Philosophy Stack Exchange
Philosophy Stack Exchange

Questions tagged [axiom]

48 questions
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What is the difference between depth and surface information?

I was looking for an answer to this question: Was Euclid's method of proof axiomatic? While doing so I ran across an abstract of Jaakko Hintikka for an article "What is the axiomatic method?" where the distinction between depth and surface…
Frank Hubeny
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Is the fact that ZFC implies that 1+1=2 an absolute truth?

This question is somehow of a follow up to to this other one, and it's something that has bugged me for a while. I understand the notion that there's no "absolute truth" in math, in the sense that every theorem follows from an assumed set of axioms.…
Juan
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Is faith required to believe any axiomatic assumption the scientific method is built upon?

It's my understanding that the scientific method builds upon certain axiomatic assumptions, such as uniformitarianism and the principle of induction. Is faith required to believe these axiomatic assumptions?
user48437
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Does reality have axioms?

Mathematics is considered the queen of sciences as it allows us to build simplified but functional models of the reality that surrounds us. However, I do not understand if this isomorphism could be possible if reality were not itself a consistent…
Yamar69
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Are pursuing the well-being and reducing the suffering of sentient beings objectively good things?

I think most people intuitively agree that increasing their own well-being and minimizing their own suffering are the right things to do. Everyone wants to be happy, enjoy a good health, etc. The whole Maslow's hierarchy of needs is a thing for a…
user48437
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Axiomatization of philosophy?

In mathematics, many theories are built on assumptions that are taken to be true, and they are most often called axioms, and then, with the help of logical laws and definitions and with various methods of proof statements are proven to be true or…
Grešnik
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What are the assumptions adopted by the scientific community?

What are the core assumptions of the modern scientific community with which they use to view the world and formulate theories etc? By assumptions I mean premises taken as fact (about the universe/reality) but which cannot be proven definitively. I…
michael
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Are axioms assumptions and should they be minimized?

Are axioms nothing but assumptions and, if yes and in accordance to Occam's Razor, should they be minimized? When postulating scientific theorems which, unlike axioms, are subject to the scrutiny of proof but do factor in axioms, are there formal…
amphibient
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Do philosophers generally reject that philosophical reasoning relies on axioms?

The way I've always thought that philosophy worked is that philosophers have a certain set of tools (deduction, laws of thought, basic sources of knowledge) which they use to come to reasoned answers to questions. Most importantly, these tools are…
Christian Dean
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What are the most rational basic beliefs?

I understand that this question might be difficult or even unresolved. But within a foundationalist view of knowledge, has anyone proposed a set of basic beliefs that seem to be the most rational for forming an accurate model of reality, or at least…
blue-raven
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Can a solid theory ever exist without any axioms?

In math, numbers and addition are logically defined by Zermelo Set Theory, a small group of axioms upon which everything else can be built. Could it be possible to have a working theory, (in any field not just math), without any preexisting axioms?
user189728
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Basic truths as self-justified or parajustified

Some foundationalists maintain that basic truths are self-justifying, which means they are allowing, in some exceptional cases at least, a form of circular reasoning; petitio principii or begging the question. This is subtly different from…
user1113719
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Is it possible to create an axiomatic system where 1+1 doesn't equal 2? What would be the consequences of such a system?

1+1=2 is a result (perhaps arguably more of a definition than a theorem?) of Peano Arithmetic, as well as other systems such as ZFC. I understand that 1+1 doesn't necessarily have to equal 2 if we consider addition modulo n, for some n in the…
mark-antoin9977
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How do philosophers formally characterise mathematical objects?

In the Stanford Encyclopedia of Philosophy article, 'Platonism in the Philosophy of Mathematics', the following formalisation is given for the existence of a mathematical object: Existence can be formalized as ‘∃xMx’, where ‘Mx’ abbreviates…
Samuel
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Can there be a solution to these three problems?

I have read many times that some problems or logical propositions do not have solutions or are outright impossible. These are three examples of such problems: [The Russell's paradox] which is deemed as contradictory with no possible solutions [The…
vengaq
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