The original question was:
Mathematicians sometimes say, “There exists a number such that . . .” Which provokes me to ask, Where does it exist? For how long has it existed? Did numbers exist before people did? Or did people somehow create (instead of discover) them?
In her “Incompleteness” quasi-biography of Godel (not a bad mathematician), Rebecca Goldstein emphasizes that he was a Platonist about math. What’s the current state of Platonism in math?
And such questions can be extended to the “laws” of physics: Do they exist? If so, where? And for how long? Are they discovered (implying prior existence) or invented/created by humans?
Some comments relating to such issues would be interesting!
Physicist: Discovered. Although most of the laws that can be re-arranged and expressed in different ways. For example you can express “conservation of total momentum” as “the velocity of the center of mass never changes”.
A good physicist (one who pick their words carefully) will avoid saying that one thing or another is “true”. Physics, and the laws we come up with, don’t exist “out there somewhere”. Boiled down to its most basic, what we study is “what has worked before, and still seems to work” as opposed to “what is true”.
For example: Einstein showed that Newtonian physics is wrong (so wrong), but it still “works”. If you learn Newton’s stuff you’ll notice that it’s fairly intuitive (compared to some other sciences at least), and seems to be true. It was taught as fact for over 200 years, but again: wrong. Taking this, and dozens of other similar stories as a warning, physicists try to talk only about what works and not what’s true.
That being said, some of the laws that have been found may actually be true, written into the nature of the universe. I’d like to say that we know at least a few of them for sure, and that if what we know is wrong then the universe is entirely fucked. However, that has been exactly the case before (I’m looking at you wave-particle duality), so who knows?
The pitiable population of "Monopoly". Are the rules they perceive the same as the rules written on the box? They could pass Go forever, and never know.
The laws we have could easily be special cases of the true laws (like Newtonian mechanics in relativistic mechanics), or could be merely the descriptions of the behavior created by those laws.
As far as the physical laws of the universe actually, physically existing in some form somewhere (this is the total extent of my understanding of Platonism): no, I don’t think there are very many scientists who think that.
In the quantum sense, things exist because we try to measure them. Do the laws of physics exist because we choose to see them? Our labels are used to measure the universe, yes? We give it a name so that we can communicate and share the idea. So just by calling it something are we creating it? What if we aren’t actually discovering anything, rather, we are creating it and it appears before our very eyes? If so, are we collectively engaged in this construction of reality? What would it take for the whole world to agree to think up a completely eutopian planet? Is such a thing possible ever / in our lifetime?
I think about gravity. Why does it exist? more mass = more gravitational pull but why is that constant throughout the universe? as if it were programmed or written?
In quantum theory things still exist whether or not we measure them. The only difference is that unmeasured things have the option of being in more than one state at once (there’s presently a handsome youtube video that covers this fairly well).
If the laws of physics were observer dependent, then you’d expect them to have changed throughout history, and that extremely unpopular theories wouldn’t work (I’m looking at you, Relativity). But that doesn’t seem to be the case.
There’s obviously a correlation between the laws of the universe and the laws we know and observe. However, the cause and effect arrow only points in the one direction.
That being said, convincing the entire world to “think peace” seems pretty worthwhile anyway.
The Truth is eternal. The Truth is God. God exist throughout the universe in every law and in every sub atomic particle. We discovered the laws of nature (Physics, chemistry, math, etc … Love also) and we named the laws after the people that discovered them, but those laws had been in the universe before solid was created. Every Truth in the universe makes up the perfect mind of God so God is the answer to every logical question. God does not have a solid body, he is not Jesus Christ (Jesus is his son) God is a spirit. His universe is in a spiritual realm just like the laws of nature are now. We can not get into the spiritual realm (Thank God) so we have no control over the laws. 1+1=2 long before any two solid object were there to count. Distance was also present but nothing solid to measure between. The laws of Truth are eternal, the laws are God.
Before the 1st physicist or mathematician was born , Nature existed already. There was gravity , energy ,…all these phenomenon were behaving to some point inside this universe of ours….when we came to this universe , we saw this behaviours and ask Why. We dig deeper and found only a couple of explanations that are not complete and we until now continue to be doubtful even on the latest explanation we know. If we question , how these behaviours come to be , I dont know , but what I do know that it was not a results of a mathematician or physicist thinking. But , in the back on my head , I do believe that Man was not the 1st mathematician and physicist in this universe….whom Paul Dirac attributed to be the Mathematician who created the universe…( ” One could perhaps described the situation by saying that God is a mathematician of a very high order , and He used very high-order advanced mathematics in constructing the universe.- The Evolution of the Physicist’s Picture of Nature , Scientific American ) …. though Dirac’s idea about a higher mathematician is doubtful to many …what is so far true is that we don’t have yet the GUT and will never be able to know and provide a complete explanation of Nature ( cf Ecclesiates 3:11 )
The physicist’s reply was interesting, but notably only answered the question about physical laws. No answer was given to the corresponding question about mathematics. For example, the law of non-contradiction (with its refinements due to the intuitionists and the paraconsistent theories), or more exactly that which corresponds to the law (in model theoretic terms, the law is the theory, but the model is what we are asking about here,) seems to be observer independent (unless you practice Zen, I guess). Gödel’s Platonism was about the “reality” of pure mathematics which, he said, was different from physical reality but, in a sense never made clear (despite the fact that he wrote about it at length), just as valid. Hence a question about physical reality does not address the question about a mathematical Platonism. I would be interested in an answer (that left out references to deities) to this question. Thanks.
We can never know reality – we can only feel it. All laws – whether they be platonic, mathematical, physical, legal or moral, are our consciously constructed descriptions of reality, so exist only in our minds. They may seem to approximate to reality but their degree of approximations is a measure of the poverty of our minds. And because, chronologically, we felt/sensed before we thought (and still do most of the time) all these so-called laws must originally have been premised exclusively upon our sensually induced feelings.
Well, ignore mathematics I say, let’s just stay with ‘logic’. If we assume that no logic exist we get a magical universe. A magical universe is not ‘a very advanced scientific’ universe, it’s a universe without logic.
So, either One think this universe will be found to answer to some logic(s), or you don’t? What we have found so far is logics, not the absence of it.
The original question was about “existence” in the physical and mathematical realms. (The question whether logic is part of mathematics or vice-verse is an ongoing debate among mathematicians, and I won’t go into that here.) The physicist dealt implicitly with the idea of physical “existence” –although the answer did not cover the debate among physicists, which is still ongoing among physicists, as to whether one can say that the wave function, which contains the information about the probabilities of a particle’s properties when measured) is as “real” as measurements; another debate is whether one can talk about “existence” for elements of a parallel universe that cannot be measured. But for logic, thankfully the definition of existence is much more precise: logical existence has to do with the role of the existence quantifier in an interpretation in a model (where “interpretation” and “model” in logic have very specific definitions). This is not just a formalist definition; a Platonist would agree. The difference between a Platonist and a Formalist is more subtle, but I won’t go into that right now because there are very few logicians who are either pure Platonists or pure Formalists. Hilbert’s Formalism bit the dust with Gödel’s results, but ironically Physics in the twentieth century made pure Platonism, as it used to be expressed, more difficult a standpoint to hold to. So most logicians are somewhere in the middle.
Well, ahh, now you got me confused 🙂 Logic is just a way of interpretation to me, in where you look at what experiments tell you, and from there try to describe something that will make sense mathematically. Mathematics is, in a way, a subset of ones logic, meaning that I do not expect there to be able to exist a logic, unable to be expressed mathematically.
That’s what I think we do when we meet new logics, as QM, and relativity? We search for, sometimes even have to invent new forms (derivations) of mathematics, to be able to describe them.
The word “logic” is thrown around rather loosely in everyday parlance, but as an academic study in mathematics, it is much more strictly defined. Essentially, Mathematical Logic (sometimes called Symbolic Logic) is the study of any formal system which contains an alphabet, a syntax, and rules of implication. A logic is one of those systems. (Microsoft Word does not recognize “logic” as having a plural, but it does.) Mostly one tries to concentrate on logics which are not provably inconsistent within themselves, but there are even logics which allow a certain amount of self-contradiction.) Mathematics, on the other hand, is more loosely defined — often the half-tongue-in-cheek “definition” is given: “Mathematics is what mathematicians do.” Very, very roughly, the difference to Mathematical Logic is that the option of using methods of reasoning which do not correspond to a formalized rule of implication remains open, as long as that method does not lead to an internal contradiction. However, in how far “not formalized” can be replaced by “not formalizable” is a matter of debate. In any case, neither a logical system nor a mathematical theory need correspond to anything in the observable universe: a proof of this stems from the fact that two systems of logic (two logics) can contradict each other, but each one independently considered valid. (The same for two theories of mathematics.)
In everyday parlance, when one says that one encounters a “new logic” for QM or relativity, one usually means a “new way of thinking”, but most of the formal mathematics was already in place for each of these physical theories. In fact, many of the important results in these two theories reversed the traditional sequence that tied together mathematics and physics ever since Galileo: instead of first taking observations and then finding a mathematical theory that would describe them, in relativity and QM the mathematics which already described some physical phenomena came first, and the surprising results of mathematical manipulation forced physicists to look for physical phenomena that fit those results.
John Faupel said:
>>>We can never know reality – we can only feel it. All laws – whether they be platonic, mathematical, physical, legal or moral, are our consciously constructed descriptions of reality, so exist only in our minds. They may seem to approximate to reality but their degree of approximations is a measure of the poverty of our minds. And because, chronologically, we felt/sensed before we thought (and still do most of the time) all these so-called laws must originally have been premised exclusively upon our sensually induced feelings<<<
I agree. "Reality" itself is already conceptual=immaterial, in other words fabricated in the brain, from the Physical world around us if not even just within our brain itself. The physical objects and phaenomena are the very material Templates at the origin of the concept "reality". Numbers (1, 2, 3, …) aequations and mathematical functions, Physical- (and Legal-) Laws, but also sensations, emotions, morality, purpose, meaning, and, importantly, all those G-Ds, which evolved during the history of mankind, angels and daemons are just "thoughts". In short, the question "do physical laws exist" can be reduced/replaced by "do thoughts exist". Kind regards from GERMANY
The laws of physics existed. Humans only discovered them. The force between two objects is given by a F = G m1m2 divided by the square of the distance (multiply the gravitational constant G by the two masses and divide the result by the square of the distance between the two masses) always existed but humans discovered what the formula for the force between two objects was equal to. The law would have to originate from a mind as some natural occurrence could not write the law.
In pre-linguistic times our distant ancestors lived and survive for thousands of generations by responding to their environment and each other entirely subjectively through their senses, just like other species of plants and animals still do. Their facial expressions, body language and the sounds they made helped them to communicate their feelings to one other. These feelings eventually evolved into language, and language into thoughts, then laws of mathematics and science and our, self-congratulatory belief that we could understood and know reality objectively because we had become more ‘intelligent’. This belief has become so dominant in the way we think and try to act, that we forget it is still premised on how we felt – no matter how far back we need to go to recognise its entirely-subjective origins. Hence, the laws of mathematics, physics and all the other so-called spiritual and secular laws we’ve invented, are our own attempts to see order in an innately indeterminate, permanently turbulent and ultimately chaotic unknowable reality. No wonder the thinking parts of our minds have created, at the expense of the feeling parts of our whole bodies, have resulted in more problems than they have solved.
If something is not already there, how can you explain it? Simple logic.
The maths were already there. We discovered them. Lets just keep this very simple for other to follow along.
A log is likely to float becuase it has positive buoyancy when thrown in the sea. If you throw a stone into the sea. It sinks. That would be because it has a negative buoyancy There we have a plus and a minus ok. Positive or negative buoyancy.
Humans did not invent that plus or negative. It is natural plus minus. We give its name plus or minus and symbols, but it already existed in nature.
We give its name plus or minus. But we could have called that donk n zonk and would know donk means positive B, zonk negative b – but either way, either word we choose to use the fact is + plus donk and – minus zonk are clearly there in nature to be observed and named in a language we can express the working to others. We did not invent that, we only invented the word or symbols to explain it….
Also If we have one coconut and then another falls from a tree we now have two .. So again we have donk in nature as we now have 2 coconuts, 1c + 1c = 2c .. Simple math. We can now remove one coconut becuase a storm surge comes washes the one nut away and off it floats to sea while one remains, or both vanish in the storm we are left with zero?? We can now call that wonk. So zonk donk and wonk we can invent.
The fact that a stone sinks is becuase of a zonk force, but we did not invent that negative force we only named it.. So in nature there are plus and minus the very basics of maths. Temps rise and fall to states of positive or negative points, again plus minus and again nothing we invented other than we invented the words to A describe and B to measure that phenomena. Yet it is there already in nature and we can only describe that process as it is mathematical and always was in nature it self, we only discover the formulas to describe and invent the names given to communicate. . So Plus and minus is already there in nature – We just invent names or symbols to describe things in nature and have given it the name maths.
You cannot explain something that is not there.