Axioms - Revision history

Dream weaver at 23:56, 8 December 2011

2011-12-08T23:56:51Z

← Older revision		Revision as of 23:56, 8 December 2011
Line 1:		Line 1:
	An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:		An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:

	* [[~~Primacy of~~ Existence]]		* [[Existence]] exists.
	* [[A is A]] ([[Aristotle]]'s law of Identity).		* [[A is A]] ([[Aristotle]]'s law of Identity).
	* [[Axiom of Consciousness\|Consciousness is Conscious]] [of something].		* [[Axiom of Consciousness\|Consciousness is Conscious]] [of something].

Sir Andrew: Re-organized for better flow

2010-10-22T21:37:29Z

Re-organized for better flow

← Older revision		Revision as of 21:37, 22 October 2010
Line 1:		Line 1:
	~~== Axioms and Axiomatic Concepts ==~~		An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:

	An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. ~~([[Axiom_Example\|Example]])~~ Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:

	* [[Primacy of Existence]].		* [[Primacy of Existence]]
	* [[A is A]] ([[Aristotle]]'s law of Identity).		* [[A is A]] ([[Aristotle]]'s law of Identity).
	* [[Axiom of Consciousness\|Consciousness is Conscious]] [of something].		* [[Axiom of Consciousness\|Consciousness is Conscious]] [of something].
			== Axioms and Axiomatic Concepts ==
	In her Introduction to Objectivist Epistemology, she describes the nature of axioms, and shows that the most basic units of man's knowledge are not propositions, but Axiomatic Concepts ("Existence", "Identity", "Consciousness"), which she described as follows:		In her [[Introduction to Objectivist Epistemology]], she describes the nature of axioms, and shows that the most basic units of man's knowledge are not propositions, but Axiomatic Concepts ("Existence", "Identity", "Consciousness"), which she described as follows:

	<blockquote>An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts. It is implicit in all facts and in all knowledge. It is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest.</blockquote>		<blockquote>An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts. It is implicit in all facts and in all knowledge. It is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest.</blockquote>

Sir Andrew: +ARL Link

2010-08-28T00:11:34Z

+ARL Link

← Older revision		Revision as of 00:11, 28 August 2010
Line 18:		Line 18:
	It is fundamental because all our higher-level [[knowledge]] rests on the fact that existence is identity. If we weren't sure of the axiom, we couldn't know whether contradictory ideas could be true, or whether facts true today would hold true tomorrow. It is irrefutable because any attempt to reject identity must rely on identity being true. For example, if one argues that “[[facts]] can be both true and false at the same time”, one assumes that the idea of facts being both true and false is itself true and not false.		It is fundamental because all our higher-level [[knowledge]] rests on the fact that existence is identity. If we weren't sure of the axiom, we couldn't know whether contradictory ideas could be true, or whether facts true today would hold true tomorrow. It is irrefutable because any attempt to reject identity must rely on identity being true. For example, if one argues that “[[facts]] can be both true and false at the same time”, one assumes that the idea of facts being both true and false is itself true and not false.

			== Further Reading ==
			*[http://aynrandlexicon.com/lexicon/axioms.html Axioms at the Ayn Rand Lexicon]
	{{M_Nav}}		{{M_Nav}}

	[[Category: Metaphysics]]		[[Category: Metaphysics]]
	[[Category:Axiom]]		[[Category:Axiom]]

Sir Andrew: Added navigation table to improve wiki traffic flow

2010-08-27T06:05:29Z

Added navigation table to improve wiki traffic flow

← Older revision		Revision as of 06:05, 27 August 2010
Line 18:		Line 18:
	It is fundamental because all our higher-level [[knowledge]] rests on the fact that existence is identity. If we weren't sure of the axiom, we couldn't know whether contradictory ideas could be true, or whether facts true today would hold true tomorrow. It is irrefutable because any attempt to reject identity must rely on identity being true. For example, if one argues that “[[facts]] can be both true and false at the same time”, one assumes that the idea of facts being both true and false is itself true and not false.		It is fundamental because all our higher-level [[knowledge]] rests on the fact that existence is identity. If we weren't sure of the axiom, we couldn't know whether contradictory ideas could be true, or whether facts true today would hold true tomorrow. It is irrefutable because any attempt to reject identity must rely on identity being true. For example, if one argues that “[[facts]] can be both true and false at the same time”, one assumes that the idea of facts being both true and false is itself true and not false.

			{{M_Nav}}

	[[Category: Metaphysics]]		[[Category: Metaphysics]]
	[[Category:Axiom]]		[[Category:Axiom]]

216.199.190.42: /* Axioms and Axiomatic Concepts */

2007-07-17T12:27:09Z

Axioms and Axiomatic Concepts

← Older revision		Revision as of 12:27, 17 July 2007
Line 1:		Line 1:
	== Axioms and Axiomatic Concepts ==		== Axioms and Axiomatic Concepts ==

	An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. ([[Axiom_Example Example]]) Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:		An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. ([[Axiom_Example\|Example]]) Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:

	* [[Primacy of Existence]].		* [[Primacy of Existence]].

216.199.190.42: /* Axioms and Axiomatic Concepts */

2007-07-17T12:26:44Z

Axioms and Axiomatic Concepts

← Older revision		Revision as of 12:26, 17 July 2007
Line 1:		Line 1:
	== Axioms and Axiomatic Concepts ==		== Axioms and Axiomatic Concepts ==

	An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. ([[Axiom_Example]]) Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:		An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. ([[Axiom_Example Example]]) Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:

	* [[Primacy of Existence]].		* [[Primacy of Existence]].

216.199.190.42: /* Axioms and Axiomatic Concepts */

2007-07-17T12:26:26Z

Axioms and Axiomatic Concepts

← Older revision		Revision as of 12:26, 17 July 2007
Line 1:		Line 1:
	== Axioms and Axiomatic Concepts ==		== Axioms and Axiomatic Concepts ==

	An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:		An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. ([[Axiom_Example]]) Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:

	* [[Primacy of Existence]].		* [[Primacy of Existence]].

GreedyCapitalist: Reverted edits by 137.226.13.2 (Talk); changed back to last version by 206.180.38.20

2007-01-15T08:41:37Z

Reverted edits by 137.226.13.2 (Talk); changed back to last version by 206.180.38.20

← Older revision	Revision as of 08:41, 15 January 2007
Line 1:	Line 1:
		== Axioms and Axiomatic Concepts ==

		An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:

		* [[Primacy of Existence]].
		* [[A is A]] ([[Aristotle]]'s law of Identity).
		* [[Axiom of Consciousness\|Consciousness is Conscious]] [of something].

		In her Introduction to Objectivist Epistemology, she describes the nature of axioms, and shows that the most basic units of man's knowledge are not propositions, but Axiomatic Concepts ("Existence", "Identity", "Consciousness"), which she described as follows:

		<blockquote>An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts. It is implicit in all facts and in all knowledge. It is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest.</blockquote>

		<cite>Ayn Rand, [[Introduction to Objectivist Epistemology]], Meridian, New York City, 1990, p. 55.</cite>

		A more lengthy discussion of axioms and their role can be found in [[OPAR]] [[Leonard Peikoff's\|Leonard Peikoff]] Objectivism: The Philosophy of [[Ayn Rand]].

		Axioms are perceptually [[self-evident]], [[primary]], [[fundamental]], and irrefutable. For example, the axiom of identity states that existence is identity, or that to be, is to be something. This axiom is [[perception\|perceptually]] self-evident because identity is affirmed in everything we experience. Every perception is of something -- having certain properties and not others. Identity is primary because it cannot be broken down into any lower concepts or proven using any lower-level facts. One can only prove that it is an axiom, not the axiom itself, because the concept of proof depends on the validity of identity.
		It is fundamental because all our higher-level [[knowledge]] rests on the fact that existence is identity. If we weren't sure of the axiom, we couldn't know whether contradictory ideas could be true, or whether facts true today would hold true tomorrow. It is irrefutable because any attempt to reject identity must rely on identity being true. For example, if one argues that “[[facts]] can be both true and false at the same time”, one assumes that the idea of facts being both true and false is itself true and not false.


		[[Category: Metaphysics]]
		[[Category:Axiom]]

137.226.13.2 at 08:21, 15 January 2007

2007-01-15T08:21:35Z

← Older revision		Revision as of 08:21, 15 January 2007
Line 1:		Line 1:
	~~== Axioms and Axiomatic Concepts ==~~

	An '''axiom''' is an irreducible truth expressed in the form of a proposition. A truth you cannot prove nor do without. Axioms are self-evident concepts that form the basis for all higher-level knowledge. Ayn Rand identified three axioms that meet these criteria:

	* [[Primacy of Existence]].
	* [[A is A]] ([[Aristotle]]'s law of Identity).
	* [[Axiom of Consciousness\|Consciousness is Conscious]] [of something].

	In her Introduction to Objectivist Epistemology, she describes the nature of axioms, and shows that the most basic units of man's knowledge are not propositions, but Axiomatic Concepts ("Existence", "Identity", "Consciousness"), which she described as follows:

	<blockquote>An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts. It is implicit in all facts and in all knowledge. It is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest.</blockquote>

	~~<cite>Ayn Rand, [[Introduction to Objectivist Epistemology]], Meridian, New York City, 1990, p. 55.</cite>~~

	~~A more lengthy discussion of axioms and their role can be found in [[OPAR]] [[Leonard Peikoff's\|Leonard Peikoff]] Objectivism: The Philosophy of [[Ayn Rand]].~~

	Axioms are perceptually [[self-evident]], [[primary]], [[fundamental]], and irrefutable. For example, the axiom of identity states that existence is identity, or that to be, is to be something. This axiom is [[perception\|perceptually]] self-evident because identity is affirmed in everything we experience. Every perception is of something -- having certain properties and not others. Identity is primary because it cannot be broken down into any lower concepts or proven using any lower-level facts. One can only prove that it is an axiom, not the axiom itself, because the concept of proof depends on the validity of identity.
	It is fundamental because all our higher-level [[knowledge]] rests on the fact that existence is identity. If we weren't sure of the axiom, we couldn't know whether contradictory ideas could be true, or whether facts true today would hold true tomorrow. It is irrefutable because any attempt to reject identity must rely on identity being true. For example, if one argues that “[[facts]] can be both true and false at the same time”, one assumes that the idea of facts being both true and false is itself true and not false.


	~~[[Category: Metaphysics]]~~
	~~[[Category:Axiom]]~~

206.180.38.20 at 19:23, 4 December 2006

2006-12-04T19:23:39Z

← Older revision		Revision as of 19:23, 4 December 2006
Line 13:		Line 13:
	<cite>Ayn Rand, [[Introduction to Objectivist Epistemology]], Meridian, New York City, 1990, p. 55.</cite>		<cite>Ayn Rand, [[Introduction to Objectivist Epistemology]], Meridian, New York City, 1990, p. 55.</cite>

	A more lengthy discussion of axioms and their role can be found in [[OPAR]] [[Leonard Peikoff's\|~~Lenoard~~ Peikoff]] Objectivism: The Philosophy of [[Ayn Rand]].		A more lengthy discussion of axioms and their role can be found in [[OPAR]] [[Leonard Peikoff's\|Leonard Peikoff]] Objectivism: The Philosophy of [[Ayn Rand]].

	Axioms are perceptually [[self-evident]], [[primary]], [[fundamental]], and irrefutable. For example, the axiom of identity states that existence is identity, or that to be, is to be something. This axiom is [[~~preception~~\|perceptually]] self-evident because identity is affirmed in everything we experience. Every perception is of something ~~â€"~~ having certain properties and not others. Identity is primary because it cannot be broken down into any lower concepts or proven using any lower-level facts. One can only prove that it is an axiom, not the axiom itself, because the concept of proof depends on the validity of identity.		Axioms are perceptually [[self-evident]], [[primary]], [[fundamental]], and irrefutable. For example, the axiom of identity states that existence is identity, or that to be, is to be something. This axiom is [[perception\|perceptually]] self-evident because identity is affirmed in everything we experience. Every perception is of something -- having certain properties and not others. Identity is primary because it cannot be broken down into any lower concepts or proven using any lower-level facts. One can only prove that it is an axiom, not the axiom itself, because the concept of proof depends on the validity of identity.
	It is fundamental because all our higher-level [[knowledge]] rests on the fact that existence is identity. If we ~~werenâ€™t~~ sure of the axiom, we ~~couldnâ€™t~~ know whether contradictory ideas could be true, or whether facts true today would hold true tomorrow. It is irrefutable because any attempt to reject identity must rely on identity being true. For example, if one argues that ~~â€œ~~[[facts]] can be both true and false at the same ~~time~~,~~â€~~ one assumes that the idea of facts being both true and false is itself true and not false.		It is fundamental because all our higher-level [[knowledge]] rests on the fact that existence is identity. If we weren't sure of the axiom, we couldn't know whether contradictory ideas could be true, or whether facts true today would hold true tomorrow. It is irrefutable because any attempt to reject identity must rely on identity being true. For example, if one argues that “[[facts]] can be both true and false at the same time”, one assumes that the idea of facts being both true and false is itself true and not false.


	[[Category: Metaphysics]]		[[Category: Metaphysics]]
			[[Category:Axiom]]