Objective Logical Laws

Húrin

If I did not exist, the laws of logic and mathematics would still exist.

If no humans existed, would the laws of logic and mathematics still exist?

Are these laws written into the fabric of the universe, or are logic and mathematics human constructs?

And the question I am really interested in: is the answer to these questions given by some decisive evidence, or is one's position on these matters essentially faith-based?

ChocolateSauce

They are most definitely human constructs. Mathematics isn't written into the fabric of the universe, we've invented an abstract means of quantifying that which we measure. We constructed maths around the universe, to fit with what we see. For example, there are two theories of gravity. They both predict the same thing and they both do it very, very well. Obviously, the universe doesn't work in two separate ways, we've just described it in two different way. How many ways could you use words to describe something and keep it accurate?

Joe1919

There is an argument that for examples triangles and circles are only ideals. So for example, the law that says that the sum of the three angles of a triangle is two right angles or pie =3.14 in the case of circles are only valid in theory as these laws only apply to ideal or perfect triangles or circles.
But perfect triangles and circles do not exist in nature and hence these laws are not part of nature but are constructed in our minds from a mixture of observations of things we see in the world that correspond approximately to triangles and circles and ideals which are imagined in our minds.
Other laws (e.g. gravity ) are mainly observations about nature and they describe but do not explain nature. These laws are valid as long as the continue to accurately describe the phenomena but are subject to revision when they no longer fulfill there usefulness.
These laws therefore are man made and are subject to error and revision.
Nothing is certain from this scientific viewpoint. On the other hand, one can feel certain and indeed have faith in anything and this has nothing to do with the truth or falisity of anything. Certainity and faith is a psychological state. http://en.wikipedia.org/wiki/Certainty
This last point ( that certainty can only be subjective) is very important to the understanding of the difference between scientific proof and religious faith and is probably best explained by Kierkegaard.
http://www.angelfire.com/md2/timewarp/kierkegaard.html

raah!

ChocolateSauce wrote: »

They are most definitely human constructs. Mathematics isn't written into the fabric of the universe, we've invented an abstract means of quantifying that which we measure. We constructed maths around the universe, to fit with what we see. For example, there are two theories of gravity. They both predict the same thing and they both do it very, very well. Obviously, the universe doesn't work in two separate ways, we've just described it in two different way. How many ways could you use words to describe something and keep it accurate?

I think you could apply this "most definatly" to physical laws perhaps, they are (mostly) empircally derived certainly. But it is a bit silly to say this about mathematical and logical ones. It seems the general consensus of philosophers on these has been that they are innate, fixed characteristics of the universe. But I haven't read sooo much of empircal philosophy (and they probably say that alot )

Húrin

ChocolateSauce wrote: »

They are most definitely human constructs. Mathematics isn't written into the fabric of the universe, we've invented an abstract means of quantifying that which we measure. We constructed maths around the universe, to fit with what we see. For example, there are two theories of gravity. They both predict the same thing and they both do it very, very well. Obviously, the universe doesn't work in two separate ways, we've just described it in two different way. How many ways could you use words to describe something and keep it accurate?

I'm sure we can all agree that masses attracted each other due to gravity before humans existed. Thus, physical laws exist independently of our descriptions.

Do not these laws display logic? They are after all seemingly uniform rather than contradictory. (One of the experts in quantum mechanics might have something to say here.)

Do mathematical laws also point to such an objective logic? Could we have made the multiplication tables, for instance, differently if we had wished?

silverharp

Húrin wrote: »

Do not these laws display logic? They are after all seemingly uniform rather than contradictory. (One of the experts in quantum mechanics might have something to say here.)

you could say that the laws display a certain consistancy, and a certain amount is necessary I guess for the universe to "keep its shape". The logic follows the rules. If gravity or the concept of entropy were not subject to specific rules , then certain logical concepts would be different as long as the universe didnt blow itself up.
Humanity's journey is to understand how the universe really works and the logic will develop along the way. what is logical to Einstein would not have ben logical to Newton, and no doubt over time things will be found that would not be logical to Einstein beacuse he couldnt see the full picture

nyarlothothep

I guess that when the universe wants to do something its obviously not going to achieve it in the way we describe it, its not going to use the square root of 2 to create some effect, it just happens. Maths is our way of interpreting that data. So, on the one hand maybe "that" which we describe through maths is embedded as a law in our existence and that there are axioms which precede the universe and inform how it operates.

Joycey

Húrin wrote: »

I'm sure we can all agree that masses attracted each other due to gravity before humans existed. Thus, physical laws exist independently of our descriptions.

But you cant know that they did beyond any doubt, or rather you can but to make any predictions of future happenings based on this would call for an additional presupposition which you are not justified in holding, namely: that the future will be like the past. What your calling a physical law is simply an assumption induced from previously observed data.

Do not these laws display logic?

How can anything other then a human display logic? Logic seems to me to be a faculty, or a capacity, not some property which one can attribute to something. When we say "that seems logical", what we are really saying is that "through the excercise of my faculty of 'logical reasoning' (whatever that is) this makes sense to me".

Do mathematical laws also point to such an objective logic? Could we have made the multiplication tables, for instance, differently if we had wished?

There is no such thing, as far as I can make sense of the term, as "objective logic". Any statement or arguement or anything which purports to be "objectively logical", rests on some formal system of representation to be transmitted or stated or whatever. Any such system in turn rests on some agent interpreting the symbols which represent in a certain way. Because there is no such thing as an eternally unchanging or "objective" agent - we are all constantly in a state of transience - it doesn't make any sense to act like the interpretations which rest of these transient beings are eternal. So although the meaning of the statement 7x5=35 might not change before humans have destroyed themselves and everything else on the planet, that doesnt mean that there is anything objectively coherent about it.

ChocolateSauce

raah! wrote: »

I think you could apply this "most definatly" to physical laws perhaps, they are (mostly) empircally derived certainly. But it is a bit silly to say this about mathematical and logical ones. It seems the general consensus of philosophers on these has been that they are innate, fixed characteristics of the universe. But I haven't read sooo much of empircal philosophy (and they probably say that alot )

It seems to me empirical philosophy is an oxymoron. It is not at all silly to say what I said, and this isn't so much my opinion as it is a matter of fact. The universe works in one particular way, and maths describes this way.

Could we have made the multiplication tables, for instance, differently if we had wished?

Yes, all we need to do is invent a new way of representing the concept. And that is just using a base ten of numbers; multiplication tables would work differently in binary or trinary, for example. Yet if you add two apples together, you always have two apples. So while the universal constants remain just that, our modes of describing them need not be so eternal.

As for logic, I would say it's a thought process, and that by definition things which do not think are not logical, they're merely constant. I'm open on this one though...

dreamlogic

Húrin wrote: »

If no humans existed, would the laws of logic and mathematics still exist?

Yes if our universe still existed

And the question I am really interested in: is the answer to these questions given by some decisive evidence, or is one's position on these matters essentially faith-based?

What do you mean by 'faith-based' - Trust in logic? Religious faith?

raah!

ChocolateSauce wrote: »

It seems to me empirical philosophy is an oxymoron. It is not at all silly to say what I said, and this isn't so much my opinion as it is a matter of fact. The universe works in one particular way, and maths describes this way.

When I used the word "empirical" I meant "related to empiricism". Perhaps I should have said "empiricist philosophy".

Why I said what you said is silly, as this is the topic of debate, and has been a major problem of philosophy for hundreds of years, and yet you brush it aside with one statement, and a degree of certitude which, without much of a backing argument, I found silly.

And if the universe works in one way, and maths describes this way, then maths only describes one thing, thus giving us objective, and fixed mathematical laws describing the universe.

ChocolateSauce

raah! wrote: »

When I used the word "empirical" I meant "related to empiricism". Perhaps I should have said "empiricist philosophy".

Why I said what you said is silly, as this is the topic of debate, and has been a major problem of philosophy for hundreds of years, and yet you brush it aside with one statement, and a degree of certitude which, without much of a backing argument, I found silly.

And if the universe works in one way, and maths describes this way, then maths only describes one thing, thus giving us objective, and fixed mathematical laws describing the universe.

I brush it aside because the mathematicians who invent the maths to describe it don't claim to have discovered anything, only to have formulated a means of describing something. They aren't fixed mathematical laws in the manner in which you mean: Newton described gravity and motion in a way which is still used today, and was believed to be the end all for over 200 years, until Einstein came along and described gravity better. However, Einstein's (and Newton's) mathematics stop making sense when dealing with the very very small. If they don't apply in all cases, how can they be said to be "universal laws"?

raah!

Many of them do. These objective laws were a big part of the philosophies of many rationalist thinkers, and many mathematicians were also famous rationalist philosophers(descartes is the most obvious example).

And regarding gravity, as you've said, they are two different descriptions of the one physical process. The mathematical formulation of these laws stops making physical sense, but not mathematical sense. What hurin has been saying is that these are flawed attempts of describing some law which is fixed, and gravity is gravity, and is fixed. If we eventually have a law which describes it exactly as it is, and fits in all cases (there's alot of talk in most popular science books about this) then that would be a physical example of the type of law that hurin is talking about.

But I never really apply this "objectivity" to physical laws. I see the question as being one more of mathematics and logic.

ChocolateSauce

Maths is essentially a language, and like the spoken word wouldn't exist without thinkers. The universe doesn't literally have an equation at its deepest levels. Who knows what it has; strings, zero dimensional spaces, etc...but not numbers. I really don't see what's so hard to grasp about this, tbh...

nobodythere

Húrin wrote: »

If I did not exist, the laws of logic and mathematics would still exist.

Egocentric much?

Húrin wrote: »

If no humans existed, would the laws of logic and mathematics still exist?

Yes. They are concepts that intend to model the real world

And the question I am really interested in: is the answer to these questions given by some decisive evidence, or is one's position on these matters essentially faith-based?

It is based on observation though not always accurate. The world isn't as deterministic as it seems or as Newtonian science would believe, look up the Double Slit Experiment on youtube. Since most scientists and casual observers are using this outdated science (though highly practical!) then it is faith based.


NEXT!

raah!

ChocolateSauce wrote: »

Maths is essentially a language, and like the spoken word wouldn't exist without thinkers. The universe doesn't literally have an equation at its deepest levels. Who knows what it has; strings, zero dimensional spaces, etc...but not numbers. I really don't see what's so hard to grasp about this, tbh...

What is hard to grasp is the certitude you display, here in the philosophy forum, without any kind of philosophical argument. You are simply repeating that there are no objective laws, and restating your original points in different ways in response to counter arguments you were given.

As I have said, regarding those physical laws too, maths is a language, describing a certain set of things, logical laws. Regardless of the form of the maths they would still describe the same laws, this is what the question is about, whether or not these laws exist. Saying "this can be described in different ways" does not disprove much.

Joycey

grasshopa wrote: »

Yes. They are concepts that intend to model the real world

Exactly, they are not reality. They are mind-dependent reductions of our perception of the natural world into abstract terms. In no way shape or form are the "laws" which we formulate, in the way we formulate them universal and necessary to the operation of the universe.

Suppose we leave aside the question which has to do with whether these phenomena (the "laws" which we are talking about) actually are universal and necessary across the universe (and which as a result would merit being called laws of nature).

What I would argue (and il welcome any response to this argument), is that it is not possible to represent (through language, maths or any other formal system of representation) some pattern of observable phenomena which would allow us to abstract from this pattern into "laws", and then call them "objective".

-It is necessary for something to be called a law that it be reduced into abstract terms and represented through some agreed set of symbols to some other human
-If this step has been taken, then the agreed set of symbols is necessarily dependent on the human minds which composed them for interpretation (7 means nothing without a mind which can interpret it and figure out what that symbol can be applied to in the real world)
-As a result, this reduction which followed from our need to categorise something as a law can not be called "objective", because even were you to assume that what is being represented is in fact something which universally and necessarily occurs, your representation of it is not universal or necessary.

-If the first stage of this process is not undertaken (i.e. you dont reduce it in order to represent it to another human), then you cant claim that you have discovered a universal and necessary law. How would anybody be able to verify your claim? Natural laws come out of empirical observation (science), one of the defining (if not the defining) characteristics of science is that it be verifiable and repeatable. Pointing to the stars and trying to transmit your discovery about the nature of gravity, say, without representing into some kind of language what your trying to say, does not qualify as verification, so there are no grounds to claim you have scientifically discovered a claim.

In short, whether or not there are these necessary laws out there, we can never know them to be necessary and universal. Much the same as we can never know whether god exists or not. They are not scientifically verifiable, neither is god, so lets stop talking about "objective laws".

dreamlogic

Joycey wrote: »

What I would argue (and il welcome any response to this argument), is that it is not possible to represent (through language, maths or any other formal system of representation) some pattern of observable phenomena which would allow us to abstract from this pattern into "laws", and then call them "objective".
...
7 means nothing without a mind which can interpret it and figure out what that symbol can be applied to in the real world

But the underlying meaning of '7', 'VII', 'seven'... is pre-existing.
Seems to me the argument is akin to the difference between discovery and invention. Someone discovered Antartica and then it was given a name and a representation on a map. But surely the place itself was pre-existing?

ChocolateSauce

raah! wrote: »

What is hard to grasp is the certitude you display, here in the philosophy forum, without any kind of philosophical argument. You are simply repeating that there are no objective laws, and restating your original points in different ways in response to counter arguments you were given.

As I have said, regarding those physical laws too, maths is a language, describing a certain set of things, logical laws. Regardless of the form of the maths they would still describe the same laws, this is what the question is about, whether or not these laws exist. Saying "this can be described in different ways" does not disprove much.

I haven't used philosophical arguments because it is a scientific question, maths being a science. As for the fine tuning of the universe, god (usually) does not play dice, so the underlying concept is the same...but the whole thread was about maths and logic, which exist only because we think.

Joycey

dreamlogic wrote: »

But the underlying meaning of '7', 'VII', 'seven'... is pre-existing.
Seems to me the argument is akin to the difference between discovery and invention. Someone discovered Antartica and then it was given a name and a representation on a map. But surely the place itself was pre-existing?

It may or may not have been (it was ). The point however is that we cant know whether it did exist or not until we discover it. Likewise, we cant know that these laws exist until we make them representable and hence mind-dependent.

So any attempt to spell out what it is that we are saying is universal and necessary is doomed to end in our statement not being necessary or universal due to the fact that it has been stated.

In order for us to come to know that what we are calling a law is indeed a law, we need to have specified the claim we have made and hence to have represented it. The only way we can actually avoid this interpretive problem is by not reducing or abstracting from the natural world. In which event we are back to gesturing expansively at the sky.

(I think)


So if the above is valid, then whether or not there are indeed such mind-independent "objective" laws which are what we are representing in our attempts to explain the world is entirely unknowable. Hence they are outside the realm of scientific enquiry and making claims about them are on the same level as making claims about God.

dreamlogic

Joycey wrote: »

we cant know whether it did exist or not until we discover it. Likewise, we cant know that these laws exist until we make them representable and hence mind-dependent.

I think it is irrelevant whether we know or not!

In order for us to come to know that what we are calling a law is indeed a law, we need to have specified the claim we have made and hence to have represented it.

Maths deals in the abstract. x + y, a + b etc. Variables.

they are outside the realm of scientific enquiry and making claims about them are on the same level as making claims about God.

But I don't think claiming that 2 + 2 = 4 is on the same level as claiming something like 'God has a long white beard' or 'God exists'.

Joycey

dreamlogic wrote: »

I think it is irrelevant whether we know or not!

But then we are in agreement. Similar to claims about God, if they do or do not exist, it makes no difference, we cannot know them. The reason its irrelevant whether we know them or not is because it is irrelevant if they exist or not, we cannot know them.

(am i just talking sh1te here or is it making sense? im working it out as i go along myself)

Maths deals in the abstract. x + y, a + b etc. Variables.

I think this takes us back to something you said earlier.

But the underlying meaning of '7', 'VII', 'seven'... is pre-existing.

First, the meaning of 7 couldnt have existed before humans. Would I be right in saying what you meant was that which "7" refers to? But I dont think this is any more mind independent then the particular conception of that which is being referred to which is evoked when we say "7". Where in the real world (whatever that is. maybe what can be perceived directly? I dont know) can we find that which "7" refers. "7" is only a means of specifying some relation of objects in the world which in and of themselves are not necessarily "7like" .

Likewise, with any other form of maths, due to its inherently abstract nature, it doesnt say anything about the world unless we interpret the variables in a certain way, thus rendering its claims once again, neither necessary or universal.

But I don't think claiming that 2 + 2 = 4 is on the same level as claiming something like 'God has a long white beard' or 'God exists'.

Clearly they signify different things, given the standard interpretation of the symbols necessary for their transmission. In fact, you could argue that it is part of the definition of 2 and 4, that 2 is half of 4 and so on. But are you saying that there is anything objective about that claim? In what sense is it, once again, necessary or universal, in the way you have represented it?

What im trying to get at is: that it is impossible to abstract from the world and make claims about it, be they scientific (empirical) or mathematical (purely abstract) without recourse to some form of representation using symbols which are dependent on conventions of meaning and minds like ours to interpret those meanings.

So even were we to assume that that to which we refer when we make claims about universal laws or even pure abstractions like 2+2=4 corellates perfectly with our claims, it is fundamentally indeterminable that this is the case.

Hence such objective laws of physics, mathematics, logic or anything else are unknowable, and it is this property that they share with any possible deities which may be floating around outside our universe or wherever it is they are supposed to reside.

dreamlogic

dreamlogic wrote: »

I think it is irrelevant whether we know or not!

Joycey wrote: »

But then we are in agreement.

Actually I notice now that how I worded that was a bit careless and could convey something different than what I meant to say! That's what I get for writing in a hurry!
Anyway what I meant was Whether we know or not is irrelevant. Or another way of saying it: Whether it is knowable or not is irrelevant.
So yeah that's basically my position on the whole thing. I don't know whether that changes what you got from what I said or not - sorry if I caused confusion!

im working it out as i go along myself

No that's cool It's a good way of testing our thoughts I find - seeing what others think about the same thing.

dreamlogic

First, the meaning of 7 couldnt have existed before humans.

Of course it could. And it did! And will exist long after we are gone...

Would I be right in saying what you meant was that which "7" refers to?

Yes.

But I dont think this is any more mind independent then the particular conception of that which is being referred to which is evoked when we say "7".

Okay I see what you're saying. But I think you're losing sight of the fact that we're talking about laws here. It's not the same as visualizing or conceiving of a table or a chair (for example). Some philosophers would argue that they too are universal forms. But I don't know if I would go that far! (Anyway that's for another separate topic..)

Where in the real world (whatever that is. maybe what can be perceived directly? I dont know) can we find that which "7" refers.

Everywhere!

"7" is only a means of specifying some relation of objects in the world which in and of themselves are not necessarily "7like"

7like LOL I love that! Well, I would put it to you that 7like might not be the same as 7 Because we are talking about laws of mathematics here. So there is either 7 of something or there isn't! If 7like has any meaning well then it could be anything ranging from 6.6 to 7.4 or whatever way you want to define it. Others might classify '7like' quantities as ranging from 7.1 to 7.9. Both definitions can be equally valid in their own way depending on the criteria you want to use. But the exact amount 7 is in its own category! It could happen that 7 also falls into the category of 7like(according to how you define that set)! But the exact amount 7 is in itself immutable and constant and universal!

Likewise, with any other form of maths, due to its inherently abstract nature, it doesnt say anything about the world unless we interpret the variables in a certain way, thus rendering its claims once again, neither necessary or universal.

Yeah we do interpret the laws. In other words the language of mathematics is the means through which we get a mental grasp/understanding of these laws. But our interpretation is not necessary for the laws to exist. The laws exist first. We interpret(discover) after the fact.

In fact, you could argue that it is part of the definition of 2 and 4, that 2 is half of 4 and so on. But are you saying that there is anything objective about that claim? In what sense is it, once again, necessary or universal, in the way you have represented it?

It is necessary/universal because 2 + 2 has always been = 4, and so long as our universe exists this will remain the case. Whether we are talking about before dinosaurs roamed earth, or after human life has self-destructed or the planet has been blown to smithereens!

What im trying to get at is: that it is impossible to abstract from the world and make claims about it, be they scientific (empirical) or mathematical (purely abstract) without recourse to some form of representation using symbols which are dependent on conventions of meaning and minds like ours to interpret those meanings.

I get what you're saying. I am saying that the laws exist in the universe. We come along and we discover them via mathematics etc. I suppose we're just not gonna agree on this...

Hence such objective laws of physics, mathematics, logic or anything else are unknowable, and it is this property that they share with any possible deities which may be floating around outside our universe or wherever it is they are supposed to reside.

Yes they(God and laws) may happen to have in common the property of not needing to be known in order to exist. And you can use this unknowability as a basis for not disbelieving in God... But otherwise God is a separate discussion here..