Axioms - What Are They?

[AnonKat]

http://www.youtube.com/watch?v=1xMMovinrSQ

http://en.wikipedia.org/wiki/Axiom


In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. That is to say, an axiom is a logical statement that is assumed to be true. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths.

[Lesolee (Sith Lord)]

Cogito, ergo sum.
:yawn:

[freethinker]

Where are you going with this? BTW that guy was boring.

[Mark A. Baker]

http://www.youtube.com/watch?v=1xMMovinrSQ

http://en.wikipedia.org/wiki/Axiom

The boy is driveling. No doubt due to reliance on his choice of 'source'. :duh:

Axioms are in logic essentially synonomous with postulates. They are the foundation assumptions of a logically developed system. As such they are effectively arbitraries, although they may seem to be 'obviously true', hence the assumption of these statements as foundational 'truths'. For example, the parallel postulate, the axiom of choice, etc.. The elimination or alteration of axioms can lead to completely different systems.

Wikipedia is more nearly correct.


Mark A. Baker

[AnonKat]

Where are you going with this? BTW that guy was boring.

educational

[Mark A. Baker]

educational

No. Misinformed. :eyeroll:

See prior post.


Mark A. Baker

[AnonKat]

The boy is trying you pompous elitist. edit: make that elitarian.


The boy is driveling. No doubt due to reliance on his choice of 'source'. :duh:

Axioms are in logic essentially synonomous with postulates. They are the foundation assumptions of a logically developed system. As such they are effectively arbitraries, although they may seem to be 'obviously true', hence the assumption of these statements as foundational 'truths'. For example, the parallel postulate, the axiom of choice, etc.. The elimination or alteration of axioms can lead to completely different systems.

Wikipedia is more nearly correct.


Mark A. Baker

[AnonKat]

Anonkats Axiom 1: I am

lol


No. Misinformed. :eyeroll:

See prior post.


Mark A. Baker

[Mark A. Baker]

Anonkats Axiom 1: I am

lol

Descartes' Axiom 1: cogito

Descartes' Lemma 1: ergo, sum


Mark A. Baker :coolwink:

[AnonKat]

Descartes' Axiom 1: cogito

Descartes' Lemma 1: ergo, sum


Mark A. Baker :coolwink:

the reason for my post was to let people see that axioms isn't a very well discussed topic.

to let exes see that axioms are not set in stone or as you say arbitrary. edit: that the axiom it isn't a hubbard invention.

bibo ergo sum

[Mark A. Baker]

... bibo ergo sum

in vino veritas :cheers2:


Mark A. Baker

[AnonKat]

in vino veritas :cheers2:


Mark A. Baker

http://dictionary.reference.com/browse/axiom


ax·i·om   /ˈæksiəm/ Show Spelled
[ak-see-uhm] Show IPA

–noun
1. a self-evident truth that requires no proof.
2. a universally accepted principle or rule.
3. Logic, Mathematics . a proposition that is assumed without proof for the sake of studying the consequences that follow from it.

[Mark A. Baker]

http://dictionary.reference.com/browse/axiom

The problem with the first two definitions is that whereas there are many statements which appear to be 'self-evident' or 'universally accepted', those conditions are not at all the same thing as necessarily being true.

Hence definition 3, the logician's choice.


Mark A. Baker :)

[Jachs]

Why didnt you tell Hubbard that Mark?

1. a self-evident truth that requires no proof.
2. a universally accepted principle or rule.

Think of all those students having realizing self-evident 'truths' in their universally accepted one stop shop.