Tautologies

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I've just checked the entry in the objectivist wiki about Axioms of objectivism and remembered that I've had a maths lesson when we discussed Tautologies, which are statements that are always true. I'll type them here and try to add some philosophical meaning to them. There's 13 of them.

Ayn Rand limits her axioms to 3 in her philosophy, which makes it hard to logically reach other conclusions. However, by learning also the tautologies below, you can be faster about making your conclusions, not to mention that there's less margin for error.

First, however, I'd like to explain the symbols I use:

<=> equivalence

! not

& and

| or

=> implication (a => b means a implies

PH: philosophical meaning of the tautology

EX: example

Here are the tautologies:

1. x <=> x (Law of Identity)

PH: A is A.

2. !(x & !x) (Law of Contradiction)

PH: It is not true that contradictions are possible (that at the same time x and not x are possible). Said in a simpler way, contradictions aren't possible.

3. x | !x

PH: Either ... or ... (Either it is x, or it is not x)

4. !(!x) <=> x (Law of double negation)

PH: If it's not true that x is not true, then x is true.

EX: "Not untrue" means "true".

5. x => (y => x) (Ex quolibet verum - Truth from anything)

PH: If x is true then any premise y guarantees that x will be true.

EX: If I love the works of Ayn Rand then my being here implies that I love the works of Ayn Rand.

6. !x => (x => y) (Ex falso quodlibet - From wrong follows arbitrary statement)

PH: If x isn't true then any statement which x implies is true.

EX: If God doesn't exist then god is good.

7. (x & (x => y)) => y (Modus Ponens)

PH: If x is true and x implies y then y is true.

EX: If I like Ayn Rand and my liking Ayn Rand means I like her work, then I like the works of Ayn Rand.

8.

a) ((x => y) & !y) => !x (Modus Tollens)

PH: If x implies y and y isn't true then x isn't true.

EX: If my going to church implies that I believe in god and I don't believe in god, then I don't go to church.

((!x => y) & !y) => x (Proof from contradiction)

PH: If a premise leads to contradiction, then the premise is wrong.

9. ((x => y) & (y => z)) => (x => z) (Syllogism)

PH: Conceptualization (If A leads to B and B leads to C then A leads to C)

EX: If I love computing and computing means programming, then I love programming.

10. ((x => y) & (y => x)) <=> (x <=> y)

PH: If A leads to B and from B follows A then A is equivalent to B, and vice versa. Equivalence is an implication that works both ways.

EX: Synonims.

11. (x => y) <=> (!y => !x)

PH: If x implies y then absence of y implies absence of x. (Also, if absence of y implies absence of x then x implies y) Confirming the general principle confirms its consequences, while negating one of the consequences negates the principle.

EX: If from my liking of Ayn Rand's works follows my liking for The Fountainhead, then from my disliking The Fountainhead would follow my disliking of the works of Ayn Rand. In other words, if I said I liked the works of Ayn Rand but also said I didn't like The Fountainhead (which is the work of Ayn Rand) then I lied for sure (because contradictions are impossible).

12. ((x <=> y) & (y <=> z)) => (x <=> z)

PH: If A is B and B is C then A is C.

EX: If I am human and human is organic then I am organic. (Ok, I'm sort of running out of examples)

13. (x <=> y) <=> (!x <=> !y)

PH: If x is y then not x isn't y.

EX: If myself and only myself am human, then everything else but myself isn't human. (See what I means about running out of examples?)

Sorry for my examples and explanations of philosophical implication being a little awkward, but I had to do them all by myself. If anyone could do it better, then please go ahead.

[Ed from OC]

Ayn Rand limits her axioms to 3 in her philosophy, which makes it hard to logically reach other conclusions.

1. She "limited" her axioms in metaphysics to just 3 because that's all there are. I don't know of any others.

2. Objectivism wasn't created and isn't structured along the lines of "reaching other conclusions" from the axioms. This implies a rationalistic approach in which the whole of her philosophy is supposed to be deduced from some starting point. On the contrary, she formed her philosophy inductively.

A simple example: how does one go from "existence" to "ethics"? There's nothing in the concept of existence (or the axiom that it exists) that would lead to a concept of ethics, let alone establish a rational ethical code. But if one oberves reality, all sorts of things show up: that men exist; that they are mortal; that they have freewill; that survival is not guaranteed, but requires a specific course of action based on the nature of the organism; that man's life requires long-term thought and planning; that irrational choices are harmful; and so on. From observation of these sorts of facts, and after much, much thought, Ayn Rand came up with an objective code of ethics.

Note how rich the inductive process is. There's a treasure trove of information out there to be had, that makes the few gems one can get through deduction seem quite small.

My point is that while deductive reasoning is a wonderful tool, it could not get anywhere without induction. After all, the premises one deduces from have to come from somewhere, which makes induction a more fundamental thought process. Moreover, the truth of one's deductions relies as much on the truth of one's premises as the structure of the argument.

[DavidOdden]

I don't exactly get the point. Formally, you don't need => or <=> (if you're looking for minimalist notation, all you need is the Sheffer stroke).

My objection to your examples labeled "philosophical meaning of the tautology" is that they are really not equivalent to the symbolic formulae. For example "A <=> A" may be translated into an expression like "A is A", but this is really not the same as the fundamental axiom of Objectivism, as explained in Galt's speech for example. "A is A" -- as Galt articulates it, says "You cannot have your cake and eat it, too" and therefore the Law of Non-Contradiction is not separate. Interestingly, while your 3 is correct as a metaphysical statement, it is untrue epistemologically -- not all statements are either true or false (cf. the discussion of arbitrary statements -- ones with no truth value). Your 5th statement is also unneeded -- if x is true, then x is true, and I really don't care about y. In addition, you make liberal -- and standard misuse, so you're not being bad -- of "=>" which means enough different things in formal logic that it should be banned. (It is used as the formal fudge for mentioning context but also is used to mean "causes", and you also use it to mean "is evidence that"). I would urge you to focus on the notion "causation", and forget the other uses.

The concrete examples of reasoning would be most useful to focus on -- the formalism does not clarify anything. But a number of them have problems. For example, a propos the idea that "Not untrue" means "true", in English saying that something is "Not untrue" does not mean that it is true, it means that there is reason to think it is true, but it's not at all certain. And in Russian (and Croatian?) "Ja ne znaju nichego" means "I know nothing", despite the double negation -- in other words, you need to distinguish language rules and principles of reasoning. In 5, the first statement -- "I love the works of Ayn Rand" -- makes it unnecessary to try to conclude that you love the works of Ayn Rand.

Do you have some examples where keeping in mind certain tautologies does help with reasoning? For the life of me, I can't think of any. What I think helps the most is just paying attention to what you're actually saying. Like if you claim that "All crows are black" then it means that you're claiming that you won't ever find a non-black crow (and if you do, you will know that you were mistaken).

[AshRyan]

These are not philosophical axioms, but a list of thirteen of the simplest tautological statements of many systems of symbolic logic. There are many more than thirteen tautologies, so thirteen items is really an arbitrary number--especially since some of the ones you've listed can be reduced to others. Also, as others have mentioned, the philosophical meanings you've listed don't really follow from the tautologies with which you've associated them. (Some are particularly grievous. How do you get "conceptualization" from #9?)

[stephen_speicher]

A simple example: how does one go from "existence" to "ethics"?  There's nothing in the concept of existence (or the axiom that it exists) that would lead to a concept of ethics, let alone establish a rational ethical code.  But if one oberves reality, all sorts of things show up: that men exist; that they are mortal; that they have freewill; that survival is not guaranteed, but requires a specific course of action based on the nature of the organism; that man's life requires long-term thought and planning; that irrational choices are harmful; and so on.  From observation of these sorts of facts, and after much, much thought, Ayn Rand came up with an objective code of ethics.

Note how rich the inductive process is.  There's a treasure trove of information out there to be had, that makes the few gems one can get through deduction seem quite small.

Very nicely expressed, and it really makes the point. Thanks!

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(Some are particularly grievous.  How do you get "conceptualization" from #9?)

Say that you've identified how C follows from B.

Now C and B are any two concretes for which it is true that C follows from B.

Then you discover how B can be a consequence of A. Here A is any statement (concrete or whatever you like to call it) for which it is true that B is its consequence.

Syllogism (Tautology #9 above) says that if A leads to B which leads to C, then you no longer need to pay attention to B, you can realize what A is and jump directly to C. If A then C.

Furthermore, you can figure out that C leads to D which leads to E, etc. etc. Then you need not to pay attention (unless necessary) to B through D, you just say if A then E. And so on. The principle is the same as concept building.

Naturally, as in mathematical theorems, these specifics I call A, B, C ... need to have certain properties to fit into some concept.

Concept building is a very good skill which can help you with predicting future. Let me give a simple, concrete example and then show you how syllogism helps you to build the concept. Forgive the trivialities of this, as I'm keeping it as simple as possible.

Say you leave an apple somewhere for a very long time. It rots. Now let's assume you know nothing about what a rotten apple tastes like, so you actually bite into it. You'll find it disgusting and you'll throw it away.

In this (trivial) example, fact A is - an apple is rotten. Fact B is - an apple tastes bad. Fact C is - you throw the apple away. When you know nothing about it, your conceptualization goes thus: If an apple is rotten it tastes bad. If an apple tastes bad, you throw it away. Now apply syllogism to it and you get: If an apple is rotten you throw it away. You don't need to pay attention to its taste. You don't need to taste every rotten apple in order to find out whether it tastes bad or not. A simple induction will tell that every rotten apple tastes bad. You don't need to find it out every time, you already know it. You may even not know WHAT a rotten apple tastes like, but from the look of it you'll see that it's rotten, and then by using the concept above, you'll simply throw it away.

You may say that throwing away rotten apples has nothing to do with the apple's taste. Quite the contrary. If rotten apples had great taste and were healthy to eat, we wouldn't throw them away. But we do throw them away, and this means that rotten apples taste bad. (note that to prove my point I here used Modus Tollens. Tautology #8a above)

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"A is A" -- as Galt articulates it, says "You cannot have your cake and eat it, too" and therefore the Law of Non-Contradiction is not separate.

So your view of this is that things which seem obvious should be left unsaid? Why then bother with axioms? Isn't it obvious that A is A? It is to me. So why bother mentioning it?

The reason lies exactly in this. If we didn't articulate that A is A, have you any idea how much harder it would be to get to the law of non-contradiction? Just try reaching a logical conclusion when your premises are unsaid and hanging in the air and labeled as too obvious to be spoken or noted.

[Travis P.]

Ayn Rand limits her axioms to 3 in her philosophy, which makes it hard to logically reach other conclusions. However, by learning also the tautologies below, you can be faster about making your conclusions, not to mention that there's less margin for error.

But what you're talking about are principles of logic to guide your thinking. She was talking about the fundamental starting points, the "foundations of everything else". While the principles of logic are consistent with Ayn Rand's metaphysical axioms, and many of them may even directly "derive" from her axioms, they have two different goals.

Logic is the art of non-contradictory identification. The "tautologies" you have mentioned are some basic principles to help guide a person in the use of logic. Before you talk about logic, however, you have to accept that existence exists. Do you see yet why they are separate things?

[DavidOdden]

So your view of this is that things which seem obvious should be left unsaid? Why then bother with axioms? Isn't it obvious that A is A? It is to me. So why bother mentioning it?

The reason lies exactly in this. If we didn't articulate that A is A, have you any idea how much harder it would be to get to the law of non-contradiction? Just try reaching a logical conclusion when your premises are unsaid and hanging in the air and labeled as too obvious to be spoken or noted.

The point is that that "A is A" is the law of non-contradiction. They are not at all different. So why bother listing it twice?

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1.  She "limited" her axioms in metaphysics to just 3 because that's all there are.  I don't know of any others.

2.  Objectivism wasn't created and isn't structured along the lines of "reaching other conclusions" from the axioms.  This implies a rationalistic approach in which the whole of her philosophy is supposed to be deduced from some starting point.  On the contrary, she formed her philosophy inductively.

1. Axioms, Ayn Rand wrote in here journal, are fundamental truths about the world which one cannot prove. She needed them in order to construct her philosophy upon them, because, as she also noted in her journals, something cannot be created out of nothing. I KNOW that some of the tautologies I wrote are the combinations of others, but that is what science is about. Philosophy is no exception. You use axioms to build upon them. That doesn't mean you use them as a dish in which you pour content, but as building blocks out of which you create this content.

2. Do you know what induction is? It is a logical construct which helps us grasp and prove the general principle or truth out of the few particular examples we have. Frankly, I don't understand your objection here. Induction starts with concretes, not axioms. It is the principle of induction which is based on axioms. You cannot preform an induction on two or more axioms. This, however, is what you suggest.

A simple example: how does one go from "existence" to "ethics"?  There's nothing in the concept of existence (or the axiom that it exists) that would lead to a concept of ethics, let alone establish a rational ethical code.  But if one oberves reality, all sorts of things show up: that men exist; that they are mortal; that they have freewill; that survival is not guaranteed, but requires a specific course of action based on the nature of the organism; that man's life requires long-term thought and planning; that irrational choices are harmful; and so on. From observation of these sorts of facts, and after much, much thought, Ayn Rand came up with an objective code of ethics.

Which means she took those facts (not the axiom that existence exists) and said that this IS. Men exist. Men are really mortal. It is not an illusion, but a fact. It IS. Note that the axiom "existence exists" only showed up here as a guide to realize that these facts ARE. Therefore, it is not upon this axiom that Ayn Rand performed an induction, but upon those facts which this axiom helped her identify as real.

Note how rich the inductive process is. There's a treasure trove of information out there to be had, that makes the few gems one can get through deduction seem quite small.

You misunderstood me. One doesn't deduct truths from AN axiom. One combines axioms and gets (deduces) truths from this which help him in his reasoning, not only on the axiomatic level, but on any level (and this is also an induction). What I posted above are axioms and the combinations which follow from combining those axioms.

You can have both induction and deduction in your reasoning. It is not either... or... question. You only need to know when to use which.

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The point is that that "A is A" is the law of non-contradiction. They are not at all different. So why bother listing it twice?

Why not? It can only be helpful.

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But what you're talking about are principles of logic to guide your thinking.  She was talking about the fundamental starting points, the "foundations of everything else".  While the principles of logic are consistent with Ayn Rand's metaphysical axioms, and many of them may even directly "derive" from her axioms, they have two different goals. 

Logic is the art of non-contradictory identification.  The "tautologies" you have mentioned are some basic principles to help guide a person in the use of logic.  Before you talk about logic, however, you have to accept that existence exists.  Do you see yet why they are separate things?

Yes, I do. I actually realized it before you posted this, only the discussion has steered, if not branched in a few tightly related topics (why they are needed and how are they used).

The tautologies are truths deduced from axioms. The reason I mentioned them here is because they are good to remember. Once you do, you don't need to make your conclusions all the way from A is A or existence exists, because you already know that these are true, so you can use these as the starting points for your proofs or arguments. That is the way of science: it proves one thing, then proves the next by using this last proof. Starting from A is A is a waste of time and effort, because you already KNOW that which is centuries more advanced than this.

And for those who are skeptical about the accepted truths upon which other truths are built can reinvent the entire science. After all, that is what Ayn Rand did with philosophy.

[source]

But what you're talking about are principles of logic to guide your thinking.  She was talking about the fundamental starting points, the "foundations of everything else".  While the principles of logic are consistent with Ayn Rand's metaphysical axioms, and many of them may even directly "derive" from her axioms, they have two different goals. 

Logic is the art of non-contradictory identification.  The "tautologies" you have mentioned are some basic principles to help guide a person in the use of logic.  Before you talk about logic, however, you have to accept that existence exists.  Do you see yet why they are separate things?

Yes, I do. I actually realized it before you posted this, only the discussion has steered, if not branched in a few tightly related topics (why they are needed and how are they used).

The tautologies are truths deduced from axioms. The reason I mentioned them here is because they are good to remember. Once you do, you don't need to make your conclusions all the way from A is A or existence exists, because you already know that these are true, so you can use these as the starting points for your proofs or arguments. That is the way of science: it proves one thing, then proves the next by using this last proof. Starting from A is A is a waste of time and effort, because you already KNOW that which is centuries more advanced than this.

And for those who are skeptical about the accepted truths upon which other truths are built can reinvent the entire science. After all, that is what Ayn Rand did with philosophy.

[Ed from OC]

Axioms, Ayn Rand wrote in here journal, are fundamental truths about the world which one cannot prove. She needed them in order to construct her philosophy upon them, because, as she also noted in her journals, something cannot be created out of nothing.

What you initially posted was a list of valid forms of arguments. They are not axioms in the same sense as existence, identity and consciousness, which are in the province of metaphysics, not epistemology.

"A is A" means something quite different from "x<=>x". "The 'identity' of an existent means that which it is, the sum of its attributes or characteristics." (OPAR, p6) More importantly, existence is identity. Historically, existence was seen as just one more attribute of a thing, on the same order as color or weight. Rand's view is unique: existence and identity are the same thing, from two different perspectives: what it is vs. what it is; whether something is real or not, and what the thing is.

To try to equate "A is A" with "x<=>x" not only obscures the meaning of the former, but confuses metaphysics and epistemology.

I KNOW that some of the tautologies I wrote are the combinations of others, but that is what science is about.

No. Science is about discovering how the world works. It is not about combining tautologies. Logic is a tool in pursuit of identifying how the world works, in that it keeps one's knowledge from containing contradictions. One still has to look out at the world.

You use axioms to build upon them.

That's not precise. The philosophical axioms act as the ultimate guardians of knowledge as such. That is, without all 3 axioms, knowledge is not possible: either nothing exists, in which case there is nothing to know; A is non-A, in which case what you knew a moment ago may no longer be true; or we are all unconscious, in which case there is no mind capable of knowing anything.

But it is not the case that axioms are somehow combined to lead to specific knowledge about reality, which was a major point of my prior post.

It is the principle of induction which is based on axioms.

What do you mean?

One combines axioms and gets (deduces) truths from this which help him in his reasoning, not only on the axiomatic level, but on any level (and this is also an induction).

I'm lost. Are you saying combinations of axioms are both deductions and inductions?

Again, if you here are talking about the "axioms" you initally posted, those are forms of arguments. Just as the laws of algebra hold for any particular equation, the rules of argumentation apply to any argument on any topic. But by themselves, without any content, one cannot manipulate the rules in some way which will create content.

By analogy, given x = y + z, one cannot say whether x = 4 or 3.225 without knowing the content -- the values -- of y and z.

[source]

No. Science is about discovering how the world works. It is not about combining tautologies.  Logic is a tool in pursuit of identifying how the world works, in that it keeps one's knowledge from containing contradictions.  One still has to look out at the world.

And I said nothing contrary to that.

You limit yourself too much to the discussion we are having. You just assumed that I think that what science is *all* about is combining tautologies and axioms. But I didn't say that! I said that that is what science is about is combining them. But it is also about studying reality, things that surround us. It is about realizing what we want and what we need to realize that wish. Science is a tool which helps us take control over reality. As such, science doesn't rise solely from the axioms we use in order to build upon them, but also from the facts of that reality. Science is shaped by reality in order to help us shape reality with it. And the above tautologies guard from making an error. Failing to mention them makes it easier to make an error.

What do you mean?

As you said in this very post, "The philosophical axioms act as the ultimate guardians of knowledge as such." And that is what I meant when I said that the principle of induction is based on axioms.

I'm lost. Are you saying combinations of axioms are both deductions and inductions?

No, combinations are deductions. An induction in what I said is that the truths can be deduced with the help of axioms on any level, as well as the axiomatic.

But by themselves, without any content, one cannot manipulate the rules in some way which will create content.

As I said here, "Science is shaped by reality in order to help us shape reality with it." Content comes from reality; existence, which exists according to the axiom. But we cannot do anything with the content which we derive or take directly from reality, if we do not know the axioms - and not just the axioms but also the truths deduced from them. Pure logic has no content, but it can help us manage content. But the same pure logic has its concepts; tautologies are deduced from axioms. They have no content, but add to them the content and they will make wonders for you (of course, not by themselves; only if you can wield them). And that is exactly why I'm saying that one should know these tautologies; because later, as you add more and more content, it becomes ever more difficult to come to a sensible conclusion from A is A and existence exists.

[stephen_speicher]

And I said nothing contrary to that.

You limit yourself too much to the discussion we are having. You just assumed that I think that what science is *all* about is combining tautologies and axioms. But I didn't say that! I said that that is what science is about is combining them.

I think that at least one major reason I personally am having difficulty following you is that you speak so much in the abstract that I really have no idea how your words are connected to reality. Could you please just focus on this one issue of "combining tautologies and axioms" in science. Please take any standard science theory and demonstrate this "combining tautologies and axioms," specifically and concretely. I do not mean for you to present a long treatise, but rather succinctly and in simple words show by concrete reference to a particular theory, or some aspect of it, the role played by this "combining."

[source]

I think that at least one major reason I personally am having difficulty following you is that you speak so much in the abstract that I really have no idea how your words are connected to reality. Could you please just focus on this one issue of "combining tautologies and axioms" in science. Please take any standard science theory and demonstrate this "combining tautologies and axioms," specifically and concretely. I do not mean for you to present a long treatise, but rather succinctly and in simple words show by concrete reference to a particular theory, or some aspect of it, the role played by this "combining."

Here's a mathematical theorem that will show to some extent the implementation and "combining" the tautologies.

Here are the new symbols I'm going to use:

V - for each

P(x, y) - 2 variable polynomial

=== - identical to

!=== - not identical to

T - true

!T - not true

E - there exists

The rest of the symbols are same as I used above.

Theorem:

For each universal system M and each P(x, y) defined on M it is true that:

1. Vx Vy P(x, y) <=> Vy Vx P(x, y) <=> P(x, y) === T

2. Ex Ey P(x, y) <=> Ey Ex P(x, y) <=> P(x, y) !=== !T

3. Ex Vy P(x, y) => Vy Ex P(x, y)

4. !(Vx Ey P(x, y)) <=> Ex Vy !P(x, y)

I'm going to have to explain (and prove) this later because I don't have enough time right now.

[stephen_speicher]

Here's a mathematical theorem that will show to some extent the implementation and "combining" the tautologies.

Here are the new symbols I'm going to use ...

I did not ask you for an abstract mathemtical theorem, but rather for an illustration in reference to a particular scientific theory. Ed from OC told you that science is about discovering how the world works, and I asked you to bring your far too abstract notions of "combining tautologies and axioms" down to the real world of science. In other words, do as you claimed. Take any scientific theory, relativity, or quantum mechanics, or classical mechanics, or whatever, and show us by specific example of the theory, or just an aspect of the theory, exactly how your abstract "combining tautologies and axioms" works in science.

[source]

Mathematics is physics without content; without reference to objects of reality. Any mathematical theorem can be and is used, implicitly, by physics, by adding content to these theorems. Not to theorems directly, but to their implementation in calculation. How to add content to number 1? What is number 1? Nothing in particular; a floating abstraction. Physics adds to it content. Mathematics says one, physics asks one what? 1 meter. 1 kilometer. 1 Newton.

There is no physical theory that works any other way. It merely adds content to the abstract mathematical formulae. v = s/t? In mathematics, that is anything. In physics, that is a formula for velocity; or if you say that v isn't velocity but density, then s is mass and t is volume, in which case it is a formula for density. It is a question of what content you add. Not all physical phenomena are so simply related to each other as are density to mass and volume, or velocity to distance and time. That is why experiments are needed; to show the relation first experimentally, then describe it mathematically. And of course, the forumulas change a little if say mass isn't equally distributed in the volume. Mathematics already gave the tools with which to make us able to take that into the account as well (see integrals).

Do you ask of me to show you how to logically, out of abstract tautologies, suddenly create content? That is contrary to the axioms. The content is taken from reality; from what is - and under the axiom that existence exists.

If, however, you are asking me to show you how to add content (how to create a theory) to an abstract mathematical formula, then I can do so. And not with a formula for a velocity. That is far too simple. I can, using simple mathematical formulas, show you how to express Kepler's laws for example. Or Maxwell's equations. All I need is free hands in order to add such content to the symbols I use as I see fit.

[stephen_speicher]

Mathematics is physics without content ...

And bread is a sandwich without meat.

What is all this, Zen Buddhism Day?

Physics is IDEAS, the ideas that identify the causal mechanisms which explain physically deterministic behavior. Mathematics, in this context, becomes the means by which we express and quantify the relationships that exist between the ideas that we identify in physics.

There is no physical theory that works any other way. It merely adds content to the abstract mathematical formulae.

I do not think you have a clue as to how physics actually works, how theories are developed and how mathematics is used.

Do you ask of me to show you

I asked you to show me what you claimed, but this is the third time and you seem to have lost sight of it. If you cannot show me, that's fine, I'll leave it at that, just a big bunch of floating abstractions that have no connection to reality.

[source]

I do not think you have a clue as to how physics actually works, how theories are developed and how mathematics is used.

I said THEORIES. You wouldn't make such assumptions and jump to invalid conclusions if you actually read what was written. You're only trying to discredit everything I say with every irrational means at your disposal. I'm beginning to wonder whether you deliberately ignore some things I mention, or are you just too lazy to read them?

I asked you to show me what you claimed, but this is the third time and you seem to have lost sight of it. If you cannot show me, that's fine, I'll leave it at that, just a big bunch of floating abstractions that have no connection to reality.

I've asked a prefectly valid question. You obviously read only the part you quoted. I never claimed that the tautologies I mentioned can suddenly create content if you combine them in some specific way. But you can ADD content to those combinations, or tautologies themselves, as I did several times (in this very thread), but you failed to see where even though I DID mark their location very clearly (to those who bother to read at least).

I admit though that I've been a little lazy about explaining how content is added to abstract principles; how abstract principles are concretized. I assumed an objectivist would know that.

[stephen_speicher]

You're only trying to discredit everything I say with every irrational means at your disposal.

Yes. I keep a black leather bag near my computer, sitting under the desk on the floor. Stitiched in bold red letters across one face of the bag can be found the words "Irrational Means." The bag is not very big, but you should know that when the content is reduced to below 25%, an order is automatically placed to my online source of Irrational Means, and delivered one-day air. So, be warned, I stand ready to counter your brilliantly rational ideas with an endless supply of Irrational Means. Doing so is what gives meaning to my life.

I'm beginning to wonder whether you deliberately ignore some things I mention, or are you just too lazy to read them?

Yup, that's me. You found me out. If deliberately ignoring some things does not work, then my intellectual laziness kicks in. I just don't seem to be motivated enough to spend time and effort doing scholarly research, so when I come across brilliant and complex insights like yours, I give in to my intellectual laziness and do not bother to read. Its a terrible fault that I have, one which explains my abject ignorance in so many different fields.

But, now that you have exposed my irrational means and my intellectual laziness, I vow to work harder to correct these problems. So, please, continue to enlighten everyone here with your great plethora of ideas, and I am sure you will get all the recognition and detailed feedback that your ideas so richly deserve.

I admit though that I've been a little lazy about explaining how content is added to abstract principles; how abstract principles are concretized. I assumed an objectivist would know that.

Oh yes, you are so right. How silly of me to ask you to add content and concretize your ideas. Any Objectivist should have already known how to do that. Please accept my ... ahem ... most sincere apology.

[Guest jrshep]

Very, very funny post, Stephen.

I can just imagine your small, black, leather bag with red lettering and an internet source for "Irrational Means."

[stephen_speicher]

Very, very funny post, Stephen.

Some things are just too silly to take seriously.

I can just imagine your small, black, leather bag with red lettering and an internet source for "Irrational Means."

And right above the bag is my blue balloon in the air with the letters imprinted in yellow: "Floating Abstractions."

Not to mention my hallway closet filled top to bottom with my collection of "Stolen Concepts."

That way, when I am running low on "Irrational Means" I can just grab a "Stolen Concept" from my closet and throw it against the balloon to shake free a few "Floating Abstractions."

Hey, in life, and in debating, you just have to be prepared!

[source]

Oh yes, you are so right. How silly of me to ask you to add content and concretize your ideas. Any Objectivist should have already known how to do that. Please accept my ... ahem ... most sincere apology. 

And once again you manage to misinterpret what I say. I don't care to explain myself to you anymore. I suggest you take a look at "The Romantic Manifesto" and check where Ayn Rand says "Concretize your abstractions."

As for your little story, it wouldn't surprise me if all of it was true.