axiomatic system
1
9.5
- noun
- /ˌæksɪəˈmætɪk ˈsɪstəm/
- Specialized
:
sistema axiomático
- Mark, at the risk of asking you to repeat yourself (and I apologize in advance for that), I have to take the opportunity to ask: is there any axiomatic system in which the concept of infinity is actually expressed as a number?
And you can prove that your axiomatic system allows for different models, the standard integers and the other integers.
- And you can prove that your axiomatic system allows for different models, the standard integers and the other integers.
Examples
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Students may perceive deontological analysis to be analogous to the application of axiomatic systems.
Academic text (2017) -
Abraham Lincoln was a fan, and the US Declaration of Independence used Euclid's axiomatic system.
Blog text (7) -
And you can prove that your axiomatic system allows for different models, the standard integers and the other integers.
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For non-consequentialists, this seems to usually result in them either simply relying on a combination of intuition (not as much a fault in ethics as in other subjects, but we should try to do better) and axiomatic systems.
Blog text (21) -
When intuition collides with an axiomatic system, or different axiomatic systems contradict one another, they don't have the ability to resolve the issue.
Blog text (21) -
When intuition collides with an axiomatic system, or different axiomatic systems contradict one another, they don't have the ability to resolve the issue.
Blog text (21) -
Infinity and division by zero call into question the nature of the axiomatic systems of numbers that we have developed, and an interesting line of thought about that all comes from Kurt Gödel.
Blog text (9) -
An axiomatic system consists of basic principles that serve as the foundation for mathematical reasoning.
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In an axiomatic system, theorems are derived logically from a set of established axioms.
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Every axiomatic system must be consistent to ensure valid conclusions can be drawn from its theorems.
Synonyms
1
9.8
A set of symbols and rules that people use to make and check proofs in logic
1
6.5
A set of rules and methods for making correct conclusions
A set of rules and ideas used to decide if an argument is correct
How Axiomatic
Surface Forms
Morphology
The sense 'a set of axioms forming a foundation' is directly compositional from 'axiomatic' (pertaining to accepted axioms) + 'system' (a set or organized structure). This modifier–noun combination follows ordinary semantic composition and is cross-linguistically transparent, so a learner who knows both constituents would readily infer the MWE meaning.
Etymology
Axiomatic system comes from the idea of a few simple truths called axioms that act like building blocks for a whole system. So, it means a set of basic rules from which all other statements in a theory are logically built, the 'foundation' of that theory.