The Logical Leap: Induction in Physics


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Meanings *of words* are "conventions in the use of language," and agreed that there's "no God of Languages handing down Definitions scribed on tablets of stone." However, definitions *of concepts* are not "conventions in the use of language," and the definition of a *concept* can be wrong. The difference between a concept and the word used to label it seems perpetually to elude several posters here.

Consider an apropos example, a concept labeled by the term "gravity." Suppose that the concept a person has in mind in using the term "gravity" is that of some kind of force which keeps physical entities from drifting apart from each other. Suppose the person defines this concept as "an unmarried woman."

Ellen,

You mean that the person would define "gravity" as "an unmarried woman"?

I'll be surprised if you don't consider that definition for that concept wrong, and probably no one would seriously propose that definition for that concept.

Which means that in order to communicate, a definition has to be accepted by the commucation partners.

Our family members have some invented words of which only we know what they refer to. We also frequently use the Vietnamese word "dong" as a kind of slang expression for 'money', although we don't have any connections to Vietnam. I liked the sound "dong" (the Vietamse currency) when watching a TV special on Vietnam several years ago, and somehow the term got ‘adopted’ into our family's vocabulary. I have always loved to play with language.

So whether the community of speakers is small or large, an audio-visual symbol has to be accepted by the community as referring to this or that, and as for dictionary definitions, they are officially accepted for a very large language community.

What Rand calls "concept-formation" refers to something very simple: categorizing and subcategorizing.

"A concept is the mental integration of of two or more units possessing the same distinguishing characteristics, with their particular measurements omitted." (ITOE, p. 13)

So e. g. two or more units (possessing the same distinguishing characteristics) can be subsumed under e. g. the category "table". "Table" in turn is a subcategory of "furniture". That's all there is to it. Such categorizing is accomplished effortlessly in the course of learning one's native language.

Imo Rand's concept formation theory is actually limited to the categorizing of countable concretes and she runs into massive linguistic problems when trying to transfer it to abstract terms. I encourage everyone here to read chapter 4 of ITOE and see if they can make sense of what is written in there.

The epistemological chaos in ITOE is hard to miss.

Rand's definition of concept can only be applied to categories of conrete countables like e. g. 'table':

"A concept is the mental integration of of two or more units possessing the same distinguishing characteristics, with their particular measurements omitted." (ITOE, p. 13).

The pot calls the kettle black. The epistemological chaos in your posts is hard to miss. :D

Ayn Rand wrote "measurements omitted", not "counts omitted." Counting and measuring partly overlap, but they are quite distinct.

Merlin,

You completely missed my point. I was speaking of countable nouns, and it is only with these that her definition of “concept” works. What she calls concept here is the category referred to by an audiovisual symbol.

Try applying Rand's (ITOE p. 13) definition of concept to e. g. "pride" and you'll see it won't work. If you think it does, please go ahead and demonstrate.

I'm kind of getting a kick out of Xray this go-around. But first, let me say that it's worse than I thought if she really did read ITOE. (I no longer read her posts, so I missed the discussions she mentioned.) So I take back what I said about her not reading it. If she quoted it several times, that's not really proof (since getting stuff from the CDROM is easy), but it's good enough to, at least, claim she read it. I'll give her the benefit of the doubt.

Michael,

I have ITOE right here on my lap and there's quite bit I've scribbled on the margin. For example "nonsense!" on p. 79 where she states that "mysticism" claims knowlegde is available without effort. :rolleyes:

But, having read it, what she displays as her understanding of Rand's meanings is woeful. It would have been better had she not read it. For instance, teleological measurement is one of Rand's cornerstones for normative abstractions, yet Xray bashes Rand for using teleological measurement for normative abstractions and calls this "epistemological chaos."

One of the messages in the post you referred to http://www.objectivistliving.com/forums/index.php?showtopic=8903&st=160&p=102907entry102907, is that Rand's “teleological measurement” described in ITOE doesn't work. If you believe it does, free to demonstrate with an example like. e. g. ‘selfishness’.

And as I pointed out in that post and # 364 here on this thread, Rand compounds the problem by letting, in ITOE, her so-called "normative abstractions" (her moral principles), suddenly flow into her epistemology, and the result is chaos because what makes epistemological-ethical cocktails indigestible is that they don't separate fact from value.

Presenting one’s personal values and preferences as an alleged “objective” hierachy (for that is exactly what Rand is doing - read her passage in chapter 4 where she claims that one can measure love - is mixing something up.

Imo epistemology was not Rand’s strong suit. She was essentially a moralist and an ideologist. .

Now for the comic part. I get her message as taking my criticism of ITOE as an endorsement for her positions, as if saying: "You see, you see, I was right all along and you agree with me."

Your personal speculation as to any 'unwritten' message has no effect on what it says in the written message:

You were right on target in calling Rand's "teleological abracadabra" "a drastic shift in the middle of the stream, no matter how you look at it". (MSK)

It would interest if anyone here disagree with your assessment of that passage in ITOE.

Then she goes merrily on her way getting Rand's meanings all wrong...

I find this entertaining in a weirdly tender sort of manner, like watching a very young little girl with an expression of serious concentration stumble about while trying to walk in her father's house shoes.

What I find entertaining is how you are trying to suggest that my mental capacities are that of a toddler when it comes to "understanding" Objectivism. :)

So both of us are entertained – shall we can coin the term CED (“Common entertainment denominator”? There is so much discussion here about ‘common conceptual denominators’, about audiovisual symbols labeling ideas, so why not go ahead and coin some new ones? Yes, we can! ;)

But kidding aside - believe me Michael, I’m fully aware that your position is not an easy one. I can put myself in your shoes, which enables me to also see things from your perspective.

The critic of a philosophy or ideology has the easier role than the defender, no question.

For the critic can point out the holes and inconsistencies in a system without having any burden to defend a system as a whole.

Now I don’t see you as defender of Objectivism as a whole because you are no dogmatic.

You yourself have pointed out often enough that you are not, and indeed I can’t see any evidence of discussing with a defensor fidei here.

I see your position more like that of a philosophical ‘tightrope walker’ who is trying to carry along with him and keep those elements of Objectivism which he has come to consider as being of permanent value to his life.

Edited by Xray
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Merlin,

You completely missed my point. I was speaking of countable nouns, and it is only with these that her definition of “concept” works. What she calls concept here is the category referred to by an audiovisual symbol.

It's no wonder, given your epistemological chaos.

You completely missed my point. That tables are countable is not what makes each table an instance of the concept TABLE per Rand. It is their measurements, and measurements are of attributes. Is length -- Rand's primary example -- a "countable noun"? Your introducing "countable nouns" seems to be another instance of your epistemological chaos.

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> the statement: X is tall - is not precisely true or false. It is contextually dependent and there are associated parameters such as tall compared to what? [baal]

You are using the word 'exact' the way a physical scientist or mathematician would use it. That's not the way Objectivists use it. "It is raining" is an exact statement. But it depends on your specifying a certain minimal level of moisture.

> Give me an exact meaning for the word "tall" or "short". [baal]

When Francisco says words have an exact meaning, he is saying as opposed to some distortion like that of a grafter 'making' money. He is not saying there is no variability of context whatsoever. Once again, you can't read the language as being the language that a mathematician would use: that's not how it's intended.

> in this kind of informal context, words and concepts are used as synonyms. [Phil]

> You mean *you're* using them as synonyms? If they're used thus in this context -- attempting to clarify "space," "time," "space-time" -- confusion is merely worsened. [Ellen]

Ellen, I was referring to words and concepts and I included this from you: "You sound just as unclear on the difference between words and concepts". Your statement was about general, informal usage of those two terms synonymously and thus so was mine. Not about space and time.

Edited by Philip Coates
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You are using the word 'exact' the way a physical scientist or mathematician would use it. That's not the way Objectivists use it. "It is raining" is an exact statement. But it depends on your specifying a certain minimal level of moisture.

All the more reason for doing what the mathematicians and physicists do.

Ba'al Chatzaf

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So, I'm back in town... When physicist talk about space, this is the same space that is used in daily usage. The difference is that physicists tell us that there is more to space than meets the eye. The reason that they often refer to space-time is that certain properties of space depend on the time coordinate that is chosen, while the combined space-time is invariant under Lorentz transformations, which gives more general results. That time goes slower the more space-time is curved has been unambiguously demonstrated by countless experiments, only we don't observe that in daily life as the effects are then extremely small, therefore it seems counterintuitive to us (but for the correct functioning of the GPS system it is essential to take this effect into account). It is not true that the physicist defines space as something different from the common concept, he merely shows that our common perceptions are only approximations and that the properties of space and time in reality are not so simple as we'd intuitively believe, they are not the independent absolute entities they may seem to us in daily life.

I have two questions:

First, what difference, if any, is there between these two statements?

1) Space is curved.

2) Light travels a curved path through space.

Second, does the notion of "spacetime" include anything significant beyond saying that space and time are not independent variables?

Ghs

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> in this kind of informal context, words and concepts are used as synonyms. [Phil]

> You mean *you're* using them as synonyms? If they're used thus in this context -- attempting to clarify "space," "time," "space-time" -- confusion is merely worsened. [Ellen]

Ellen, I was referring to words and concepts and I included this from you: "You sound just as unclear on the difference between words and concepts". Your statement was about general, informal usage of those two terms synonymously and thus so was mine. Not about space and time.

Phil, first, again, how much easier discussion with you might be if you would at least bother to give the numbers of the posts from which you are quoting (since you quite refuse to use the reply function which provides a link to the quoted post).

I'm not going to search back through the thread for the details of the sequence.

The issue being discussed which started all this word-vs.-concept sideshoot was physicists' speaking of space as "curved." You were calling this a misuse of language. (And George was mistrusting it as possibly a category error.) Hence a discussion of words having more than one meaning developed. Also there were objections from the physics-knowledgeable about philosophers trying to dictate to physicists how the latter use their terms. Part of the discussion pertained to the same word sometimes being used for more than one concept. In this total context, you plunk down Francisco's comment about words having exact meanings. Thus adding to confusion, and sounding to me confused yourself. Indeed, from your continuing explanations, I think you still sound confused.

And my statement was not about "general, informal usage" of "word" and "concept" synonomously. It pertained to the error of confusing "word" and "concept."

Ellen

Edited by Ellen Stuttle
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Rand's theory of definitions is very good. It leaves ample room for different definitions of the same word, depending on the context.

Everyone who opens a monolingual dictionary can see evidence of this basic fact. Rand did not find out anything which was new in that field.

Since communication always takes place in a specific context, it naturally follows that definitions can't be isolated from that context.

Suppose you come across the phrase "That's a pretty kettle of fish." As a competent speaker of the English language, you will know that the phrase does not give a value judgment about any concrete kettle of fish. :)

If physicists can redefine words, then why can't philosophers?

Like Ba'al said, they can and do.

Here is an example from your own text corpus:

In Why Atheism, you present to the reader a term you coined: "personal atheist".

No one could understand what the term refers to without the definition you gave. By giving the definition, you made clear what exactly you meant.

What you chose to call "personal atheist" refers to someone who has abandoned their former belief in a god.

You might as well have chosen another audiovisual symbol as a label, like e. g. "ex-believer".

What counts in communication is that you can make unmistakeably clear what you mean.

Problems would only arise if you claimed that the (arbitrary) choice of the audiovisual label you used to refer to a former non-believer is the only "correct" one.

Edited by Xray
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Meanings *of words* are "conventions in the use of language," and agreed that there's "no God of Languages handing down Definitions scribed on tablets of stone."

True. However, this fact seems to seems to perpetually elude a lot of Objectivists. For example, I recently came across this gem over at Solopassion:

Leonid: "The problem is that original meaning of words became perverted as result of "conventional" altruist dominant philosophy. Ayn Rand doesn't redefine words, but rather brings back their original meaning."

(Amusingly, he then cites Rand's alleged "dictionary" meaning of selfishness, which AFAIK no-one has ever traced back to an actually existing dictionary or supposedly "original" precedent. And wasn't Rand's virtuous version of selfishness supposed to be unprecedented anyway?? )

Further, this fact seemed to elude Rand herself. See Rand's discussion of science in the ITOE where she claims it is the philosopher's job to tell scientists what their terms mean (don't have the quote handy but I've regularly brought this up).

So, in Objectivism you do have a "God of Languages handing down Definitions scribed on tablets of stone." It's called the philosopher.

However, definitions *of concepts* are not "conventions in the use of language," and the definition of a *concept* can be wrong. The difference between a concept and the word used to label it seems perpetually to elude several posters here.

This surprises me, as it's a rather obvious distinction. However, I can understand the confusion in Objectivism due to Rand's sudden outbreak of nominalism on the subject of "labels" in the otherwise essentialist ITOE (As no clear explanation is given as to how this fits with the rest of her exposition, I put this down to her usual disregard for consistency). Additionally, just because the two things are different doesn't you don't end up with the same practical problems arguing over concepts as you do over the definitions of words, basically because concepts are represented by words anyway. Until we get the Vulcan mind-melding sorted out that is...;-) The example you give below is strikes me as being the same as the "puppy" one I've discussed ad nauseum, and I don't really see how it gets around the problems I've already tiresomely outlined. It seems to me you end up down the same rabbit-hole.

Consider an apropos example, a concept labeled by the term "gravity." Suppose that the concept a person has in mind in using the term "gravity" is that of some kind of force which keeps physical entities from drifting apart from each other. Suppose the person defines this concept as "an unmarried woman." I'll be surprised if you don't consider that definition for that concept wrong, and probably no one would seriously propose that definition for that concept. But some major physicist did define "gravity" as a force of attraction which acts at a distance. Is "gravity" a force of attraction, or is it a force carried by a particle or wave? Does it act at a distance or not? These are questions to be answered in order to form a correct definition of the concept being referred to by the label "gravity."

"Gravity", being a label, can be stuck on to any of these ideas, so arguing over what it should "truly" be stuck on is not resolvable, as Randian dogma claims, by "logic". (Hence we see Objectivists like Leonid - and indeed Rand herself - appealing to the mystical authority of historical convention rather than doing as the ITOE proposes and giving us a logical demonstration as to how they arrived at the true meanings of terms!) All the term "gravity" is is a useful answer to the problem "what shall we call a force that acts at a distance?"

It comes down to this: The word "gravity" either is a mere label for a mental idea, or it isn't. If it is, we should treat it accordingly, and get on with developing the testable propositions by which we can further develop our ideas instead. Trying to have it both ways seems to be a fallacy.

Edited by Daniel Barnes
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> It pertained to the error of confusing "word" and "concept."

And I pointed out to you that in -informal- use those terms are synonyms.

What part of it was unclear when I said it the first time?

Edited by Philip Coates
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See Rand's discussion of science in the ITOE where she claims it is the philosopher's job to tell scientists what their terms mean (don't have the quote handy but I've regularly brought this up).

So, in Objectivism you do have a "God of Languages handing down Definitions scribed on tablets of stone." It's called the philosopher.

I would be very surprised if Rand ever defended the position that you attribute to her. I think you will find that Rand speaks of the role of philosophy in science, not of the role of philosophers per se. Scientists can, and often do, engage in philosophic reasoning. This is not a matter of professional philosophers telling scientists what their basic terms mean.

Ghs

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> See Rand's discussion of science in the ITOE where she claims it is the philosopher's job to tell scientists what their terms mean

George is correct, that's not what she said. She said (and you are free to look up the exact words) that philosophy can veto certain scientific statements which violate the laws of logic or other purely philosophical principles.

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My own understanding is space is distance between at least two objects and traveling through space is reducing the distance because you are one of the objects.

--Brant

My understanding of 'space-time' as opposed to 'space' and 'time' is this; The idea of absolute space and time means a universe in which one can set up a cartesian coordinate system with an origin and project the axis to indefinitely in all directions in absolute straight lines. In this system objects move according to some absolute time reference and all motion can be described by measurements relative to the absolute static coordinate system. This is not the universe we live in. There is no such thing as a straight line extended indefinitely as 'straight' loses meaning in the vastness of the universe. We know that even light bends and so it is impossible for anything to travel in a straight line. If this was possible we should eventually reach a boundary of some sort, assuming the universe is not infinite in size, and then the question immediately arises - what is on the other side of this boundary? In a 4-dimensional space-time continuum one can travel forever and never reach a boundary and yet the universe can be finite in size.

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See Rand's discussion of science in the ITOE where she claims it is the philosopher's job to tell scientists what their terms mean (don't have the quote handy but I've regularly brought this up).

So, in Objectivism you do have a "God of Languages handing down Definitions scribed on tablets of stone." It's called the philosopher.

I would be very surprised if Rand ever defended the position that you attribute to her. I think you will find that Rand speaks of the role of philosophy in science, not of the role of philosophers per se. Scientists can, and often do, engage in philosophic reasoning. This is not a matter of professional philosophers telling scientists what their basic terms mean.

She said (and you are free to look up the exact words) that philosophy can veto certain scientific statements which violate the laws of logic or other purely philosophical principles.

The quote which Daniel interprets as Rand declaring philosophy's dictatorial prerogative over science is this:

ITOE, 1990 Expanded Edition,

pg. 189

Philosophy is not dependent on the discoveries of science; the reverse is true.

Here is a post which shows how Daniel interprets the passage. (I changed the formatting of the original post, since it used ">"s instead of quote blocks.)

In the next post, I'll copy the whole section from ITOE linked in MSK's quoted comments.

The interpretation you claim I made is not an interpretation at all. It is stated quite clearly by Rand. How else can the following (from here) be "interpreted"?

Like I said, simple to complex.

The issue is who is the authority over the other.? Who is allowed to question who? Who is dependent on who?

The phrase you object to ("Philosophy is not dependent on the discoveries of science; the reverse is true"), which I deleted above, is to be understood in that context (simple to complex). Not a master-slave context. It doesn't get any clearer. If you don't see it, it is because you don't want to. The words are there, both before and after the phrase.

I return the challenge: the authoritarian implication is clearly there. If you can't see it, well, I'm sorry.

(And please do not try to establish Gotthelf as the authority here. That gives me heartburn. The person making the distinctions is Rand.)

This hardly makes the situation any better. Again: who declared Rand the authority over what all science shall and shall not consider?

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Here's the full passage from ITOE.

Expanded Second Edition, 1990

pp. 289-90

Philosophic vs. Scientific Issues

Prof. B: Is the concept of "matter" a philosophical concept or a scientific one?

AR: In the way we are using it here, as a very broad abstraction, it is a philosophical concept. If by "matter" we mean "that of which all the things we perceive are made," that is a philosophical concept. But questions like: what are different things made of? what are the properties of matter? how can you break it down? etc.—those are scientific problems.

Philosophy by its nature has to be based only on that which is available to the knowledge of any man with a normal mental equipment. Philosophy is not dependent on the discoveries of science; the reverse is true.

So whenever you are in doubt about what is or is not a philosophical subject, ask yourself whether you need a specialized knowledge, beyond the knowledge available to you as a normal adult, unaided by any special knowledge or special instruments. And if the answer is possible to you on that basis alone, you are dealing with a philosophical question. If to answer it you would need training in physics, or psychology, or special equipment, etc., then you are dealing with a derivative or scientific field of knowledge, not philosophy.

Prof. B: I'd like to apply this to the "mind-brain" issue—that is, what is the relation of conscious activity to brain activity? That would be a scientific question.

AR: Yes.

Prof. B: With certain provisos from philosophy, such as that consciousness is causally efficacious and that free will is possible.

AR: Philosophy would have to define the terms of that question. In asking what's the relationship between "mind" and "brain," scientists have to know what they mean by the two concepts. It's philosophy that would have to tell them the [general] definitions of those concepts. But then actually to find the specific relationship, that's a scientific question.

Properties of the Ultimate Constituents

Prof. E: Could you argue, on metaphysical grounds, that all observed properties of an entity are ultimately explicable in terms of, or reducible back to, properties of their primary constituents?

AR: We'd have to be omniscient to know. The question in my mind would be: how can we [as philosophers] make conclusions about the ultimate constituents of the universe? For instance, we couldn't say: everything is material, if by "material" we mean that of which the physical objects on the perceptual level are made—"material" in the normal, perceptual meaning of the word. If this is what we mean by "material," then we do not have the knowledge to say that ultimately everything is sub-subatomic particles which in certain aggregates are matter. Because suppose scientists discovered that there are two different kinds of primary ingredients—or three, or more? We would be in the same position as the pre-Socratics who were trying to claim that everything was air, water, earth, and fire because that's all they knew.

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> It pertained to the error of confusing "word" and "concept."

And I pointed out to you that in -informal- use those terms are synonyms.

What part of it was unclear when I said it the first time?

Phil, you can re-read the whole sequence for yourself instead of asking me to go back and quote from it and show how it developed. If you don't see, upon re-reading it, that what you were writing was indicating that there is a correct definition *for a word*, then you don't see it.

(And note that along with not providing the number of the post from which you quoted, you didn't even identify whom you were quoting. You're getting worse instead of better. :P)

Ellen

Edited by Ellen Stuttle
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This notion that philosophy does not rely on scientific discovery is poorly defined and in effect artificial and arbitrary. The biggest problem is human nature, which is a complex scientific matter. A proper knowledge of human nature requires a bit of knowledge of things like the nature of evolution and human sexuality which are not at all obvious to the average scientifically untutored adult. I understand her general premise, but it is merely a rule of thumb, and nowhere near set in stone or axiomatic. Cosmological questions, such as how Existence can be both eternal and finite, or how man can have free will, do need advances in conceptual understanding of a scientific sort to be come tractable. The real problem is when her notion leads to license for one to make assertions which one holds to be above empirical review.

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I noticed in looking in ITOE for the passage quoted in #393 a comment which shows that Rand quite misunderstood the method Einstein used in the 1905 paper "On the Electrodynamics of Moving Bodies."

Coincidentally, Larry and I just a couple days ago were again admiring the introduction to that paper.

Later, I'll quote the introduction and explain why AR is misunderstanding it.

Ellen

Edited by Ellen Stuttle
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I would be very surprised if Rand ever defended the position that you attribute to her. I think you will find that Rand speaks of the role of philosophy in science, not of the role of philosophers per se. Scientists can, and often do, engage in philosophic reasoning. This is not a matter of professional philosophers telling scientists what their basic terms mean.

Thanks, Ellen, for providing the quote. Let's look at a key section:

Prof. B: I'd like to apply this to the "mind-brain" issue—that is, what is the relation of conscious activity to brain activity? That would be a scientific question.

AR: Yes.

Prof. B: With certain provisos from philosophy, such as that consciousness is causally efficacious and that free will is possible.

AR: Philosophy would have to define the terms of that question. In asking what's the relationship between "mind" and "brain," scientists have to know what they mean by the two concepts. It's philosophy that would have to tell them the [general] definitions of those concepts. But then actually to find the specific relationship, that's a scientific question.

Is anyone really going to seriously propose that scientists must engage in "philosophic reasoning" in order to define the terms "mind" and "brain"!? That philosophy is somehow going to "tell them" what these terms mean?

Are those poor, verbally deprived scientists not in possession of a dictionary?

Think about what she's saying here.

Let's leave aside, for now, the issue of issuing "certain provisos" as to what science might and might not question.

I do admit that the idea that the philosophers' job might be philosophy is a typically reckless leap on my part...;-)

PS: Ellen, interesting to note how Rand herself uses "terms" and "concepts" interchangeably.

Edited by Daniel Barnes
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This notion that philosophy does not rely on scientific discovery is poorly defined and in effect artificial and arbitrary.

Yes. Why wouldn't both science and philosophy benefit from mutual criticism?

And consider: what might this folly accomplish?

Edited by Daniel Barnes
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Consider an apropos example, a concept labeled by the term "gravity." Suppose that the concept a person has in mind in using the term "gravity" is that of some kind of force which keeps physical entities from drifting apart from each other. Suppose the person defines this concept as "an unmarried woman." I'll be surprised if you don't consider that definition for that concept wrong, and probably no one would seriously propose that definition for that concept. But some major physicist did define "gravity" as a force of attraction which acts at a distance. Is "gravity" a force of attraction, or is it a force carried by a particle or wave? Does it act at a distance or not? These are questions to be answered in order to form a correct definition of the concept being referred to by the label "gravity."

"Gravity", being a label, can be stuck on to any of these ideas.

No, since not all those ideas can be true statements of the nature of the phenomenon one is defining.

All the term "gravity" is is a useful answer to the problem "what shall we call a force that acts at a distance?"

No. The definition you gave there presumes an answer to an hypothesis, an answer which at the current time seems to be false. If the force which keeps physical entities from drifting apart from each other is claimed by definition to be a force that acts at a distance, the definition is factually incorrect (as best we know at this time).

Ellen

PS: Your puppy problem is an invented problem and doesn't address the issue of correct definitions of concepts, as has been tiresomely gone over.

Edited by Ellen Stuttle
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My own understanding is space is distance between at least two objects and traveling through space is reducing the distance because you are one of the objects.

--Brant

My understanding of 'space-time' as opposed to 'space' and 'time' is this; The idea of absolute space and time means a universe in which one can set up a cartesian coordinate system with an origin and project the axis to indefinitely in all directions in absolute straight lines. In this system objects move according to some absolute time reference and all motion can be described by measurements relative to the absolute static coordinate system. This is not the universe we live in. There is no such thing as a straight line extended indefinitely as 'straight' loses meaning in the vastness of the universe. We know that even light bends and so it is impossible for anything to travel in a straight line. If this was possible we should eventually reach a boundary of some sort, assuming the universe is not infinite in size, and then the question immediately arises - what is on the other side of this boundary? In a 4-dimensional space-time continuum one can travel forever and never reach a boundary and yet the universe can be finite in size.

I don't really understand this, GS, but how about light coming from the source--is this bent except by gravity?

--Brant

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