The Neccesary Connection Between Mathematics, Logic & The Existence Of A Perfect Transcendent Being

[hansard]

It’s entirely possible that we will, in distant eons, contact beings from other star systems, who will quite possibly have minds and technologies far superior to ours.
When they express mathematical and scientific principles in a language and form that we cannot understand, where will that leave us, I wonder?
How would God express 2+2=4?
Mathematics exists as a construct of the human intellect, as a function of our propensity to seek order. It relies, as do all human endeavours, on language and understood symbols (e.g. alphabets, words, syntax, mathematical symbols, and so on).

Task: prove to me that 2+2=4, but you can’t use any form of language, nor any human-devised symbols.

 

[warpspeedpetey]

No, it’s called a paradox for a reason. You start out with 1 star, and end up with 2 stars, and each of the new stars is identical (mathematical term: isomorphic) to the original star, so it is a case of 1 = 2.

under the assumption that we are using actual stars and not just some system of points, as ive suggested thats not much of a paradox, the stars arent identical in anything but geometry, the density is cut in half for every iteration. frankly, i think that we are really discussing points and not actual stars, which makes it a conceptual and not applicable to the actual universe. so we can talk about it as a concept, but its not a physical possibility for 1=2

 

[warpspeedpetey]

But when the experiment is performed with both slits open, no photons show up at the detector. Classical reasoning doesn’t apply at all.

the justification here for your argument seems to be based on a common misunderstanding of QM.

en.wikipedia.org/wiki/Double_slit_experiment#Importance_to_philosophy

It is a widespread misunderstanding that, when two slits are open but a detector is added to the experiment to determine which slit a photon has passed through, then the interference pattern no longer forms and the experimental apparatus yields two simple patterns, one from each slit, superposed without interference. Such a result would be obtained only if the results of two experiments were superposed in which either one or the other slit is closed.

the double slit experiment only demonstrates the behavioral duality of quantum particles, not that classical reasoning doesnt apply to the universe, but rather that we dont have a complete understanding of QM. as evidenced bu the 11 or so interpretations. not much of a basis for a logical system.

 

[warpspeedpetey]

Task: prove to me that 2+2=4, but you can’t use any form of language, nor any human-devised symbols.

–	----
----	–

obviously my keyboard cannot produce anything but human derived symbols. but this is my attempt

thsi is how it has been done.

voyager.jpl.nasa.gov/spacecraft/goldenrec1.html

 

[warpspeedpetey]

… have i told youse guys lately how much i love you? http://www.pic4ever.com/images/banana_smiley_11.gif

:hug1:

 

[Just_Lurking]

under the assumption that we are using actual stars and not just some system of points, as ive suggested thats not much of a paradox, the stars arent identical in anything but geometry, the density is cut in half for every iteration. frankly, i think that we are really discussing points and not actual stars, which makes it a conceptual and not applicable to the actual universe. so we can talk about it as a concept, but its not a physical possibility for 1=2

Given that the mathematics of geometry is not applicable to the actual universe, why am I supposed to believe that it is somehow an eternal truth or a transcendent reality?

 

[Just_Lurking]

the justification here for your argument seems to be based on a common misunderstanding of QM.

en.wikipedia.org/wiki/Double_slit_experiment#Importance_to_philosophy

It is a widespread misunderstanding that, when two slits are open but a detector is added to the experiment to determine which slit a photon has passed through, then the interference pattern no longer forms and the experimental apparatus yields two simple patterns, one from each slit, superposed without interference. Such a result would be obtained only if the results of two experiments were superposed in which either one or the other slit is closed.

This paragraph is discussing the case when “a detector is added to the experiment”. I am discussing the experiment without any detectors.

the double slit experiment only demonstrates the behavioral duality of quantum particles, not that classical reasoning doesnt apply to the universe, but rather that we dont have a complete understanding of QM. as evidenced bu the 11 or so interpretations. not much of a basis for a logical system.

The double slit experiment demonstrates both the behavioral duality of quantum particles and that classical reasoning doesn’t apply. If a photon can be both a particle and a wave, then why can’t some shape be both a circle and a square?

The multiple interpretations of quantum mechanics illustrate that there are still problems with the theory. That’s why I was basing my conclusions on actual, uncontested, experimental results instead of theory alone. I am becoming increasingly convinced that this is the problem of metaphysics, insisting that making up unverifiable arguments is a more effective route to the truth than the scientific method.

Even if you add uncertainty to classical logic, so that each proposition is not just true or false but has a degree of “truthiness”, it is still the case that (A or B) is more truthy than either A or B alone. Yet in the double slit experiment, opening another slit B actually decreases the truthiness of (A or B), which makes quantum logic very different than classical logic, even when modified to include uncertainty.

 

[warpspeedpetey]

Given that the mathematics of geometry is not applicable to the actual universe, why am I supposed to believe that it is somehow an eternal truth or a transcendent reality?

its a problem with the language, you dont really wind up with 2 identical stars, you still have the same value as before. so while you can construct two identical stars geometrically, in physical terms you would have simply divided the original value. its a word game. so while true conceptually, its not physically possible. that however doesnt affect its basic truth.

 

[Just_Lurking]

its a problem with the language, you dont really wind up with 2 identical stars, you still have the same value as before.

Mathematically, you end up with double the value as before. Physically, you can’t perform the decomposition.

This mathematical result is an existence proof rather than a construction, so this has some mathematicians doubt the validity of non-constructive proof. The debate on constructivism illustrates even more how mathematics is a social construct.

 

[warpspeedpetey]

This paragraph is discussing the case when “a detector is added to the experiment”. I am discussing the experiment without any detectors.

um…?

en.wikipedia.org/wiki/Double_slit_experiment

However, it is found that **unblocking both slits **makes some points on the screen brighter, and other points darker.

The double slit experiment demonstrates both the behavioral duality of quantum particles and that classical reasoning doesn’t apply. If a photon can be both a particle and a wave, then why can’t some shape be both a circle and a square?

as above your still in the same position. the detector doesnt matter. both slits open still allows photons through. as to why light behaves that way we dont know. but that doesnt eliminate the truth of classical logics.

The multiple interpretations of quantum mechanics illustrate that there are still problems with the theory. That’s why I was basing my conclusions on actual, uncontested, experimental results instead of theory alone.

those conclusions would lack the information necessary to be valid, one can use those experiments, but not understanding reasons for that behavior means that its built on certain assumptions, new information, say the discovery of hidden variables, or a GUT may invalidate the entire system of logic based on those assumptions. considering the youth of the QM field in general that doesnt seem a stable base to make decisions on.

I am becoming increasingly convinced that this is the problem of metaphysics, insisting that making up unverifiable arguments is a more effective route to the truth than the scientific method.

im not aware of any arguments that are made up in the field, which ones are you refering to?

Even if you add uncertainty to classical logic, so that each proposition is not just true or false but has a degree of “truthiness”, it is still the case that (A or B) is more truthy than either A or B alone. Yet in the double slit experiment, opening another slit B actually decreases the truthiness of (A or B), which makes quantum logic very different than classical logic, even when modified to include uncertainty.

if you add a “truthiness” variable to mimic uncertainty that results in fuzzy logic. an already well known system. as quantum logic is based on experiments with unknown causes, therefore its version of truth is subject to new information from new experiments., i dont think then that one can make the claim that the universe is better represented by quantum logic than by classical logic.

 

[Just_Lurking]

im not aware of any arguments that are made up in the field, which ones are you refering to?

The one made by MindOverMatter in post #1 of this thread.

Evi dont think then that one can make the claim that the universe is better represented by quantum logic than by classical logic.

It’s clear to me that quantum mechanics experimentation shows that the universe is not represented by classical logic. I am not alone in this belief, otherwise, quantum logic would not have been invented.

I just think that if you want to prove that God exists, then books like Josh McDowell’s Evidence that Demands a Verdict are the way to go, instead of metaphysical argumentation.

 

[warpspeedpetey]

Mathematically, you end up with double the value as before. Physically, you can’t perform the decomposition.

This mathematical result is an existence proof rather than a construction, so this has some mathematicians doubt the validity of non-constructive proof. The debate on constructivism illustrates even more how mathematics is a social construct.

not to delve into consructivism too deeply, but it relies on a lack of information to deny the law of the excluded middle, essentially claiming there is a range for what can be considered true, i contend that any range of truth can be divided from the lowest value of “truthiness” into a bivalent structure, ergo, all values in a range from the lowest one up are true, all of them below that point are false. if that range can be divided thusly, subjective experience wouldnt seem to matter. im not sure at all that mathematics is a social construct. if aliens show up, they may use hexadecimal mathematics, but it will still fall in the logical structures that math derives from. maybe the is a way to talk about mathematics as a subjective experience, but then that seems to deny the truth of any mathematical propisition. could an alien add 2+2 and get 3,045? if they could im at a loss as to how they can build a technology capable of getting here.

 

[warpspeedpetey]

The one made by MindOverMatter in post #1 of this thread.

oh…thats experimental metaphysics so to speak. it isnt an official argument. your in the lab here.

It’s clear to me that quantum mechanics experimentation shows that the universe is not represented by classical logic. I am not alone in this belief, otherwise, quantum logic would not have been invented.

see, thats not clear to me because the issues of QM are extremely far from settled, they are based on a lot of assumptions that may be changed with just one experiment. so i dont know that one can claim it reperesents the universe any better than classical logic.

I just think that if you want to prove that God exists, then books like Josh McDowell’s Evidence that Demands a Verdict are the way to go, instead of metaphysical argumentation.

mcdowell does have a great book, that i havent gotten around to reading yet, the synopsis ive seen though are rehashments of arguments that we have been using for a while. i should really read uit through though.

metaphysics though, when properly understood, leaves you with no possibility but G-d, i can even give proof beyond anykind of reasonable doubt that it must be the Christain G-d from the mathematical odds of convergent prophecy. i wouldnt discount metaphysics, though i understand what your saying.

 

[Just_Lurking]

im not sure at all that mathematics is a social construct. if aliens show up, they may use hexadecimal mathematics, but it will still fall in the logical structures that math derives from. maybe the is a way to talk about mathematics as a subjective experience, but then that seems to deny the truth of any mathematical propisition.

Historically, mathematics has changed so much from century to century that I’m reluctant to say that the current state of mathematics is what aliens will be using. For example, we went from infinitesimals as “ghosts of departed quantities”, to banishing infinitesimals and replacing them with limits, to infinitesimals are non-standard numbers in ultrafilter-based models of the real numbers.

And not to say that the French are aliens, but when I had to translate French math papers to English for my degree, it wasn’t just translating the words, but remapping the actual concepts. For example, the French word “corps” literally means “division ring”, but you were supposed to translate it as “field” (= commutative division ring) if that concept was more appropriate or natural in English.

Finally, there have been studies of newly discovered cultures to see what things really are human universals (e.g., Whopper vs. Big Mac). I haven’t seen anything to indicate that these new cultures use any of our mathematical concepts beyond simple counting, e.g., quadratic formula, differential equations.

could an alien add 2+2 and get 3,045? if they could im at a loss as to how they can build a technology capable of getting here.

Maybe if we could figure out how to add 2+2 and get 3,045, that would be the breakthrough we need for faster than light travel.

 

[warpspeedpetey]

Finally, there have been studies of newly discovered cultures to see what things really are human universals (e.g., Whopper vs. Big Mac). I haven’t seen anything to indicate that these new cultures use any of our mathematical concepts beyond simple counting, e.g., quadratic formula, differential equations.

i think that the simplest things like counting, and basic geometries would be the universal language, so did sagan and the crew that sent the plaques. makes sense to me, it may just be the foundation, but its a place to start.

Maybe if we could figure out how to add 2+2 and get 3,045, that would be the breakthrough we need for faster than light travel.

im betting on teleportation, less energy.

 

[jfoges]

I think this is a pretty good argument. I think this is an example of how absolute being can be shown to exist through arguments, such as the ontological argument. This begs the question, however, as to what the nature of this absolute being is. Is it the Judeo-Christian God or something like the God of Spinoza?

1. I think that the reality of logic and mathematics is in fact an abstraction of an intrinsic order that we have found in the reality of being. This is my first premise.

2. Out of absolute nothing comes nothing, thus truth cannot be founded on nothing because there is no truth in absolute nothing.

3. The eternal truth and existence of logic and mathematics can only make sense in terms of an absolute perfect being that is transcendent of change and limitation. Anything which begins to exist cannot be the reason why 2 + 2 = 4 because it has limitations in its being and thus lacks an absolute order. If it where true that the truth of 2 + 2 began to exist, It would mean that truth is relative to change. Which means that it can be true at one time, but not true at another. But we know that it is always true that one cannot have a square circle and that 2 + 2 always = 4, and this true irrespective of time and change. As soon as one understands the proposition, one can see that these are self-evident and necessary truths. Thus they are not true because of anything that begins to exists or potentially exists.

Conclusion. Therefore, the reality of logic and mathematics is a necessary abstraction of an intrinsic order that is necessarily reflective of a being that is absolute, timeless and transcendent of all physical limitations.

 

[MindOverMatter]

What you are describing here (“it is one or the other, but we don’t know which”) is uncertainty, which is modeled in quantum mechanics as a statistical mixture. This is completely different than the state of Schrodinger’s cat, which is a known state which equals the quantum mechanical superposition of the two states alive and dead.

I am not going to challenge you interpretation, i am not an expert, but i will say that i don’t agree with the idea that objective empirical events should be the basis for interpreting what is logically true. I believe that if we experience an object as appearing to be actual in several places at once, then this has to be interpreted as merely an appearance, an illusion of perspective, and not as the actual truth of what is occurring, as this would be to infer the impossible, and the impossible cannot happen. For example, seeing things from different dimensions may make something appear like a paradox, when in actuality, once one has seen it as it truly is, there is no paradox, accept in ones interpretation. So to me, its a matter of knowledge and perspective. The mere possibility of this seems to me to undo any basis for accepting Quantum logic. But i don’t want to get into that right this moment.

What i really what to discuss is the consequence of accepting something like Quantum Logic, which seems to me to be the Hegelian dialectic, and what that would mean for other sciences and the whole concept of truth. Don’t you think that by saying that a triangle can be a square at the same time in the same way in the same space, one is giving up any authority concerning the interpretation of empirical events. For example, what stops one from saying that the universe actually began to exist yesterday and also began to exist 400 billion years ago at the same time. With out classical logic, theres no basis for determining whether this statement is not necessarily true. It seems to me that the universe becomes totally unintelligible.

Isn’t it not true that Quantum physicists use Mathematical “truth” in order to build models that reflect actual reality. Doesn’t one need classical logic in this respect? Hows is the use of mathematics not tautological given your interpretation of empirical events.

Most people consider quantum logic to be completely different from classical logic.

Well in order for Quantum Logic to be representative of objective truth, surely it would have to deal with eternal truths? Otherwise, what stops it from being just a tautology.

 

[Just_Lurking]

IDon’t you think that by saying that a triangle can be a square at the same time in the same way in the same space, one is giving up any authority concerning the interpretation of empirical events. For example, what stops one from saying that the universe actually began to exist yesterday and also began to exist 400 billion years ago at the same time. With out classical logic, theres no basis for determining whether this statement is not necessarily true. It seems to me that the universe becomes totally unintelligible.

You are still confusing a paradoxical quantum mechanical superposition state with the absence of information or the inability to make any meaningful statements. Just because there could exist an object that is both a triangle and a square doesn’t mean that every object could be both a triangle and a square, or that we can’t say anything about the shapes of objects. Constructing objects that are both triangles and squares is experimentally very difficult, but forms the basis for quantum computing.

Whether the universe is both 1 day old and 400 billion years old at the same time is not ruled out based on necessity (a priori?), but based on observed experimental evidence.

Isn’t it not true that Quantum physicists use Mathematical “truth” in order to build models that reflect actual reality. Doesn’t one need classical logic in this respect? Hows is the use of mathematics not tautological given your interpretation of empirical events.

I’m not a physicist, but it looks to me as though they just plug numbers into formulae to get predictions for experimental results, without worrying too much about mathematical rigor. In mathematics, we can prove that there is no function f(x) satisfying f(x) = 0 for x <> 0 and having integral 1. In physics, they call that Dirac’s delta function and ignore the fact that it isn’t really a function.

Well in order for Quantum Logic to be representative of objective truth, surely it would have to deal with eternal truths? Otherwise, what stops it from being just a tautology.

I don’t understand what you are saying here. Quantum logic can say with certainty that the spin of an electron lies in the set {+1/2, -1/2}.

 

[Just_Lurking]

I think this is a pretty good argument. I think this is an example of how absolute being can be shown to exist through arguments, such as the ontological argument. This begs the question, however, as to what the nature of this absolute being is. Is it the Judeo-Christian God or something like the God of Spinoza?

I’m still not convinced that metaphysics has any ability whatsoever to tell us about God, even though I admit the relevance of metaphysics as the basis for evaluating and/or accepting the scientific method.

In that vein, here is my metaphysical argument that God isn’t perfect:

1. Real numbers exists; that’s why mathematicians call them “real”.
2. Real numbers must therefore have been created, with God as the creator.
3. Imaginary numbers don’t exist; that’s why mathematicians call them “imaginary”.
4. In 1843, Kummer invented ideal numbers, which don’t exist but should, because they are better than the numbers that God invented.
5. Therefore God isn’t perfect.

In a related note, I was listening to a science fiction story where robots were using metaphysics to argue that they were not created by man, because it would be impossible for inferior beings (i.e., mankind) to create such superior beings (i.e., robots).

 

[MindOverMatter]

I’m still not convinced that metaphysics has any ability whatsoever to tell us about God, even though I admit the relevance of metaphysics as the basis for evaluating and/or accepting the scientific method.

In that vein, here is my metaphysical argument that God isn’t perfect:

1. Real numbers exists; that’s why mathematicians call them “real”.
2. Real numbers must therefore have been created, with God as the creator.
3. Imaginary numbers don’t exist; that’s why mathematicians call them “imaginary”.
4. In 1843, Kummer invented ideal numbers, which don’t exist but should, because they are better than the numbers that God invented.
5. Therefore God isn’t perfect.

In a related note, I was listening to a science fiction story where robots were using metaphysics to argue that they were not created by man, because it would be impossible for inferior beings (i.e., mankind) to create such superior beings (i.e., robots).

So you are saying that numbers determine the truth of reality?