy in Paris in 1900. The notions themselves may not necessarily need to be stated; Susan Haack (1978) writes, "A set of axioms is sometimes said to give an implicit definition of its primitive terms."
• Euclidean geometry: Under Hilbert's axiom system the primitive notions are point, line, plane, congruence, betweeness, and incidence.
• Euclidean geometry: Under Peano's axiom system the primitive notions are point, segment, and motion.
• Philosophy of mathematics: Bertrand Russell considered the "indefinables of mathematics" to build the case for logicism in his book The Principles of Mathematics (1903).

See also

• Axiomatic set theory
• Foundations of geometry
• Foundations of mathematics
• Mathematical logic
• Notion (philosophy)
• Object theory
• Natural semantic metalanguage