On the Universality and Uniformity of Physical Law

[BaalChatzaf]

In order to do science we must found our sciences on postulate systems that contain at least on universally quantified proposition. Otherwise we would have only a finite list of particular and individual declarative sentences from which little could be inferred.

We refer to such universally quantified propositions as -physical laws-. Examples abound: the assumptions of thermodynamics, the conservations laws, the symmetry laws, etc.

But do notice that we have not, nor can we establish the truth of these laws by empirical means. No finite set of verifying instances establishes the truth of a universal physical law at all places for all time. On the other hand we have no choice but to posit such laws or science would not be possible.

Which leads to the conclusion that the best of our sciences may be taken as provisionally true. Our physical theories are upheld by millions of instance observation under a wide variety of conditions in many places and no refuting condition has yet been found empirically. So we have sufficient reason for holding these laws to be true, but we DO NOT HAVE absolute proof that these laws are everywhere and forever true.

We are in the position of the man who holds induction to be valid because it has always worked so far. Do you see what the problem is?

Those closest thing we have to certain knowledge is a set of particulars known first hand. And even there mistakes are possible. Everything else is second hand or inferential, and this is far from absolute or certain.

Bottom line: Our best scientific theories should be regarded as provisionally and contingently true, not absolutely or certainly true.

Ba'al Chatzaf

[tjohnson]

I would almost describe many of the post here as having an obsession with the word 'true', or 'truth'. Since the word is not the thing it represents (the map is not the territory) the only possible content of 'knowledge' is structure. Theories are not 'true' or 'false', they are relatively similar or dissimilar in structure to the structure we perceive.

[Brant Gaede]

In order to do science we must found our sciences on postulate systems that contain at least on universally quantified proposition. Otherwise we would have only a finite list of particular and individual declarative sentences from which little could be inferred.

We refer to such universally quantified propositions as -physical laws-. Examples abound: the assumptions of thermodynamics, the conservations laws, the symmetry laws, etc.

But do notice that we have not, nor can we establish the truth of these laws by empirical means. No finite set of verifying instances establishes the truth of a universal physical law at all places for all time. On the other hand we have no choice but to posit such laws or science would not be possible.

Which leads to the conclusion that the best of our sciences may be taken as provisionally true. Our physical theories are upheld by millions of instance observation under a wide variety of conditions in many places and no refuting condition has yet been found empirically. So we have sufficient reason for holding these laws to be true, but we DO NOT HAVE absolute proof that these laws are everywhere and forever true.

We are in the position of the man who holds induction to be valid because it has always worked so far. Do you see what the problem is?

Those closest thing we have to certain knowledge is a set of particulars known first hand. And even there mistakes are possible. Everything else is second hand or inferential, and this is far from absolute or certain.

Bottom line: Our best scientific theories should be regarded as provisionally and contingently true, not absolutely or certainly true.

Ba'al Chatzaf

Absolutely.

--Brant

[Dragonfly]

Right, just what I've always said.

[BaalChatzaf]

I would almost describe many of the post here as having an obsession with the word 'true', or 'truth'. Since the word is not the thing it represents (the map is not the territory) the only possible content of 'knowledge' is structure. Theories are not 'true' or 'false', they are relatively similar or dissimilar in structure to the structure we perceive.

What obession?

A map is "true" if it accurately represents its corresponding territory up to scale and features to be shown. For example a street map does not show elevations, but which streets cross which streets and relative distances at a reasonable scale.

You would not want a map that misrepresented locations or left out features which were intended to be represented by the map.

The adjective true is a predicate describing the relation between a representation and thing represented.

Bob Kolker

[tjohnson]

What obession?

A map is "true" if it accurately represents its corresponding territory up to scale and features to be shown. For example a street map does not show elevations, but which streets cross which streets and relative distances at a reasonable scale.

You would not want a map that misrepresented locations or left out features which were intended to be represented by the map.

The adjective true is a predicate describing the relation between a representation and thing represented.

Bob Kolker

Yes, but it is a poor adjective with hundreds of years of mis-understanding behind it. In your original post you have essentially set up 3-value system; true....provisionally and contingently true...false, which is fine, I just think it would be better to abandon 'true' altogether, except in the most casual conversation, and think in terms like; similar......various degrees of similarity....disimilar. This is because nothing can be absolutely true in a natural language so we should stop using the word in any serious discussion.

[Daniel Barnes]

Dragonfly:

>Right, just what I've always said.

What Ba'al, Dragonfly, Brant said. And what Ayn Rand and Leonard Peikoff deny with fiery rhetoric on one hand, yet cheerully accept on the other once suitably self-contradictory terminology ("contextual certainty", "contextual absolute" etc) has been engineered.

Perhaps their anti-skeptical rhetoric is more about marketing, packaging, and brand differentiation, than actual content. Either that or they genuinely believe in their distinction without a difference.

[Ellen Stuttle]

[snip]

Bottom line: Our best scientific theories should be regarded as provisionally and contingently true, not absolutely or certainly true.

Ba'al Chatzaf

Absolutely.

--Brant

Brant,

I don't know if you were being facetious or if you seriously believe that there's a fallacy of self-exclusion involved in claiming as certain that one can never conclusively demonstrate the universal truth of the laws of physics.

Whether you were just quipping or not, I've numerous times seen people in these discussions making similar quips: Oh, you're sure that you can never know for sure that such and such universal is true? Laugh, laugh. Caught you out there!

I'm going to try -- once -- to explain the issue in a way which I hope might make it clear.

Archemides is reputed to have said that if he had a lever and a place to stand, he could move the earth. Leaving aside the physical details of whether a long enough, strong enough lever to do the job could be made (and any other problems, such as keeping him alive wherever he's standing, etc.), the "picture" presented is one which makes sense. The earth isn't the whole of existence. One can get outside the earth and still be part of existence.

But consider the claim that you could know for sure of every instant of existence which was, is, or will be that a universally quantified statement is true. Where are you going to stand to do the counting? How are you going to count every instance that ever occurred or could occur to be counted, since your counting is itself such an instance? In order to perform the enumeration, you'd have to be nothing nowhere engaged in no process in relationship to an existence that had ceased to exist.

I hope you can see that this proposed scenario is self-contradictory. It would require that you were both something and nothing both counting and not counting from both somewhere and nowhere at both some time and no time.

Thus, one can show by straightforward deductive logic that a claim of performing an exhaustive universal enumeration leads to contradiction. Thus, yes, you can know for sure that one can never know for sure that the laws of physics hold universally. In general, one isn't making a self-exclusionary claim in claiming certainty for the non-certainty of a universally quantified statement.

I hope that helps.

Ellen

___

[tjohnson]

In general, one isn't making a self-exclusionary claim in claiming certainty for the non-certainty of a universally quantified statement.

I hope that helps.

Ellen

___

Wow, that's quite a mouthful there, Ellen, but I think I understand what you are saying.

Have you ever heard about Russel's theory of types? This is generalized in Korzybski's general semantics and solves the problem of "self-exclusionary claims". So if I say "all generalizations are untrue" I can't include the one I just made or else it leads to a vicious circle. What Korzybski suggested is that we consider a statement about other statements to be one of a higher order. This new statement cannot apply to itself and so we interpret "all generalizations are untrue" to mean "all generalizations are untrue except this one", or "all previous generalizations are untrue". It reminds me of when we say to our children "I don't care what I said before, this is what I'm saying now!", just in case you ever said that to your children. (or even have children)

[Michael Stuart Kelly]

Ellen,

The more I see this problem discussed, the more I become convinced that there is an axiom about entities that has not been properly included. I wrote about this once, see below (I highlighted the axiom part):

I am starting to believe that induction is the identification of an entity (or other existent) as a member of a group. I think I mentioned this before, but the more I ponder on this, the more I see that inductive reasoning is this process (identifying an existent as a unit). And I am beginning to see some holes in normal arguments against induction.

By going from observing a sample to projecting a truth about a group, one does not make a statement about contradicting a proposition, other than a proposition about the existence of the group itself. A person only makes a statement about creating a mental category of existents that, in fact, actually exist with such differences and similarities as observed.

In the classic example: "I have observed several white swans, therefore all swans are white," is a misuse of induction. The correct use is: "I have observed several white swans, therefore white swans exist as a category of reality." This implies that other white swans exist and rests on an axiom (one I have not seen anywhere in my reading, yet) that if two or more existents are observed and identified as a group, other unobserved members of that group exist. Science actually rests on this axiom in addition to deduction.

Obviously induction can be used to speculate, so the classic swan problem qua speculation is not a misuse of induction. But I am using induction here to mean a form of reasoning (or logic) for identification, i.e., for gaining knowledge. As a form of using induction for gaining knowledge qua knowledge, the classic problem as stated is a misuse of induction.

Finding a black swan does not disprove the knowledge of white swans gained by induction, because finding a black swan does not contradict the validity of the category. It only contradicts a proposition of closing the category off to new knowledge of the type of entity (closing swans off to any other color than white). In fact, a black swan causes the category of swan to be divided into two subcategories: white swans and black swans (more precisely, at that point, the categories are white swans and at least one black swan, and this will only become "white swans and black swans" when more than one black swan is observed).

When this kind of reasoning is applied to the is/ought problem (along with deduction), it becomes very easy to derive ought from is. One does not close the categories involved. One merely makes a statement about the categories that have already been identified.

In fact, there can be no deduction without categories. Induction is nothing more than volitional concept formation.

I have not had time to do the heavy reading on all this that I need to, but I do think this axiom needs to be included in the reasoning process of the "are you sure you can't be sure?" type.

By accepting the following axiom from above:

When two or more existents are observed and identified as a group, other unobserved members of that group exist,

one can be sure (or certain) that other individual examples of that group are out there somewhere. We cannot be sure that members with variations do not exist (in fact we can almost be sure that they do because the universe is so big). As an aside, we also can be sure that we can break individual existents (in any group) down into components that will form new groups. Reductionism is predicated on this premise.

The axiom above is kind of like an axiom of identity for groups. If applying this to inanimate matter bothers people, at least we can easily observe that with living entitiel, species do exist in reality. They may be made up of individual entities, but they also exist with group characteristics that do not apply to other groups (especially reproduction).

Michael

[BaalChatzaf]

Yes, but it is a poor adjective with hundreds of years of mis-understanding behind it. In your original post you have essentially set up 3-value system; true....provisionally and contingently true...false, which is fine, I just think it would be better to abandon 'true' altogether, except in the most casual conversation, and think in terms like; similar......various degrees of similarity....disimilar. This is because nothing can be absolutely true in a natural language so we should stop using the word in any serious discussion.

The following statement is true. At 10:11 I am sitting in front of my computer and typing a reply to your posting.

I am not abandoning anything.

Ba'al Chatzaf

[Daniel Barnes]

Mike:

>By accepting the following axiom from above:

"When two or more existents are observed and identified as a group, other unobserved members of that group exist"

Mike, your problem is that this is not an axiom (at least in the Objectivist sense).

"An axiom is a proposition that defeats its opponents by the fact that they have to accept it and use it in the process of any attempt to deny it." - Ayn Rand

[Brant Gaede]

[snip]

Bottom line: Our best scientific theories should be regarded as provisionally and contingently true, not absolutely or certainly true.

Ba'al Chatzaf

Absolutely.

--Brant

Brant,

I don't know if you were being facetious or if you seriously believe that there's a fallacy of self-exclusion involved in claiming as certain that one can never conclusively demonstrate the universal truth of the laws of physics.

Whether you were just quipping or not, I've numerous times seen people in these discussions making similar quips: Oh, you're sure that you can never know for sure that such and such universal is true? Laugh, laugh. Caught you out there!

I'm going to try -- once -- to explain the issue in a way which I hope might make it clear.

Archemides is reputed to have said that if he had a lever and a place to stand, he could move the earth. Leaving aside the physical details of whether a long enough, strong enough lever to do the job could be made (and any other problems, such as keeping him alive wherever he's standing, etc.), the "picture" presented is one which makes sense. The earth isn't the whole of existence. One can get outside the earth and still be part of existence.

But consider the claim that you could know for sure of every instant of existence which was, is, or will be that a universally quantified statement is true. Where are you going to stand to do the counting? How are you going to count every instance that ever occurred or could occur to be counted, since your counting is itself such an instance? In order to perform the enumeration, you'd have to be nothing nowhere engaged in no process in relationship to an existence that had ceased to exist.

I hope you can see that this proposed scenario is self-contradictory. It would require that you were both something and nothing both counting and not counting from both somewhere and nowhere at both some time and no time.

Thus, one can show by straightforward deductive logic that a claim of performing an exhaustive universal enumeration leads to contradiction. Thus, yes, you can know for sure that one can never know for sure that the laws of physics hold universally. In general, one isn't making a self-exclusionary claim in claiming certainty for the non-certainty of a universally quantified statement.

I hope that helps.

Ellen

___

Ellen, I was having a little fun, true, but I was not being facetious. I was merely demonstrating that the absolutism of philosophy underpins the tentativeness of science. I'm too soused to read and properly understand and critique the rest of your post as I've been drinking ever since I had to abandon my mother at rehab--for today--without saying goodbye to her for she can't, now, comprehend "goodbye." Maybe tomorrow.

--Brant

[Michael Stuart Kelly]

Daniel,

I have thought of that and this is the reason I have not expounded more. I am getting ready to travel now, so I cannot flesh out any ideas on paper right now.

This is the tip of the iceberg of the problem with entities that I keep harping on, however. Entities are not exclusively independent blobs floating around in time/space and sometimes bumping into each other, and then we come along and add some kind of mental content to arbitrarily group them.

Part of the law of identity would have to include the possibility of being a part of an entity group or structure of like entities.

I think this was what Nathan Hawking (rest his soul) was driving at when he proposed the axiom: organization exists.

No time. More later on this.

Michael

[Ellen Stuttle]

In general, one isn't making a self-exclusionary claim in claiming certainty for the non-certainty of a universally quantified statement.

I hope that helps.

Ellen

___

Wow, that's quite a mouthful there, Ellen, but I think I understand what you are saying.

Hmm. I suspect you didn't, considering your subsequent comments pertaining to Russell's Theory of Types. ;-)

Here's the context of my remarks: When statements are made claiming that the laws of physics can never be established as certain, the Objectivists on this list (those who read the Analytic-Synthetic thread and similar discussions) tend to come back with questions of the sort, "Are you certain of that?" I was taking a shot at trying to explain to them why the anser is, "Yes." My point is that there's no contradiction in claiming certainty for the claim that you can't claim certainty for the laws of physics. Instead there would be a contradiction in claiming certainty for those laws. The point has been made numerous times by Daniel, Dragonfly, and Ba'al Chatzaf in various discussions, but it doesn't get through. I had the possibly -- nay, probably -- idle hope that presenting the issue by means of a visualization -- a comparison to the Archimedes-and-a-lever story -- might do the trick.

Heading back (fingers crossed) to the lurk mode I was in before recent list events enticed me out of hiding...

Ellen

___

[Ellen Stuttle]

[....] I'm too soused to read and properly understand and critique the rest of your post as I've been drinking ever since I had to abandon my mother at rehab--for today--without saying goodbye to her for she can't, now, comprehend "goodbye." Maybe tomorrow.

--Brant

Brant,

My deepest sympathies and fond best wishes. That sort of situation -- saying "goodbye" to one whose "personhood" has gone before the body -- is terribly difficult.

Ellen

___

[Michael Stuart Kelly]

Brant,

My heart is with you. Kat's too.

Hang in there.

Michael

[tjohnson]

The following statement is true. At 10:11 I am sitting in front of my computer and typing a reply to your posting.

I am not abandoning anything.

Ba'al Chatzaf

I'm confused, you say "Our best scientific theories should be regarded as provisionally and contingently true, not absolutely or certainly true. ", but then you say a statement like "At 10:11 I am sitting in front of my computer and typing a reply to your posting" can be absolutely true? Hmm...was that 10:11 your time? Anyway, you are free to speak any way you wish, of course, it was only a suggestion for the sake of clarity.

You also said "So we have sufficient reason for holding these laws to be true, but we DO NOT HAVE absolute proof that these laws are everywhere and forever true."

And I would add that we never will since at best these laws can only be similar in structure to the events they represent.

Edited June 30, 2007 by general semanticist

[BaalChatzaf]

The following statement is true. At 10:11 I am sitting in front of my computer and typing a reply to your posting.

I am not abandoning anything.

Ba'al Chatzaf

I'm confused, you say "Our best scientific theories should be regarded as provisionally and contingently true, not absolutely or certainly true. ", but then you say a statement like "At 10:11 I am sitting in front of my computer and typing a reply to your posting" can be absolutely true? Hmm...was that 10:11 your time? Anyway, you are free to speak any way you wish, of course, it was only a suggestion for the sake of clarity.

You also said "So we have sufficient reason for holding these laws to be true, but we DO NOT HAVE absolute proof that these laws are everywhere and forever true."

And I would add that we never will since at best these laws can only be similar in structure to the events they represent.

I said it was true.

In addition to which it is a singular or particular statement. Scientific theories are applied postulational systems which at least one postulate which is a universally quantified statement.

Now, is my assertion that I was sitting in front of my computer absolutely true? Could I have been hallucinating? Is my memory accurate or did I just imagine that I was sitting in front of my computer at the specified time? Perhaps my clock was wrong. All these are possibilities, but by my own witness I claim I was sitting in front of my computer at the specified time. If there had been another witness to this, then the assertion would have an overwhelming probability of being true. But witnesses can be mistaken. If there we ten independent witnesses attesting to the same particular, the probability would even be greater. But it is possibler for ten people to be mistaken.

When I encounter a proposition attested to by a number of independent witnesses who I have no reason to believe are lying or mistaken I tend to accept the truth of their witness as true, even though I do not have first hand knowledge of the matter. Most of what we "know" is of this nature. We know some things first hand. Most of what we -believe- to be true is second hand from sources believed to be reliable and somethings we -infer- from what we know first hand or accept second hand.

Very little of what we know is known to be the case absolutely.

The only universal proposition I believe absolutely is the law of non-contradiction. Everything else I accept provisionally, including this assertion. I might be hallucinating. I might be mistaken. It is possible, i.e. the assumption that I am in error does not lead to a flat out contradiction, even though I believe I am not in error.

Many Objectivists believe that assenting to the possibility of error is equivalent to utter and radical skepticism. Such is not the case. They usually cover their hind quarters by invoking "contextual certainty", whatever that is.

Ba'al Chatzaf

[tjohnson]

I said it was true.

In addition to which it is a singular or particular statement. Scientific theories are applied postulational systems which at least one postulate which is a universally quantified statement.

Now, is my assertion that I was sitting in front of my computer absolutely true? Could I have been hallucinating? Is my memory accurate or did I just imagine that I was sitting in front of my computer at the specified time? Perhaps my clock was wrong. All these are possibilities, but by my own witness I claim I was sitting in front of my computer at the specified time. If there had been another witness to this, then the assertion would have an overwhelming probability of being true. But witnesses can be mistaken. If there we ten independent witnesses attesting to the same particular, the probability would even be greater. But it is possibler for ten people to be mistaken.

When I encounter a proposition attested to by a number of independent witnesses who I have no reason to believe are lying or mistaken I tend to accept the truth of their witness as true, even though I do not have first hand knowledge of the matter. Most of what we "know" is of this nature. We know some things first hand. Most of what we -believe- to be true is second hand from sources believed to be reliable and somethings we -infer- from what we know first hand or accept second hand.

Very little of what we know is known to be the case absolutely.

The only universal proposition I believe absolutely is the law of non-contradiction. Everything else I accept provisionally, including this assertion. I might be hallucinating. I might be mistaken. It is possible, i.e. the assumption that I am in error does not lead to a flat out contradiction, even though I believe I am not in error.

Many Objectivists believe that assenting to the possibility of error is equivalent to utter and radical skepticism. Such is not the case. They usually cover their hind quarters by invoking "contextual certainty", whatever that is.

Ba'al Chatzaf

So why not say "it's my impression" or something instead of it's true? Don't you think 'true' has a connotation of being universal? Another device is dating statements like "I said (in 2005) that ...." so now it may or may not be the case anymore.

[BaalChatzaf]

So why not say "it's my impression" or something instead of it's true? Don't you think 'true' has a connotation of being universal? Another device is dating statements like "I said (in 2005) that ...." so now it may or may not be the case anymore.

The you know the difference between the following kinds of statements?

1. A statement that asserts a particular fact.

2. An existentially quantified statement.

3. A universally quantified statement.

When you have this sorted out, we will talk some more.

Ba'al Chatzaf

[tjohnson]

So why not say "it's my impression" or something instead of it's true? Don't you think 'true' has a connotation of being universal? Another device is dating statements like "I said (in 2005) that ...." so now it may or may not be the case anymore.

The you know the difference between the following kinds of statements?

1. A statement that asserts a particular fact.

2. An existentially quantified statement.

3. A universally quantified statement.

When you have this sorted out, we will talk some more.

Ba'al Chatzaf

Who cares?

[BaalChatzaf]

So why not say "it's my impression" or something instead of it's true? Don't you think 'true' has a connotation of being universal? Another device is dating statements like "I said (in 2005) that ...." so now it may or may not be the case anymore.

The you know the difference between the following kinds of statements?

1. A statement that asserts a particular fact.

2. An existentially quantified statement.

3. A universally quantified statement.

When you have this sorted out, we will talk some more.

Ba'al Chatzaf

Who cares?

It is the basis of talking rationally and sanely about how language works. If you do not make these distinctions you do not understand language, logic, mathematics nor science.

Ba'al Chatzaf

[tjohnson]

It is the basis of talking rationally and sanely about how language works. If you do not make these distinctions you do not understand language, logic, mathematics nor science.

Ba'al Chatzaf

That's what you think.