The Axioms.

[trivas7]

But what do you mean by "experience"? Does Sarah Palin experience the existence of God, or following his commandments is based upon the experience of God? What evidence does she have the He exists? What can she point to in all of reality -- the facts, mind you -- that would indicate that it all came to be because of some supernatural spiritual entity? To say existence exists and only existence exists is to say that all of your assertions must be based upon the facts that are available via perception -- i.e. seeing, hearing, touch, smell, taste -- if one cannot ground one's assertions on these then they have no objective value and are meaningless.

So, having in mind something like "existence exists" and staying consistent with the fundamental fact that existence exists leads one to reject anything not based upon the facts of existence. Most people do not hold it in their mind that explicitly, and therefore do not follow through logically (also based on observation) but rather take things at some people's word if those people are convincing enough -- convincing by what standard? blank out, because they cannot name that their ideas are based upon the facts.

Objectivism, by the way, is based upon observation, and the axioms are wide abstractions based upon abstracting from observations. It is not as if once one has the axioms one can deduce that man has rights or that romantic realism is the best art for man; for this requires further observations. Existence exists covers politics and art, but one cannot say something like existence exists, therefore Obama is a bad Presidential candidate until one looks at the facts regarding Obama and other facts related to man's nature, etc.

And just because someone might accept the axioms, it does not necessarily mean that they will be rational about everything, and therefore they are not necessarily Objectivists.

Experience is what an individual undergoes. Surely you're familiar w/ the term.

I don't understand how the axioms are abstractions from observations. What logical bridge connects an empirical observation re something specific in one's ken to a generalization re all of existence? You say that Objectivism is based on observation. But everyone observes. Are you saying that the axioms are simple empirical statements of fact? Inference, BTW, is a perfectly sound means of acquiring knowledge that goes beyond observation.

Please excuse my bullheadedness, but I'm sure that others share my response. Let me know if I'm justing being hopelessly obtuse.

[trivas7]

The difference isn't so much in believing in self evident truths but in knowing without question that those truths the are real and not believing in non-evident superstitions, fallacies and dogma.

The difference re what, exactly? How does knowing w/o question that self-evidence truths are real differ from acknowledging self-evidence truths?

[Thomas M. Miovas Jr.]

I don't understand how the axioms are abstractions from observations. What logical bridge connects an empirical observation re something specific in one's ken to a generalization re all of existence? You say that Objectivism is based on observation. But everyone observes. Are you saying that the axioms are simple empirical statements of fact?

Yes, the axioms are abstractions from observation in that everything is abstracted from all observations of fact, except for the fact that it exists. So, "existence exists" is a conceptual term, but one of the most fundamental ones, and it cannot be denied without utilizing it, which is why it is an axiom. How do you know this applies to all of existence? Well, how can you say you have observed something that does not exist? Once one grasps "existence exists" then anything else one discovers about existence goes into that folder -- i.e. the dog exists, fleas exist, cells exist, animals exist, the earth exists, planets exist, galaxies exist, etc. (going both ways). So, it is not an issue of projecting what might exist, but rather a concept including everything that one knows exists, and like all concepts it is open ended, meaning that it also includes everything else that will be discovered that has the same attributes. For existence exists, this includes the fact of anything existing as discovered in the future. How does one confirm that it exists as opposed to not existing? Well, one observes it. In Objectivism, every concept, including axiomatic concepts, are grounded in reality via observations.

[MichaelH]

The difference re what, exactly? How does knowing w/o question that self-evidence truths are real differ from acknowledging self-evidence truths?

You've focused on the wrong part of Zip's argument. Let me clarify the sentence structure. The difference is believing truths that are self-evident versus non-evident.

The self-evident truths: existence, identity, and consciousness, are required for any philosophy. Even counter-arguing these requires use of them.

Non-evident truths include things like "an invisible all-powerful superperson made everything around us. You can't see, touch, hear, taste, or smell him/her, but he's there". Although there are psychological reasons for such constructs, that doesn't make them valid or true. It's entirely possible to dispute such non-evident "truth"s without invoking the disputed "truth".

I strongly recommend anyone troubled by this issue read Objectivism: The Philosophy of Ayn Rand (OPAR). The book develops Objectivism quite rigorously and explains common concerns with respect to the axioms.

[MichaelH]

The difference re what, exactly? How does knowing w/o question that self-evidence truths are real differ from acknowledging self-evidence truths?

You've focused on the wrong part of Zip's argument. Let me clarify the sentence structure. The difference is believing truths that are self-evident versus non-evident.

The self-evident truths: existence, identity, and consciousness, are required for any philosophy. Even counter-arguing these requires use of them.

Non-evident truths include things like "an invisible all-powerful superperson made everything around us. You can't see, touch, hear, taste, or smell him/her, but he's there". Although there are psychological reasons for such constructs, that doesn't make them valid or true. It's entirely possible to dispute such non-evident "truth"s without invoking the disputed "truth".

I strongly recommend anyone troubled by this issue read Objectivism: The Philosophy of Ayn Rand (OPAR). The book develops Objectivism quite rigorously and explains common concerns with respect to the axioms.

[TuringAI]

IMO there is an inherent contradiction in Objectivism: it wants to base itself on the pure fact of existence while couching this in the language of something called axiomatic concepts. And existence as such isn't a concept. Statements to which no truth value can be ascribed are linguistically nonsensical. "Existence exists", like the phrase "things exist" is a tautology. This confusion bt levels of concepts and reality permeates Objectivism.

A tautology is a valid proposition, for not only is a tautology something that is necessarily true as a whole, though not necessarily implying anything about its parts, it does also reveal some things about language, and validity as a whole, which implies identity. In fact, HAVING language is a big sign that not only existence exists, but it is also knowable to some conscious entity as ourselves.

[Zip]

The difference re what, exactly? How does knowing w/o question that self-evidence truths are real differ from acknowledging self-evidence truths?

Knowing by definition is not arbitrary

know:

1. to perceive or understand as fact or truth; to apprehend clearly and with certainty

Therefore the idea that the axioms are known w/o question or at least without perceived fact is not true.

The difference is between believing and knowing.

I could choose to believe in the Flying purple spaghetti monster. But there is by definition no way to know that such a thing exists.

Is that better?

[trivas7]

A tautology is a valid proposition, for not only is a tautology something that is necessarily true as a whole, though not necessarily implying anything about its parts, it does also reveal some things about language, and validity as a whole, which implies identity. In fact, HAVING language is a big sign that not only existence exists, but it is also knowable to some conscious entity as ourselves.

I deny that tautologies are valid propositions. Like a contradiction, a tautology has no truth value. To determine the truth or falsity of a proposition, it is not enough to consider the terms themselves, one must find out if they agree w/ reality. Tautologies are devoid of logical form, in which proposition and reality agree.

[DavidOdden]

I deny that tautologies are valid propositions.

Do you understand what "tautology" means, and what a "valid proposition" is?

Like a contradiction, a tautology has no truth value

So is it your position that the statement "This cat is simultaneously living and not living" is neither true nor false? I myself would have gone with the position that the statement is false. I'm just wondering if you are confused about "truth" and you think it means "something that you don't know".

Tautologies are devoid of logical form, in which proposition and reality agree.

That would imply then that there is no such thing as "false".

[TuringAI]

I deny that tautologies are valid propositions. Like a contradiction, a tautology has no truth value. To determine the truth or falsity of a proposition, it is not enough to consider the terms themselves, one must find out if they agree w/ reality. Tautologies are devoid of logical form, in which proposition and reality agree.

Have you ever taken a course on mathematical logic? A tautology is a formula which is everywhere true, regardless of its elements. IE it is something that is true based on its defintion.

Definitions are abstractions that have metaphysical value (IE correspondence to reality) based on whether or not they can be reduced into concrete referents. A statement, or 'formula' such as "All bachelors are unmarried" can be broken down conceptually because bachelors are unmarried males, and males and marriage both exist. On the other hand, a statement such as "All unicorns have horns" cannot be broken down in the same manner. Rather, it is the statement that, in history, people referred to horned horses as unicorns. Horses exists. Horns exist. Unicorns do not exist, but because they have meaning to some people they are still imagined by some people.

Notice that even though "All unicorns have horns" cannot be reduced directly, it can be reduced indirectly if we accept the concept "imagination" and that it refers to something a conscious entity has.

[trivas7]

Have you ever taken a course on mathematical logic? A tautology is a formula which is everywhere true, regardless of its elements. IE it is something that is true based on its defintion.

Definitions are abstractions that have metaphysical value (IE correspondence to reality) based on whether or not they can be reduced into concrete referents. A statement, or 'formula' such as "All bachelors are unmarried" can be broken down conceptually because bachelors are unmarried males, and males and marriage both exist. On the other hand, a statement such as "All unicorns have horns" cannot be broken down in the same manner. Rather, it is the statement that, in history, people referred to horned horses as unicorns. Horses exists. Horns exist. Unicorns do not exist, but because they have meaning to some people they are still imagined by some people.

Notice that even though "All unicorns have horns" cannot be reduced directly, it can be reduced indirectly if we accept the concept "imagination" and that it refers to something a conscious entity has.

But tautological propositions aren't mathematical formulae, your point is moot.

Edited November 13, 2008 by trivas7

[trivas7]

Yes, the axioms are abstractions from observation in that everything is abstracted from all observations of fact, except for the fact that it exists.

Except for the fact that it exists in wouldn't be an observation.

[TuringAI]

But tautological propositions aren't mathematical formulae, your point is moot.

Regardless of what we call tautological propositions, they exist in math. A is A is always true, also known as A = A or A -> A. A could be true or A could be false, but what's true IS true and what's false IS false.

This applies to any other options chosen for A, whether they are dependent or independent of a true/false distinction. An apple is an apple. A dog is a dog. A work of art is a work of art.

Furthermore, since your assertion is that they aren't mathematical formulas, and since clearly tautological propositions exist in mathematics, the burden is on you to explain what a formula is and isn't.

[trivas7]

Except for the fact that it exists in wouldn't be an observation. What you abstracted were multiple instances of observation, not the fact that things exist, which is a tautology.

[trivas7]

What logical bridge connects an empirical observation re something specific in one's ken to a generalization re all of existence?

Tentatively answering my own question, the concept of unit is the bridge that connects the empirical observation of entities and the axiom of existence. All entities are units; their similarity consists of the fact that they are all measurable. This is what the axiom of existence expresses. While based on observation, the axiom of existence itself is a conceptual product.

[LovesLife]

Regardless of what we call tautological propositions, they exist in math. A is A is always true, also known as A = A or A -> A.

In mathematics, A = A is an axiom. It can't be deduced or proven; it is true by observation or by postulate.

[Steve D'Ippolito]

In essence a tautology is any expression that must be true. If you reduce it to symbolic logic like (A' and or (A and or (A and B') or (A' and B'), then run all possible combinations values of the variables through it, and it *always* comes out true, it's tautological. The one I just gave is a tautology because you are ORing together four expressions, one of which will be true whether A or B, or neither, or both, happens to false.

[TuringAI]

In essence a tautology is any expression that must be true. If you reduce it to symbolic logic like (A' and or (A and or (A and B') or (A' and B'), then run all possible combinations values of the variables through it, and it *always* comes out true, it's tautological. The one I just gave is a tautology because you are ORing together four expressions, one of which will be true whether A or B, or neither, or both, happens to false.

You might want to turn off smilies when you post.

Here, I did it so that the quoted text in the reply will be what you were actually trying to say.

[TuringAI]

I've been thinking of a system where E represents such a basic fact as existence, and it can be a truth that is outside the domain of the 'not' predicate, which you used in your example as a comma. Then we could go and do things like given a good enough definition of I, which represents identity, it can be shown that it is a corollary of E. Now the trick is to define I properly. The test to see whether or not I is a good enough definition is to test it against itself and the non-invertible nature of E. Let's say it's because allowing I to be in the domain of 'not' would make I false and thus, say, puts E in the domain of the 'not' predicate and therefore can not be allowed. This would, in simpler terms, mean that if identity was allowed to be a false concept, then it would by default be false, since identity means there are no allowable contradictions. Then if we allowed contradictions we could contradict anything, including the absoluteness of existence and what it means to exist.

Likewise I'm sure there's a way to show from I that E is a precondition. Objectivist mathematicians would love this since it's basically the process in reverse, and it is a conclusion that is entailed by the 'given' nature of the problem and which means that the system is internally consistent.

I've basically introduced a concept of non-invertible propositions and the incomplete nature of the 'not' predicate. If there are any problems with this concept please let me know. I will explain it to you.

[Steve D'Ippolito]

You might want to turn off smilies when you post.

Here, I did it so that the quoted text in the reply will be what you were actually trying to say.

Dang, I hate that dude with the sunglasses. I usually remember to put a space in, but I forgot this time. Also I have learned the hard way. that a lower case 'b' gets the same result.

[Thomas M. Miovas Jr.]

I've been thinking of a system where E represents such a basic fact as existence, and it can be a truth that is outside the domain of the 'not' predicate, which you used in your example as a comma. Then we could go and do things like given a good enough definition of I, which represents identity, it can be shown that it is a corollary of E. Now the trick is to define I properly.

I don't think coming up with a rigorous mathematical equation for the axioms is necessary at all, since the axioms of Objectivism are verified by direct observation. You observe that existence exists and only existence exists (and no evidence to the contrary); you observe that you have a consciousness when you realize that you are aware of existence and can direct that awareness; you observe that an entity acts according to what it is rather acting according to what it is not.

Besides, the rest of Objectivism is not deduced from the axioms. One does not start with the observation that existence exists and deduce that emotions are not tools of cognition, but rather one observes that one's emotions are based upon subconsciously held evaluative premises and that these may or may not be in accordance with actual objective values. Likewise one does not start with existence exists and deduce that man has certain inalienable rights, rather it is something one observes about man's nature and the necessity of using one's mind to live one's life.

In short, if making a rigorous mathematical presentation of the axioms is an attempt to deduce everything else, that is the wrong approach.

[trivas7]

Besides, the rest of Objectivism is not deduced from the axioms. One does not start with the observation that existence exists and deduce that emotions are not tools of cognition, but rather one observes that one's emotions are based upon subconsciously held evaluative premises and that these may or may not be in accordance with actual objective values. Likewise one does not start with existence exists and deduce that man has certain inalienable rights, rather it is something one observes about man's nature and the necessity of using one's mind to live one's life.

I'm uncomfortable w/ this remark. IMO Objectivism is an integrated hierarchy of ideas. It is only b/c one acknowledges that if A is A it follows that emotions are not tools of cognition.and may or may not be in accordance w/ actual objective values. B/c existence exists and things are what they are it follows that man is a being possessing certain inalienable rights, etc.

[Thomas M. Miovas Jr.]

I'm uncomfortable w/ this remark. IMO Objectivism is an integrated hierarchy of ideas. It is only b/c one acknowledges that if A is A it follows that emotions are not tools of cognition.and may or may not be in accordance w/ actual objective values. B/c existence exists and things are what they are it follows that man is a being possessing certain inalienable rights, etc.

Objectivism is an integrated philosophy because it integrates observations in a hierarchical manner. The axioms are a guide to what is or is not rational, in the sense that if it does not exist in any way whatsoever it cannot be integrated with the rest of one's knowledge. However, it is not as if once one grasps existence exists one can deduce that man has a brain and neurons or that cats meow. These are things that are abstracted from observation and then non-contradictorily identified and integrated. In other words, one could never come up with an equation from which one could plug in the numbers and get Veranda font from that equation, as in A=A therefore there exists Veranda font without making the observation that Veranda font is something in reality.

Now, once one has made enough integrations, one can come up with statements or equations that automatically include that field of study -- i.e. physics equations for momentum include all momentums and therefore once one understand the equation one can figure out the momentum for a specific case. But I don't think one could have an equation for the axioms and conclude or not conclude that there is life on Mars, for example. Nor does the phrase A is A make it possible to deduce that there are galaxies. However, once one discovers the galaxies, one incorporates that observation into A is A, a galaxy is a galaxy, it is not a puppy dog. But if we never looked out at the universe, say Aristotle holding that A is A, we could not deduce that there were galaxies without further observations. One could not reduce philosophy to a set of equations because philosophy is inductive, not deductive, at least properly done. But, one could say that something conceived violates the law of identity, and therefore say that it cannot exist.

[TuringAI]

I'm uncomfortable w/ this remark. IMO Objectivism is an integrated hierarchy of ideas. It is only b/c one acknowledges that if A is A it follows that emotions are not tools of cognition.and may or may not be in accordance w/ actual objective values. B/c existence exists and things are what they are it follows that man is a being possessing certain inalienable rights, etc.

It does not follow from deduction, but INDUCTION. So I suppose the problem here is to formalize induction using an entirely different approach than mathematics currently uses but from which a compatible system could emerge.

I've considered it this far: There is an ideal construction of our faculty of sensation. Say we consider only the sense of sight. In fact, let's simplify this by saying light hits a camera. The camera takes in certain data and conveys it to a computer, which has no tools other than the camera to perceive the outside world. The light has a source, external objects, and reflects off of them perfectly. Now it is obvious at this point that we're not talking about the real world, so let's make some more simplifying assumptions, which will lend towards making the process simpler: The world is 2D and there is a 1D interface. The 2D world is chunky and fits into a 2D grid. The lens is a 1D ruler which fits perfectly with the grid. The camera is able to move but only in quantities determined by the 1D ruler. It cannot move 'between'. The camera relays the information on the 1D ruler seamlessly to the computer regardless of its position. The computer doesn't move but rather stays put and its field of vision doesn't intersect with itself.

The very first questions in my mind are these: What qualities must the computer have to make sense of the data and to model the outside world? What possible qualities of the observable world are able to be modeled? These are reciprocal questions, but to make the system both solvable and interesting we must give the observable world one set of rules and the computer a unique set of rules.

Now I'm rather curious. What two sets of rules do we need? On one hand, the observable world needs a set of rules that are based off of its reality of being on a 2D grid. On the other hand the computer needs a set of 'computing' rules, a sort of builders set for induction.

I don't think we could get away with certain constructions... in fact I daresay this is a daunting task to make the scenario both solvable AND interesting.

[trivas7]

It does not follow from deduction, but INDUCTION. So I suppose the problem here is to formalize induction using an entirely different approach than mathematics currently uses but from which a compatible system could emerge.

Yes, I take your point re to induction. You seem to want to mathematize logic, which IMO can't be done.