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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 Ancient Greek word ἀξίωμα ( axíōma ), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
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Meaning Postulate is a formula to express an aspect of the sense of a predicate. The formula is expressed with - so-called - connectives. The used connectives are: paraphrase ≡ "if and only if" entailment → "if" binary antonomy ~ "not" Following examples will simplify this: 1. "If and only if X is a man, then X is a human being."
In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause [1] attitudes and taught by Aristotelians, and nuanced versions of first principles are referred to as postulates by Kantians.
The postulate was long considered to be obvious or inevitable, but proofs were elusive. Eventually, it was discovered that inverting the postulate gave valid, albeit different geometries. A geometry where the parallel postulate does not hold is known as a non-Euclidean geometry.
A presupposition of a sentence must normally be part of the common ground of the utterance context (the shared knowledge of the interlocutors) in order for the sentence to be felicitous. Sometimes, however, sentences may carry presuppositions that are not part of the common ground and nevertheless be felicitous.
Ramsey sentences are formal logical reconstructions of theoretical propositions attempting to draw a line between science and metaphysics. A Ramsey sentence aims at rendering propositions containing non-observable theoretical terms (terms employed by a theoretical language) clear by substituting them with observational terms (terms employed by an observation language, also called empirical ...
The sentence states that, when a particular sequence of steps is used to construct another sentence, that constructed sentence will not be provable in F. However, the sequence of steps is such that the constructed sentence turns out to be G F itself. In this way, the Gödel sentence G F indirectly states its own unprovability within F. [4]