Postulates Definition and 62 Threads

An axiom, postulate or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is a premise or starting point for reasoning.As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic).
When used in the latter sense, "axiom", "postulate", and "assumption" may be used interchangeably. In most cases, a non-logical axiom is simply a formal logical expression used in deduction to build a mathematical theory, and might or might not be self-evident in nature (e.g., parallel postulate in Euclidean geometry). To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms), and there may be multiple ways to axiomatize a given mathematical domain.
Any axiom is a statement that serves as a starting point from which other statements are logically derived. Whether it is meaningful (and, if so, what it means) for an axiom to be "true" is a subject of debate in the philosophy of mathematics.

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  1. M

    What Are the Experimental Foundations of Quantum Mechanics?

    I have the mathematical background to compute things in quantum mechanics. If you give me a standard QM problem to solve I could probably do it. However, I have an extreme lack of understanding of why the postulates of QM are set up the way they are - that the complete description of a particle...
  2. I

    Exploring the Relationship between SR Postulates 1 & 2

    Hi all I was recently told that certain postulates of SR are equivalent or one can be derived from the other. Namely 1) The speed of light in vacuum is constant and is independent of the speed of emitting body; 2) The speed of light is impassable limit; I did some search and found quite...
  3. V

    Postulates of Quantum Mechanics

    In my course of modern Physics one postulate i read is "Associated with any particle moving in a conservative field of force is a wave function which determines everything that can be known about the system" A question arised in my mind is if the particle is moving in non conservative field...
  4. H

    Usign postulates to prove validity of a theorem

    Hello, recently I got this question on my Logic Design course exam, Prove the following theorem using postulates: X OR 1 = 1 I explained it using a simple argument, a variable can be considered as a switch in a circuit, if it is 1 then the switch is on, if it is 0 then the switch...
  5. Z

    Exploring the Postulates of Quantum Physics: Principles and Implications

    Hi everybody, First, I want to excuse myself for the mistakes in this message (and in the others that I will write), because I am not an english speaker and I am not accustomed to write in english. It is the reason why I come here, to improve my English :smile: . If I make a big mistake, I...
  6. L

    Can SR be derived from other postulates than the constancy of c

    The usual foundation for deriving SR is the constancy of the speed of light. Are there other ways to derive SR, and eventually some more general? Have you ever read something about that? Thanks, Michel
  7. T

    Question about continuity postulates

    I had a search for an answer but I turned up nothing, if this has been covered before could someone point me in the right direction? To the question. I'm studying QM at the moment but I'm having trouble with two of the postulates. Is the constraint that the wavefunction must be continuous...
  8. R

    Special Relativity: 1st & 2nd Postulates Explained

    Hello everyone. I've just received my gr 12 physics textbook today and began reading the chapter on Special Relativity, because I find it fascinating. So I'm new to the topic, please bear with me. The first postulate states that "the laws of physics have the same form in all inertial...
  9. Ε

    General Relativity Postulates and History of Publication

    What I've read on special relativity has built it up from its two postulates, the principle of relativity (in the restricted sense) and the constancy of the propagation of light in vacuo. But I haven't seen general relativity's postulates in such a concise listing. I assume the equivalence...
  10. M

    Condition Postulates: Definition & Explanation

    What is "Condition Postulates" ? I'd be happy if someone explains.. Thanks.
  11. V

    Why are the fundamental postulates of special relativity controversial?

    could someone be kind enough to explain to me why the fundamental postulates of special relativity introduced thanks
  12. L

    Book which can describe SR & GR straight from its postulates

    Hello, Id like to ask any of you to suggest to me a book which can describe SR & GR straight from its postulates all the way to the forumals used through math but also through detailed explanations. Does such a book exist ? I have almost complted reading elegant universe and it is pretty...
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