Axioms are neither proved nor disproved.

Exactly! They are superior to proven facts! They are the basis for ALL proof. They are the 'gods and goddesses' of proof as a concept in our consciousness!.

They're far above 'proof'. They're the perfect absolute truth.

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Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
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How does Objectivism equate with Myths, Legends, and Conspiracies...???

Going back to about last year Rush and I along with Knightmate and several other regulars debated the 'how do you know what you know' issues in relation to various claims in here the 'myths, legends, and conspiracies' thread. It's impossible to talk about what is a 'valid' , hoax, indeterminate, etc etc ufo claim, bigfoot sighting, demonic possession etc etc without resorting to epistemology. Which of course, is the 2nd main branch of philosophy.

Otherwise...if there is no standards then all ideas are equally valid. Things are both true and false at the same time. The Loch Ness monster exists and does not exist at the same time and so on.

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Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
I did NOT authorize this belly writing!

Geometers (mathematicians) were first and foremost philosophers.

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Capitalize on this good fortune, one word can bring you round ... changes.

Axioms are neither proved nor disproved.

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Capitalize on this good fortune, one word can bring you round ... changes.

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

Ayn Rand's philosophy is based on three axioms: the axiom of Existence, the law of Identity, and the axiom of Consciousness. Rand defined an axiom as "a statement that identifies the base of knowledge and of any further statement pertaining to that knowledge, a statement necessarily contained in all others whether any particular speaker chooses to identify it or not. An axiom is a proposition that defeats its opponents by the fact that they have to accept it and use it in the process of any attempt to deny it."[5] As Leonard Peikoff noted, Rand's argumentation "is not a proof that the axioms of existence, consciousness, and identity are true. It is proof that they are axioms, that they are at the base of knowledge and thus inescapable."[4]

Objectivism states that "Existence exists" (the "axiom of Existence") and "Existence is Identity." To be is to be "an entity of a specific nature made of specific attributes."[5] That which has no attributes does not and cannot exist. Hence, "A is A" ("Law of Identity:") a thing is what it is. Whereas "existence exists" pertains to existence itself (whether something exists or not), the law of identity pertains to the nature of an object as being necessarily distinct from other objects (whether something exists as this or that). As Rand wrote, "A leaf cannot be all red and green at the same time, it cannot freeze and burn at the same time. A is A."

That which is exists is definable (by its attributes) is a questionable statement.
What are the points of undefined terms and axioms?
To avoid circular reasoning.
It is from undefined terms, then definitions, then axioms, that propositions and their proofs follow.

From Euclid until Hilbert, axioms were statements taken to be true without proof. These statements were viewed as "self-evident." Interesting? The current approach to axioms is that there does not need to be any self-evidence. The axioms may even be about mathematical structures for which there is no currently known way to view them in the ways we perceive the universe, so how can we talk about them being self-evident? However, the axiomatic system must be consistent.
It cannot lead to two if-then statements later on which contradict each other.

As an example, what a straight line is in Euclidean geometry is different from what a straight line is in Hyperbolic geometry. Which, if either, is the geometry of "reality"? It is not known yet. Empirical attempts to measure this have taken place and some are probably still under way.

Sorry, you are arguing against straw men.

Objectivism does not NOT hold that axioms are self evident. Show us where that was quoted??

Axioms are those first principles that MUST be presumed to be true in any effort to attempt to disprove them.

Philosophy is NOT Euclidean geometry. You're doing nothing but forcing straw men (ie false) arguments into the topic.

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Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
I did NOT authorize this belly writing!

The same point applies to concepts denoting specific forms of error. If we cannot ever be certain that an argument is logically valid, if validity is unknowable, then the concept of "invalid" reasoning is impossible to reach or apply. If we cannot ever know that a man is sane, then the concept of "insanity" is impossible to form or define. If we cannot recognize the state of being awake, then we cannot recognize or conceptualize a state of not being awake (such as dreaming). If man cannot grasp X, then "non-X" stands for nothing.

Ok....you know I am loathe to have this kind of discussion in here....but just for the sake of argument....

Doesn't it also stand to reason, then, that " impossible " cannot be defined because man has not yet discovered everything which IS possible??

Huh? Knightmate, it's impossible to discuss whether or not 'Bigfoot' videos or Ufo abductions are valid or rising or falling interest rates do this or that to such and such segment of the economy without epistemology. Your protestations to the contrary notwithstanding.

What do you mean that

Doesn't it also stand to reason, then, that " impossible " cannot be defined because man has not yet discovered everything which IS possible??

Did you mistype? Hmmm....so air plane flight is 'not discovered as possible'?

You typed a message. Hell, you created a whole thread going back 2 years almost and ipso facto that is 'possible'. Hell, man, you did it. And it is certainly 'possible'...nay, a 'fact' that you are reading this right now.

What do you mean that mankind has NEVER DISCOVERED ANYTHING TO BE 'POSSIBLE' ?

That isn't what I said Robert. You misread my intention.

What I said was.....man has not yet discovered everything that IS possible. There are new discoveries being made on a daily basis.

As in the days of the Wright Brothers....what may seem impossible today...may be commonplace in the near ( relatively speaking ) future.

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

Ayn Rand's philosophy is based on three axioms: the axiom of Existence, the law of Identity, and the axiom of Consciousness. Rand defined an axiom as "a statement that identifies the base of knowledge and of any further statement pertaining to that knowledge, a statement necessarily contained in all others whether any particular speaker chooses to identify it or not. An axiom is a proposition that defeats its opponents by the fact that they have to accept it and use it in the process of any attempt to deny it."[5] As Leonard Peikoff noted, Rand's argumentation "is not a proof that the axioms of existence, consciousness, and identity are true. It is proof that they are axioms, that they are at the base of knowledge and thus inescapable."[4]

Objectivism states that "Existence exists" (the "axiom of Existence") and "Existence is Identity." To be is to be "an entity of a specific nature made of specific attributes."[5] That which has no attributes does not and cannot exist. Hence, "A is A" ("Law of Identity:") a thing is what it is. Whereas "existence exists" pertains to existence itself (whether something exists or not), the law of identity pertains to the nature of an object as being necessarily distinct from other objects (whether something exists as this or that). As Rand wrote, "A leaf cannot be all red and green at the same time, it cannot freeze and burn at the same time. A is A."

That which is exists is definable (by its attributes) is a questionable statement.
What are the points of undefined terms and axioms?
To avoid circular reasoning.
It is from undefined terms, then definitions, then axioms, that propositions and their proofs follow.

From Euclid until Hilbert, axioms were statements taken to be true without proof. These statements were viewed as "self-evident." Interesting? The current approach to axioms is that there does not need to be any self-evidence. The axioms may even be about mathematical structures for which there is no currently known way to view them in the ways we perceive the universe, so how can we talk about them being self-evident? However, the axiomatic system must be consistent.
It cannot lead to two if-then statements later on which contradict each other.

As an example, what a straight line is in Euclidean geometry is different from what a straight line is in Hyperbolic geometry. Which, if either, is the geometry of "reality"? It is not known yet. Empirical attempts to measure this have taken place and some are probably still under way.

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Capitalize on this good fortune, one word can bring you round ... changes.

How does Objectivism equate with Myths, Legends, and Conspiracies...???

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Account frozen...

The same point applies to concepts denoting specific forms of error. If we cannot ever be certain that an argument is logically valid, if validity is unknowable, then the concept of "invalid" reasoning is impossible to reach or apply. If we cannot ever know that a man is sane, then the concept of "insanity" is impossible to form or define. If we cannot recognize the state of being awake, then we cannot recognize or conceptualize a state of not being awake (such as dreaming). If man cannot grasp X, then "non-X" stands for nothing.

Ok....you know I am loathe to have this kind of discussion in here....but just for the sake of argument....

Doesn't it also stand to reason, then, that " impossible " cannot be defined because man has not yet discovered everything which IS possible??

Huh? Knightmate, it's impossible to discuss whether or not 'Bigfoot' videos or Ufo abductions are valid or rising or falling interest rates do this or that to such and such segment of the economy without epistemology. Your protestations to the contrary notwithstanding.

What do you mean that

Doesn't it also stand to reason, then, that " impossible " cannot be defined because man has not yet discovered everything which IS possible??

Did you mistype? Hmmm....so air plane flight is 'not discovered as possible'?

You typed a message. Hell, you created a whole thread going back 2 years almost and ipso facto that is 'possible'. Hell, man, you did it. And it is certainly 'possible'...nay, a 'fact' that you are reading this right now.

What do you mean that mankind has NEVER DISCOVERED ANYTHING TO BE 'POSSIBLE' ?

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Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
I did NOT authorize this belly writing!

And goodness knows...if it weren't " important " than no one would bother to borrow it as a way of life.

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Air Cold, the blade stops;
from silent stone,
Death is preordained

Calm Chaos Forums : Everyone Welcome

All I know is, that everybody follows a borrowed philosophy. Few are original thinkers.

Everybody? Really?

That must be alot of people.

Several Billion.

I agree. Only a few of the brightest and most originative of thinkers have any thing of value historically to add to philosophy especially when it comes to actually forming a 'school' of thought as we call it.

I appreciate your praise and obvious reverence for what it takes to be such a creative and monumental individual that possess the rarest qualities. If it were easy or common it wouldn't be that important would it? I suppose Einstein should be dismissed since most of us never thought of his ideas before or Copernicus should be ignored since even today almost no layman has a clue what his reasonings were.

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Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
I did NOT authorize this belly writing!

All I know is, that everybody follows a borrowed philosophy. Few are original thinkers.

Everybody? Really?

That must be alot of people.

Several Billion.

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All I know is, that everybody follows a borrowed philosophy. Few are original thinkers.

Everybody? Really?

That must be alot of people.

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Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
I did NOT authorize this belly writing!

All I know is, that everybody follows a borrowed philosophy. Few are original thinkers

And people complain about Jeffrey's Q'uranic cut and pastes! LOL!!!

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Capitalize on this good fortune, one word can bring you round ... changes.

All I know is, that everybody follows a borrowed philosophy. Few are original thinkers.

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The same point applies to concepts denoting specific forms of error. If we cannot ever be certain that an argument is logically valid, if validity is unknowable, then the concept of "invalid" reasoning is impossible to reach or apply. If we cannot ever know that a man is sane, then the concept of "insanity" is impossible to form or define. If we cannot recognize the state of being awake, then we cannot recognize or conceptualize a state of not being awake (such as dreaming). If man cannot grasp X, then "non-X" stands for nothing.

Ok....you know I am loathe to have this kind of discussion in here....but just for the sake of argument....

Doesn't it also stand to reason, then, that " impossible " cannot be defined because man has not yet discovered everything which IS possible??

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Air Cold, the blade stops;
from silent stone,
Death is preordained

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I actually had an occasion to ask Dr. Peikoff a question regarding the Cartesian doubts. He knew Rand and were lifelong friends.

This ends the epistemology lesson for today.
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Doubting without a basis is the equivalent of—is indeed a form of—asserting without a basis. Both procedures, being arbitrary, are disqualified by the very nature of human cognition. In reason, certainty must precede doubt, just as a grasp of truth must precede the detection of error. To establish a claim to knowledge, what one must do is to prove an idea positively, on the basis of the full context of evidence available; i.e., a man must prove that he is right. It is not incumbent on anyone—nor is it possible—to prove that he is not wrong, when no evidence of error has been offered.

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Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
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It is possible, the skeptic argument declares, for man to be in error; therefore, it is possible that every individual is in error on every question. This argument is a non sequitur; it is an equivocation on the term "possible."

What is possible to a species under some circumstances, is not necessarily possible to every individual member of that species under every set of circumstances. Thus, it is possible for a human being to run the mile in less than four minutes; and it is possible for a human being to be pregnant. I cannot, however, go over to a crippled gentleman in his wheelchair and say: "Perhaps you'll give birth to a son next week, after you've run the mile to the hospital in 3.9 minutes—after all, you're human, and it is possible for human beings to do these things."

The same principle applies to the possibility of error—or of truth. If someone maintains that New York City is made of mushroom soup, he cannot defend his idea by saying: "It is possible for human beings to reach the truth, I am human, so maybe this is the truth." No matter what is possible under some conditions, a man cannot be "possibly" right when he is blatantly wrong. By the same token, no skeptic can declare that you are possibly wrong, when you are blatantly right. "It is possible for man … " does not justify "It is possible that you … " The latter claim depends on the individual involved, and on the conditions.

"Maybe you're wrong" is an accusation that must be supported by specific evidence. It cannot be uttered without context, grounds, or basis, i.e., arbitrarily.





Leonard Peikoff,
"'Maybe You're Wrong,'" The Objectivist Forum,

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And a little more....



The crusading skepticism of the modern era; the mounting attack on absolutes, certainty, reason itself; the insistence that firm convictions are a disease and that compromise in any dispute is men's only recourse—all this, in significant part, is an outgrowth of Descartes' basic approach to philosophy. To reclaim the self-confidence of man's mind, the first modern to refute is Kant (see Introduction to Objectivist Epistemology); the second is Descartes.

Observe that Descartes starts his system by using "error" and its synonyms or derivatives as "stolen concepts."

Men have been wrong, and therefore, he implies, they can never know what is right. But if they cannot, how did they ever discover that they were wrong? How can one form such concepts as "mistake" or "error" while wholly ignorant of what is correct? "Error" signifies a departure from truth; the concept of "error" logically presupposes that one has already grasped some truth. If truth were unknowable, as Descartes implies, the idea of a departure from it would be meaningless.

The same point applies to concepts denoting specific forms of error. If we cannot ever be certain that an argument is logically valid, if validity is unknowable, then the concept of "invalid" reasoning is impossible to reach or apply. If we cannot ever know that a man is sane, then the concept of "insanity" is impossible to form or define. If we cannot recognize the state of being awake, then we cannot recognize or conceptualize a state of not being awake (such as dreaming). If man cannot grasp X, then "non-X" stands for nothing.

Fallibility does not make knowledge impossible. Knowledge is what makes possible the discovery of fallibility.

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Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
I did NOT authorize this belly writing!

Fascinating... Thank you for the link!

I must admit my philosophical knowlege base is pretty narrow, so I'm left sort of reeling, and feeling compelled to say something totally inappropriate in response... Something along the lines of "Woah, man... Deep!"

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