Argument from Math

[Bevels]

Hi, I am relatively new to CAF but I had an idea the other day that I wanted to share. I was wondering if anyone had proposed this argument before. I call it Argument from Math. Please pick it apart as you like and add your thoughts as to how it can be improved.

Math is a form of logic. Math is also perfectly logical. The principles of math are true in and of themselves and are not dependent on any outside source for their truth. Math exists eternally and outside the universe. That is, if the universe did not exist, the logical principles behind math would still be true i.e. 2+2 would always equal 4. There would simply be no humans to contemplate these principles and no universe for these principles to apply to. Another way to say this is to say that the logical relations behind mathematics do not necessarily apply to physical reality but can be comprehended on a purely conceptual basis. Therefore, math (a form of logic) exists eternally and outside of the universe.

Science is based on mathematics. Every single part of our universe operates through mathematical principles. All evidence suggests that the universe follows mathematical laws and is in this way ordered. This is unlikely to change since science models the universe using mathematics. Even complete randomness follows order. If it did not, the study of probability and statistics would be impossible.

Since all evidence suggests that the entirety of the universe follows logical order, the universe is altogether logical. Further, it has been proven that there must necessarily be a First Cause operating outside the universe which caused the universe and itself remains uncaused. Since Logic exists eternally outside of the universe and is itself uncaused, logic must exist with the First Cause and must be a property of the First Cause.

Therefore, the First Cause (which we call God) must be logical. Further, since logic is present in the entirety of the universe and God is logic, God must be present everywhere in the universe (omnipresence). Also, since God caused the universe and everything in it and ordered the universe, this First Cause must be all powerful (omnipotent). If this First Cause is a personal being, it follows logically that He would be all knowing (omniscient) as well.

 

[coolduude]

I like it up until you claim that a First Cause has been proven to be the cause of the universe. One would think this is true, but no athiest is going to buy it.

Otherwise, I like the proof a lot

 

[Bevels]

This is meant to be viewed along with the cosmological argument in order to further what can be said of the nature of God. I claim that a First Cause has be proven because it has. If an atheist were to deny the validity of that argument then you are right they would certainly deny the validity of mine or anyone elses. Here is what the Catechism says about the First Cause. 32 refers to Aquinas’ proofs.

31 Created in God’s image and called to know and love him, the person who seeks God discovers certain ways of coming to know him. These are also called proofs for the existence of God, not in the sense of proofs in the natural sciences, but rather in the sense of “converging and convincing arguments”, which allow us to attain certainty about the truth. These “ways” of approaching God from creation have a twofold point of departure: the physical world, and the human person.

32 The world: starting from movement, becoming, contingency, and the world’s order and beauty, one can come to a knowledge of God as the origin and the end of the universe.

 

[JM3]

Hi, I am relatively new to CAF but I had an idea the other day that I wanted to share. I was wondering if anyone had proposed this argument before. I call it Argument from Math. Please pick it apart as you like and add your thoughts as to how it can be improved.

Math is a form of logic. Math is also perfectly logical. The principles of math are true in and of themselves and are not dependent on any outside source for their truth. Math exists eternally and outside the universe. That is, if the universe did not exist, the logical principles behind math would still be true i.e. 2+2 would always equal 4. There would simply be no humans to contemplate these principles and no universe for these principles to apply to. Another way to say this is to say that the logical relations behind mathematics do not necessarily apply to physical reality but can be comprehended on a purely conceptual basis. Therefore, math (a form of logic) exists eternally and outside of the universe.

Science is based on mathematics. Every single part of our universe operates through mathematical principles. All evidence suggests that the universe follows mathematical laws and is in this way ordered. This is unlikely to change since science models the universe using mathematics. Even complete randomness follows order. If it did not, the study of probability and statistics would be impossible.

Since all evidence suggests that the entirety of the universe follows logical order, the universe is altogether logical. Further, it has been proven that there must necessarily be a First Cause operating outside the universe which caused the universe and itself remains uncaused. Since Logic exists eternally outside of the universe and is itself uncaused, logic must exist with the First Cause and must be a property of the First Cause.

Therefore, the First Cause (which we call God) must be logical. Further, since logic is present in the entirety of the universe and God is logic, God must be present everywhere in the universe (omnipresence). Also, since God caused the universe and everything in it and ordered the universe, this First Cause must be all powerful (omnipotent). If this First Cause is a personal being, it follows logically that He would be all knowing (omniscient) as well.

‘The principles of math are true in and of themselves and are not dependent on any outside source for their truth.’

Math is a form of reason used by humans to understand the universe around them. It is only ‘logical’ as far as humans can understand logic.

‘Math exists eternally and outside the universe.’

You have no evidence of this. Does making a statement without proof make it true, just because you think it is?

‘if the universe did not exist, the logical principles behind math would still be true i.e. 2+2 would always equal 4. There would simply be no humans to contemplate these principles and no universe for these principles to apply to.’

With ‘no humans to contemplate’ math, it would have no reason to exist and, therefore, would not.

‘Logic exists eternally outside of the universe and is itself uncaused’

What is your evidence that ‘logic’ is eternal?

‘logic must exist with the First Cause’

Why?

Question: Does an attribute of an eternal being have the right to say it is ‘uncaused’?

 

[JM3]

Consider:

1 2 3 4 5 6

1+2=3
2+3=4
3+4=5
4+5=6

This follows a ‘logical’ progression. Why is it not true? Because a human uses the symbols in a different manner and would not understand their use in this equation. This makes the equation illogical and untrue.

 

[Catholicdeacon]

Hi, I am relatively new to CAF but I had an idea the other day that I wanted to share. I was wondering if anyone had proposed this argument before. I call it Argument from Math. Please pick it apart as you like and add your thoughts as to how it can be improved.

Math is a form of logic. Math is also perfectly logical. The principles of math are true in and of themselves and are not dependent on any outside source for their truth. Math exists eternally and outside the universe.

I think this is the big flaw in your argument. This statement can not be proven (but there are indication that perhaps it is not true.). It is easy to imagine universes in which “Our” math do not work. Think of non-euclidean geometries for example, we will never encounter these types of geometries however we can conceptualize them. So it seems that math only applies to a type of universe (ie. universes in which euclidean geometry is possible).

In order to prove this statement we would have to observe these other universes and see if in fact only euclidean geometries apply.

PS. In case you are wandering Euclidean geometries are geometries in which the angles of a triangle add to 180 degrees. Non-euclidean are geometries in which these angles add to more or less than 180 degrees.

Viva Cristo Rey!!

Catholic Deacon

 

[Los_Angeles]

Consider:

1 2 3 4 5 6

1+2=3
2+3=4
3+4=5
4+5=6

This follows a ‘logical’ progression. Why is it not true? Because a human uses the symbols in a different manner and would not understand their use in this equation. This makes the equation illogical and untrue.

I have never seen this logic before. Can you please explain how adding numbers that result in the wrong sum follows a logical pattern?

If anything I have said is against the Catholic Church, let it be anathema.

 

[Los_Angeles]

Hi, I am relatively new to CAF but I had an idea the other day that I wanted to share. I was wondering if anyone had proposed this argument before. I call it Argument from Math. Please pick it apart as you like and add your thoughts as to how it can be improved.

I applaud your innovative thinking, however I do not think we can arrive at the properties of a omnipotent, omniscent God purely from logic alone.

I think revelation from God is necessary, specifically through the Bible. The reason being is that the Christian has the advantage of “hindsight” to building the logical steps necessary to arriving at his concept of God from having read the Bible. A non-believer that does not accept the Bible as the Word of God, would have the advantage of perpetually questioning the assumptions made by a Christian trying to create a “proof” for the properties of God.

There is actually a discussion about this going on right now in the philosophy section forums.catholic-questions.org/showthread.php?t=526042&page=1

If anything I have said is against the Catholic Church, let it be anathema.

 

[JM3]

I have never seen this logic before. Can you please explain how adding numbers that result in the wrong sum follows a logical pattern?

You are assuming that 1 2 3 4 5 6 are numbers, because you understand it to be this way. Are they numbers or something else? Does ‘+’ mean addition or ‘=’ mean equals? Is the last symbol a ‘sum’ of the previous symbols? Could ‘+’ mean ‘,’ or ‘=’ mean ‘not equal to’?

Math is only logical to us, because we apply a non-changeable idea to a symbol. It is not logical when we do not understand how the symbols are being used.

 

[Bevels]

You have no evidence of this. Does making a statement without proof make it true, just because you think it is?

The fact that I can conceptualize math without applying it to something in the universe is evidence enough. I say it without proof because I believe it to be self evident. You could try to say 2+2=5 but you would be wrong. I don’t have to limit this argument with math. Any logically true principle would apply in the same way. I am talking about underlying mathematical principles, not human characterizations of them.

With ‘no humans to contemplate’ math, it would have no reason to exist and, therefore, would not.

There is an underlying logical reality behind math. Just because humans use specific symbols to describe these realities does not mean that the principles would not exist. For example, if there were no humans, the principles of derivatives describing the rate of change of distance to velocity would still exist and exist universally as our experience has shown them to. When I say math I am talking about the underlying reality and not our human descriptions of it.

What is your evidence that ‘logic’ is eternal?

All evidence of human experience suggests that the universe is arranged by math. The universe also changes according to mathematical laws. Math itself is not contingent while the universe is and has been shown to be by Aquinas. Something contingent cannot be its own cause for it is illogical for something to cause itself. Unlike the universe, math does not change but only changes the universe around it. If mathematical principles were to change, we could not determine anything about the universe.

Why? [must logic exist with the First Cause]

Because math is unchanging just like the First Cause is unchanging. Since the First Cause caused the universe and the universe operates through unchanging mathematical laws, these laws must be present in that which caused them. Otherwise where could they have come from? Further, if they are present with the First Cause, they are necessarily eternal.

Question: Does an attribute of an eternal being have the right to say it is ‘uncaused’?

I don’t understand what you mean here. Maybe you could rephrase it?

Consider:

1 2 3 4 5 6

1+2=3
2+3=4
3+4=5
4+5=6

This follows a ‘logical’ progression. Why is it not true? Because a human uses the symbols in a different manner and would not understand their use in this equation. This makes the equation illogical and untrue.

You example is flawed because regardless of how we characterize mathematical truths, they are still fundamentally true. I am talking about underlying mathematical principles – not semantics.

 

[Bevels]

I think this is the big flaw in your argument. This statement can not be proven (but there are indication that perhaps it is not true.). It is easy to imagine universes in which “Our” math do not work. Think of non-euclidean geometries for example, we will never encounter these types of geometries however we can conceptualize them. So it seems that math only applies to a type of universe (ie. universes in which euclidean geometry is possible).

In order to prove this statement we would have to observe these other universes and see if in fact only euclidean geometries apply.

PS. In case you are wandering Euclidean geometries are geometries in which the angles of a triangle add to 180 degrees. Non-euclidean are geometries in which these angles add to more or less than 180 degrees.

Viva Cristo Rey!!

Catholic Deacon

The problem with taking this stance is that one could just as easily say that a universe exists where any number of logical principles do not exist. For example imagine a universe where absolute truth both exists and doesn’t exist (which is absurd). Taking this stance is subscribing to subjectivism and if one argues from this kind of stance, no rational arguments could be made at all because X universe could exist where nothing is logical.

 

[Los_Angeles]

You are assuming that 1 2 3 4 5 6 are numbers, because you understand it to be this way. Are they numbers or something else? Does ‘+’ mean addition or ‘=’ mean equals? Is the last symbol a ‘sum’ of the previous symbols? Could ‘+’ mean ‘,’ or ‘=’ mean ‘not equal to’?

Math is only logical to us, because we apply a non-changeable idea to a symbol. It is not logical when we do not understand how the symbols are being used.

I am still confused. I am trying to understand the point you were trying to make.

I understand mathematics to be logically true not becuase of the arbitrary symbols that we use to represent numbers or operations, but because of the underlying logic behind them.

It appears that you were changing the conventional use of symbols to be something else entirely without redefining what they mean.

If your point was to re-define symbols to prove a point, why did you specifically change the meaning of the mathematical symbols and not the meaning of the characters used in the english language in your post?

If anything I have said is against the Catholic Church, let it be anathema.

 

[michael_legna]

You have a small problem called Godel’s Incompleteness Theorem. It states that no consistent system of axioms whose theorems can be listed by an “effective procedure” is capable of proving all facts about the natural numbers. This means that any such system will contain statements about the natural numbers that are true, but that are unprovable within the system. It also shows that IF such a system is also capable of proving certain basic facts about the natural numbers, THEN the system cannot prove is the consistency of the system itself.

A layman’s summary (as it relates to math) would be that because mathematics is complex enough to cover all the universe it must not be able to prove its own consistency - something you argument relies on for its final conclusion.

ML

 

[promethius]

Math is a form of logic. Math is also perfectly logical. The principles of math are true in and of themselves and are not dependent on any outside source for their truth. Math exists eternally and outside the universe.

This statement is an error. Mathmatical constructs are dimension based. Outside of our universe our mathematical statements have no meaning. This is why, scientifically, we can’t know anything about what occurs beyond the edge of our finite universe: because the scientific law breaks down at that border. The incongruity means that scientific law is only constant accross the physical universe… and unfortunately for your argument, that includes math.

 

[Los_Angeles]

This statement is an error. Mathmatical constructs are dimension based. Outside of our universe our mathematical statements have no meaning. This is why, scientifically, we can’t know anything about what occurs beyond the edge of our finite universe: because the scientific law breaks down at that border. The incongruity means that scientific law is only constant accross the physical universe… and unfortunately for your argument, that includes math.

So if I understand you correctly, are you saying that you know of a circumstance in which the number 1 does not equal itself, or 2 + 2 does not equal 4?

If anything I have said is against the Catholic Church, let it be anathema.

 

[promethius]

So if I understand you correctly, are you saying that you know of a circumstance in which the number 1 does not equal itself, or 2 + 2 does not equal 4?

Inside the universe, a number always equals itself. Outside the universe, scientific law is not constant and therefore we don’t know. No empirical statement can be made about anything outside the universe.

As to 2 + 2 = 4, that statement only holds as an absolute in terms of single dimension math. For vector addition (which is what 2 + 2 = 4 is in a single dimension) in 3 dimensions, then 2 + 2 can equal any number between -4 and 4.

If anything I have said is against the Catholic Church, let it be anathema.

It’s not that it’s against the church, it’s just that the church does not teach that scientific law is constant even outside and independent of the finite universe. Furthermore, science recognizes that scientific law (including mathematical laws) are incongruous at the edge of the universe, and thus we cannot emperically make any statement about that which is not inside the universe.

As a result, to say that math is a logical lawset that is independent of the universe is not a scientifically valid emperical statement.

 

[Los_Angeles]

Inside the universe, a number always equals itself. Outside the universe, scientific law is not constant and therefore we don’t know. No empirical statement can be made about anything outside the universe.

I have never been outside the known universe so I wouldn’t know if it would or would not hold true that the number 1 equals itself outside the known universe.

I appears to be a kind of non-sequitur to assume that numbers potentially may not equal themselves outside of the known universe because as Catholics I thought we were supposed to believe that the universe was finite, so how would we be able to know that were were outside the universe if it were impossible to be outside the universe while still alive.

In theory, I guess if when we die and hopefully meet God, we would not be able to converse or reference the Bible with God by chapter and verse if numbers did not hold up outside the known universe.

As to 2 + 2 = 4, that statement only holds as an absolute in terms of single dimension math. For vector addition (which is what 2 + 2 = 4 is in a single dimension) in 3 dimensions, then 2 + 2 can equal any number between -4 and 4.

I will learn about vectors next semester in school so I’ll take your word for it for now.

It’s not that it’s against the church, it’s just that the church does not teach that scientific law is constant even outside and independent of the finite universe. Furthermore, science recognizes that scientific law (including mathematical laws) are incongruous at the edge of the universe, and thus we cannot emperically make any statement about that which is not inside the universe.

As a result, to say that math is a logical lawset that is independent of the universe is not a scientifically valid emperical statement.

I always try to include that statement at the end of my posts as a disclaimer.

If anything I have said is against the Catholic Church, let it be anathema.

 

[itinerant1]

I would like to say a few things about mathematics, the universe and God, though I may not have time to participate much in this thread, as much as I would like to.
First, let us consider or define the universe as the “totality of consistently interacting things.” The universe as such will embody a specific set of mathematics that in principle are discoverable by human reason. The Old Testament supports this position where it says, “You, however, ordered all things by measure, number and weight.” (Book of Wisdom 11:20)

In this sense, the universe is not mysterious because it has all the clarity that mathematics can provide. There is a limitation here, though, as far as how much clarity mathematics can provide about the universe. Mathematics or physics cannot demonstrate the ultimate reason for the universe being is the way it is rather than some other possible way.

The clarity of mathematics is limited by Godel’s incompleteness theorems, according to which no non-trivial set of arithmetic propositions can contain the proof of its own consistency. So, here we see there is a limitation on using math to conclusively prove the truth of any non-trivial arithmetical proposition.

Does this limitation pose a problem for proving the existence of God from strictly mathematical considerations? One can take the position that no natural science, including physics and mathematics, can demonstrate the existence of God. While mathematics seems to be in a class of its own, being more abstract in nature than the other natural sciences, my opinion is that the natural sciences, mathematics included, “by themselves” cannot be used to prove the existence of God. Such a proof reaches beyond the scope and competency of these disciplines.

Note that the foregoing consideration is other than that of using “philosophical” reflections on the nature of math to prove a philosophical conclusion. And such an argument would be similar to arguing from the existence of truth to the existence of Truth itself, or from the existence of human reason to that of a Supreme Reason.

Proving the existence of a Supreme Being requires a philosophical demonstration (such as Aquinas’ five ways). But there is something to mathematical considerations. What it is, as it seems to me, math reflects design and order in the universe. We express this design in mathematical equations. But more fundamentally, it is the design itself that testifies to a Designer or Rational Mind. I use the word “design” but not in the sense of “Intelligent Design” theory (Behe, Dembskski, et al.). I am not speaking in the context of ID theory.

Science can only exist because there is design in the universe. Or, we can say science presumes design, even though some scientists make the false philosophical assumption that everything is ultimate chance and randomness, which somehow results in the appearance of design. I am not concerned with that here.
Peter Kreeft presents an argument from design, which I will refer you to: peterkreeft.com/topics/design.htm

Also, if we develop an argument for the existence of God, such as the argument from design, an argument from beauty, or any of a hundred possibilities, we cannot then draw too much from the conclusion such as by saying further that God is omnipotent, omniscient, omnipresent, personal and so on. Each of these aspects of God should require their own philosophical demonstration.

 

[Los_Angeles]

Science can only exist because there is design in the universe. Or, we can say science presumes design, even though some scientists make the false philosophical assumption that everything is ultimate chance and randomness, which somehow results in the appearance of design. I am not concerned with that here.
Peter Kreeft presents an argument from design, which I will refer you to: peterkreeft.com/topics/design.htm

I agree with this paragraph. Glad you wrote it.

Also, if we develop an argument for the existence of God, such as the argument from design, an argument from beauty, or any of a hundred possibilities, we cannot then draw too much from the conclusion such as by saying further that God is omnipotent, omniscient, omnipresent, personal and so on. Each of these aspects of God should require their own philosophical demonstration.

Are you saying that there exists irrefutable undeniable self-supporting philosophical “proof” of God and/or his characterisics?

Why is a “proof” from philosophy even needed if God gave us the Catholic Church and the Holy Bible? Wouldn’t a philosophical “proof” be in direct competition with the Word of God?

If anything I have said is against the Catholic Church, let it be anathema.

 

[itinerant1]

I agree with this paragraph. Glad you wrote it.

Are you saying that there exists irrefutable undeniable self-supporting philosophical “proof” of God and/or his characterisics?

That’s what I said. The God’s existence can be demonstrated by philosophical argument.

Why is a “proof” from philosophy even needed if God gave us the Catholic Church and the Holy Bible? Wouldn’t a philosophical “proof” be in direct competition with the Word of God?

Have you ever wondered why St. Thomas, St. Anselm and countless other Catholic theologians and philosophers thought it necessary to present philosophical proofs for God’s existence?

Philosophical demonstrations for God’s existence are worth knowing for the sake of knowledge alone. Philosophy constitutes another way of knowing, knowing God by the use of our intellect through the things that he has created.

Philosophical demonstrations are also useful for evangelization and apologetics when dealing with non-believers. The educated Catholic is able to use reason to prove the existence of God when confronted by the skeptic. He is also capable of demonstrating to the skeptic that the Catholic faith is not contrary to reason.

When used in this manner, classical philosophy is an aid, it is used to support and defend the truth of the Catholic faith, according to the words of the Apostle, “bringing into captivity every thought to the obedience of Christ.”