I am not convinced that this is true. Two of Peirce's major objectives for philosophy were to make it more mathematical (by which he meant diagrammatic) and to "insist upon the idea of continuity as of prime importance." Surely he must have considered these efforts to be complementary, rather than contradictory. — aletheist

I think you have presented to most essential issue. I understand the dilemma, but understand that Bergson had truly mastered all mathematics of his time but never sought to use it in any of his writings. One cannot use a fatally flawed approach to arrive at more knowledge no matter how difficult it is to admit to these flaws.

So concretely, a discrete approach cannot uncover the nature of a continuous ontological reality. Other approaches must be used and unfortunately current mathematics is simply not equipped. It is only adequate for discrete approximate measurements and predictions of non-living matter. It cannot be used to understand the nature of a continuous universe.

As far as I can tell, mathematics is totally reliant on the discrete and because of this limitation constantly makes philosophical ontological errors. Admission to this major limitation would allow philosophy to move ahead. As long as philosophers are pinned to mathematics then paradoxes will continue to confound. To put it concretely, discrete can never model continuous and any confusion will necessarily to paradoxes.

He certainly did not think so. Could you please point me to the proof? Note, I acknowledge that the real numbers serve as a useful mathematical model of a continuum. — aletheist

Does mathematics actual model a continuum? I don't think so. If it did, it wouldn't lead to do many paradoxes and incorrect descriptions of experiences. Mathematics, I believe, provides a rough models of discrete, measurable actions , which in themselves are practical for certain applications, but are also quite distant from experiences. For example, it is impossible to divide space or time (duration). This simple observation, which addresses the OP, makes all the difference in the world. Far from being parenthetical, it totally changes the way one views the nature of life and the universe.

Understanding this, addresses the question of why Einstein was incapable of understanding what Bergson was presenting and why Bergson understood Einstein but disagreed. And as the OP points out, with this understanding Zeno's paradox is dissolved.

Yes, this I would fully agree with.

There are areas of the quote that I would agree with and there are others that I would phrase differently. Utmost is the issue that science way over steps it's bounds when it begins to replace everyday experiences with symbolic equations and declaring the equations to be more real. If such was true, we couldn't move or more ernestly we all become illusions of equations. This is what Bergson and Bohm objected to.

What I mean to say is that carving up space, in imagination, is a matter of convenience, mathematical or otherwise. Space is continuous as is real time (duration). Mathematics is simply a symbolic tool to aid in measurement (along with actual observations). However, scientific equations themselves have no ontological value simply because of this disconnect with actual experience. Using mathematical equations as a substitute for actual experience leads to all kinds of paradoxes such as time travel, twins aging differently, and of course Zeno's.

Bohm pointed out that where there are paradoxes there are some really nasty problems with assumptions.

I should add that with this simple observation, that space is indivisible, all mathematical theories about nature that rely on mathematical divisibility of space, automatically lose all ontological meaning. They still have practical value but they have no ontological value. This again was Bergson's primary insight into Special and General Relativity.

Yes, this was precisely Bergson's solution. The assumption that space is divisible is a matter of convenience, it does not reflect experience.

Your information is totally biased. Immediately you lose all credibility when you edit scientific positions to suit your purposes and then mix some of your metaphysical biases into your heavily edited presentations of science. Your scientific argument to appeal to polls is ludicrous. I don't even know how to attach such a frivolous stance. When you start to push an agenda, you are no longer a scientist.

Read about how scientists make new discoveries. Einstein constantly illuded to thought experiments - alternatively described as creative imagination. Equations are nothing. It is the images it conjours up in the mind that lead to discoveries. Equations are dead, lifeless, purely descriptive. It is the creative mind that provides the new ideas. Bell also described his process.

Succinctly, scientists such as Bohm, who have life to the notion of non-local actions by the quantum potential, describes the process as seeking differences within similarities and similarities within differences. This is precisely the process I used in my computer science career. It is fundamental to creative thought.

If you don't want to define laws of nature and enumerate examples, there is nothing to discuss. Should we move on to God, which may be somewhat more concrete?

You can look at the equation from now to doom's day and there is nothing about entanglement. It is a leap of creative intuition. Bohm describes the process quite meticulously in his essay on Creativity. In fact, the development of the concept of entanglement was quite a long one and involved several intuitive leaps. This process is fundamental to scientific discovery. I have no idea where you get the idea that by staring at a lifeless equations, out pops something new. It just emerges from the paper?

The road to entanglement had nothing to do with analyzing some lifeless equations. It was the result of extraordinary intuition by Bohm and Bell followed by some fascinating creativity by Aspect which ultimately resulted in confirmation experiments by Aspect and others. The equations are simply some symbolic representations of the quality of the minds of these scientists and are confirmed by repetition.

If you wish to claim that creative intuition is the heart and soul of scientific discovery, then I would agree.

OK. Define what is a law of nature and enumerate them. Then we'll have something concrete to talk about. My first comment on this thread is that it is impossible to discuss a term without a clear definition and concrete examples. It's like talking about God. Do you have a definition?

All of the equations and observations are always approximate and subject to change. It was the discrepancies in physics and chemistry experiments that drove scientists to a new understanding of nuclear and quantum physics, which is also changing.

There is no need for the concept in science and I actually never read a scientific paper that called upon the notion of laws to make its presentation. Laws of nature is just an ambiguous term without any concrete value that is called upon by some metaphysical viewpoints. I have yet to have such enumerated. I guess it is more convenient to suggest they exist without any need for a concrete definition. The article I presented earlier is but one example of how disorganized and messy the topic gets if philosophers or scientists are actually called upon to provide a concrete example with definitions.

A more unbiased, less hysterical, and less metaphysical report on current scientific understanding of wave-particles. In time, as Bohm suggested, it will be understood that the quantum potential field is real, particles are a manifestation of field perburtations (as De Broglie described), that non-local action is the result of this quantum potential, and all will be well again in physics.

http://www.nature.com/news/quantum-physics-what-is-really-real-1.17585

I enjoy well written and will presented ideas that present the true current state of disagreement and discussion.

"In 2005, de Broglie–Bohmian mechanics received an experimental boost from an unexpected source. Physicists Emmanuel Fort, now at the Langevin Institute in Paris, and Yves Couder at the University of Paris Diderot gave the students in an undergraduate laboratory class what they thought would be a fairly straightforward task: build an experiment to see how oil droplets falling into a tray filled with oil would coalesce as the tray was vibrated. Much to everyone's surprise, ripples began to form around the droplets when the tray hit a certain vibration frequency. “The drops were self-propelled — surfing or walking on their own waves,” says Fort. “This was a dual object we were seeing — a particle driven by a wave.”

How many times did it repeat in the 50 years between its discovery and the first time it was observed? — tom

I don't know. Do you have an exact number or an approximation?

Entanglement is repetitious. That is how it is confirmed. Scientific experiments confirm this.

The discovery itself is the result of human intuition and creativity which one can put under the umbrella of science of one wishes. Are you suggesting that sciencific discoveries are the result of human intuition! I'm on board with this.

I'll tell you what, if you are going to make a scientific claim as a scientist, then why don't you:

1) Present all of the evidence

2) Admit to the ongoing discussions and disagreements among scientists (there are always opposing points of views),

3) Refrain from presenting your metaphysical ideas and desires as scientific facts (there is no such thing)

4) And clearly mark boundaries when you cross them, e.g. calling upon a priori knowledge to support a metaphysical definition as a settled scientific issue.

Most scientists would be better off if they refrained from pushing their own metaphysics as settled science.

A priori is not scientific term nor is a particle a scientifically defined term, yet you've seen one. Remarkable! You are mixing up science with metaphysical ideas and desires (as does Relativity in a truck full) and coming up with a mess. A desire for something is not the same as scientific evidence.

No one had seen an atom or particle. It is impossible with the Uncertainty Principle. You can only see an aspect as defined by the instruments used and the experimental set up.

Scientists are working on all aspects of Bohmian Mechanics but all solutions require a change in view and perspective, especially in regards to Relativity and the paradoxical notions that emanate from it. There is a ton of scholarly papers on Google scholar on this subject.

If you want to be metaphysical then just say so.

Heck, you can see an atom. Good for you.

Enjoy yourself. Your just another scientist overstepping boundaries and using some age old tactics to justify yourself. You are in no position to make the statements you are making from a scientific evidence perspective. If you want to put on your metaphysical hat, then go right ahead.

http://physics.stackexchange.com/questions/45572/how-do-we-know-particles-exist-arent-they-just-waves

Your eyes are better than mine.

The intuition of possible meanins is not in the equations in is in the minds that create the possibilities. It all begins with Schrodinger's intuition that quanta phenomenon may be described by a wave equation. Similarly, Einstein and his associates looked for possible contradictions in the meaning of the equations. It is the always the mind's intuition that is driving science into new creative directions. The equations themselves may act as an enabler or an inhibitor. It all depends.

Glad to hear that relativity had some value with approximations and that gravity affects satellite clocks. All theories have problems, Relativity is nothing but problems. They are just a mumbo jumbo of paradoxes that are inherently conflicting and on the surface nothing more than a nice theory for science fiction writers. You can see an atom? Not really. Instruments can register an image that they are designed to register. Please don't drag me into the age old trap of replacing real things with symbolic images. You know that photograph. It's not you and it doesn't even approximate you. Thanks for the update though.

So that your time isn't wasted, this scientist will teach you something new. Enjoy it! The are no particles. There are field perturbations.

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/quantum_theory_waves/index.html

Well what I mean is that scientists expect chemicals for example to behave the same tomorrow as they did today. Or when hypothesizing about, for example geological formations, they assume that materials behaved the same millions of years ago as they do today. Or when they are hypothesizing about galaxy formation or even what would have happened just after the Big Bang, they assume that different elements, particles and materials would have behaved as expected in the hypothesized conditions.Without such assumptions science could never get started — John

Science depends upon mathematical equations that describe repetitious events that are approximately the same, enough so that they can be used for practical purposes. That Newton's Equations are imprecise does not mean that they are impractical. In some cases they may be impractical in which case other equations are used.

The concept of laws of nature is not only unnecessary in science, it is totally misleading.

In philosophy it is only needed by determinists who use this generality for want of specifics. It is more of a desire than anything concrete.

To b respond, I am not as infatuated with relativistic physics as some scientists may be. Any set of theories that on one hand demands reciprocity (Special Relativity) and then contradicts itself by allowing for non-reciprocity in accelerated systems, is just too muddled for my taste and predictably leads to uncomfortable paradoxes such as time travel and cars that sunny fit into garages sometimes. Bohm once wrote that where there are paradoxes there are problems and the paradoxes need to be resolved in order to move forward. Relativistic theory is chock full of paradoxes, enough so that it should minimally be considered highly questionable at its core. Both theories actually provide very little practical usefulness, other than describing how gravity may affect the behavior of systems, and I see no reason to discard a strong theory such as Bohm's in favor of a confounding theories like Relativity. In time both Special and General will most certainly be discarded. That Einstein became somewhat of a pop figure because of his hair and his science fiction theories of time travel is something science c will have to deal with. They should have dealt with the problems very early on.

As I described the De Broglie-Bohm wave theory is the latest updated version. This is how De Broglie described it hits essay. It is used to describe the Bohm-Abrohomov effect. This illustration appears in Bohm's book:

Your dismissal of Bohmian Mechanics is a choice you make for yours. That other scientists choose muddled theories such as the Copenhagen a Interpretation or wildly speculative, science-fiction theories such as the Many-World Interpretation is of no consequence to me. Metaphysical intuitions are for each individual to explore as they wish. My preference for Bohmian mechanics is that the wave is real, it fits all experimental data, explains phenomenon such as the delayed choice experiment, was the foundational theory for Bell's theorem, and leaves open the possibility of free will. Far more concrete than the completely unintelligible Copenhagen Interpretation or the far out Many-Worlds. Had Bohm been satisfied with Vsn Neumann's "proof", we would still be sitting here without a real wave, causal but not deterministic) theory for quantum mechanics. But it is all a matter of taste.

As for particles, they don't appear to exist. What does exist, is a wave and what we measure as particles are wave perburtations. De Brogle was apparently correct all along. The Bohm quantum potential field offers the best explanation I have read that addresses this unnecessary ambiguity of how a wave spontaneously turns into a particle, by simply doing away with the concept of a distinct particle. And while there is a body of support for my interpretation, some scientists continue to utilize the concept of particles to simplify discussion even though it is grossly misleading. Some ideas are hard to bury. I provided one scholarly article which suits my position that scientific texts should stop referring to. particles

Some scientists make this assumption others are much more careful. Here is one such discussion about laws and you will easily notice the widely held views on the subject, among scientists and philosophers. Many scientists will readily admit that the equations they rely on are simply useful approximations and therefore should not be considered immutable laws of nature. Without consensus at any level, it is difficult to use a term such as laws of nature or scientific laws. Best just discuss the specific subject and about the ambiguous and undefined general term.

https://blogs.scientificamerican.com/observations/deep-in-thought-what-is-a-law-of-physics-anyway/

My views on scientific laws are closely aligned with this view:

http://www.iep.utm.edu/lawofnat/

"In 1959, at the annual meeting of the American Association for the Advancement of Sciences, Michael Scriven read a paper that implicitly distinguished between Laws of Nature and Laws of Science. Laws of Science (what he at that time called "physical laws") – with few exceptions – are inaccurate, are at best approximations of the truth, and are of limited range of application. The theme has since been picked up and advanced by Nancy Cartwright."

As for my own understanding, the Copenhagen Interpretation is rather muddy, inconclusive, and unsatisfying - by choice. But the Interpretation is simply that and since it is metaphysical in nature is free to make these claims, despite its limitations. Metaphysics is all about intuition, imagery, and finding patterns. There needs to be a distinction between this, e.g. quantum interpretations, and quantum equations, which are quite limited in their nature.

My own preference is to avoid limiting options. As it appears there exists opposites for everything (call it the apogee and perigee of the waves) I always leave open the possibility for something that I am missing. I consider laws not only erroneous and overly constraining, but also impediments to growth in knowledge. Knowledge comes from resolving paradoxes or another way to look at it would be to find the opposite and from that comes new ideas. The does not appear to be an end to this process.

Not an absolutist. I am a philosopher who prefers precision to grandiose claims or overreaching descriptions. Just describe it as it is and be good with it.

It is the law that there is an irreducible degree of lawlessness in the world. It is simply a corollary of the fact that classicality can fulfill its determinstic desires to the degree it makes any real difference. — apokrisis

I would say that there is aspect of quantum physics that need upon current observations, there is at this time a limit to precision and completeness of measurements (one can be more precise this if one wishes). I don't like embuing more into something than it is entitled to. Quantum physics is a new way of thinking about the behavior of fields and matter, but much is still left to be discovered and understood. It doesn't appear to be absolute or final, and it appears to be evolving. Beyond this, it appears to be practical for certain types of applications.

There does appear to be spontaneity in our lives but I would say it is peripheral to quantum theory, though one is free to speculate, as many do, the origination of this spontaneity which could very well undermine any possibility of a law.

Yes, but logically speaking the possibilities are that the tendency of nature to form habits is universal and invariant or that the tendency of nature to form habits is not universal and invariant, no?

And actually prior to the logical possibilities regarding the tendency of nature to form habits are the logical possibilities that the behavior of nature is simply universal and invariant or that nature tends to forms habits and hence its behavior at the most fundamental levels evolves, or that nature at the most fundamental levels behaves arbitrarily and the fact that there are observations that seem to show the contrary is a matter of pure chance. — John

In hesitate to limit possibilities since there also seems to be more of them. Heraclitus declared all is in flux. In his own way, Bergson adopted a similar stance, using a more formal description. One could say that Heraclitus' view that everything is always changing, is a ubiquitous observation, I would agree. To call it a law, would contradict the observation so there is no reason to say so. It depends upon whether the universe is in continuous change, or to put it another way, does the pendulum really stop at apex at the point of reversal?

As for the fundamental level of nature, I believe it is intelligence that is always changing because it is learning.

There is nothing special about a square. It is a shape. It is a shape with for sides that are equal. What two people may see may be completely different internally (the is no way of verifying that internal images are more or less alike). However, if one person says that the box in question has four sides, all equal, and all at right angles to each other they may or may not agree that it is a square, but if they both were educated in a similar manner they will probably agree that the word square is a simplified way of describing the box. (One could also say it's a rectangle).

However, if one wanted to win a bet, one can also claim that it is not a square, but rather a shape with unequal sides and angles, and precise measurements would verify that this observation is not only valid but that the external image is also constantly changing. There is a very fine line between consensus and disagreement.

The concept of square is just part of a convenient learned belief sysyem that has been agreed upon, usually by the mechanism of formal education. In itself, the concept and word only serves as a communication device for what is some formed belief that had become part of one or more individual's memory.

I would call it an observation that there seems to be habits in nature that change over time and between each repetition. Law, as commonly used, implies an invariance, which I don't subscribe to.

Habits is a way to understand nature other than laws.

I habitually wake up in the morning, however the time I awake constantly changes, and yes it is possible that I will not awake at all. Habits are not cast in stone, they are just highly probable with deviations. Habits provide some degree of stability while still allowing for enumerable possiblities.

Useful mathematical equations are not actual laws of nature, but that simple fact does not tell us that there are no laws of nature. — Querius

It therefore remains that the question that the OP is asking cannot be answered until someone presents a concrete law of nature. If nature can be best described as tendencies or habits that are somewhat repetitive or habitual then that is all there is. Everything is subject to unexpected, ambiguous, unanticipated changes. There is no fully repetitious or predictable event and therefore no law that can precisely define such events. There is a huge gap between some theoretical notion of general behavior vs actual behavior as it unfolds.

To put it more concretely, the concept of a law of nature is rather elastic and loose, and really doesn't provide any additional insights into what is happening, though it is sometimes called upon to justify some pre-determined path of events. Under such conditions, I have no idea how to answer the OP other than to say, I guess not because I can't seem to find any law of nature anywhere, just some generalized habits which have no claim to irreducibly.

There is a speculative mathematical description of how gravity behaves which is one thing. However, this description is not gravity. Gravity is something we feel and acts upon objects in all directions and all distances. There is no law of gravity, there are just some tentative equations which may be useful for synchronizing clocks. The non-reciprocity of accelerated bodies in General Relativity appears to be in contraction to the reciprocity of all systems which is the basis of Special Relativity. I do not know if any such requirement in quantum physics which rests on an entirely different foundation.

Without cohesion, we just have useful mathematical equations but certainly no laws.

Successful, precise predictions never occur. What does occur are useful guesses and approximations. This is why I prefer Sheldrake's preferred use of habit as opposed to law, allowing for approximate repetitive events but not precisely what is predicted. Bergson made a point of nothing ever repeating because what might be is always necessarily different than what was.

I agree. Talking about physical laws in some abstract manner serves no purpose. It is easier and more productive to just discuss the specifics that are applicable. No reason to maintain the concept of natural physical laws. It just muddies the water for lack of precision.