# Nature of Logic and Mathematics, and its relationship with God and materialism

I believe that logic is infallible, mathematics is true and that an entirely mathematical description of the entire universe is possible.

Are these inconsistent with materialism and atheism? Can somebody help me reconcile these? My problems are as follows:

1. Does infallible logic even as a concept, imply the existence of God?

2. Is the truth and reality of mathematics inconsistent with materialism?

3. If an entirely mathematical description of the entire universe is possible, does that mean God exists?

EDIT:

Clarification of Question no. 1: If logic is infallible, does it mean that it is more than just a human created thing? That something in the real world makes possible the infallibility of logic? Does it have to originate from a being such as God?

Clarification of Question no. 2 and 3: If mathematics is real, it is more than a invention of mankind, ryt? Since it is such a brilliant describer of reality, does it have to originate from God?

• What do you mean by “logic is infallible”? Where does Gödel fit in? – Jim Garrison Apr 25 '18 at 6:32
• @JimGarrison Godel's theorems demonstrate the limitations of a formal axiomatic system of mathematics, right? Not limitations of logic itself? – BlowMaMind Apr 25 '18 at 7:00
• Following Jim Garrisson, it seems to me that Gödel's incompleteness theorems already show that logic is not "infallible" (depending on what you mean by that). It was formulated in a specific system but seems to tell us more general things such that : 1) we can't have a perfect logical formalization of mathematics 2) a formal logical system can't show its own consistency. It also applies to other "logical formatting" and produce an inevitable lack of certainty. – Boris Apr 25 '18 at 8:54
• Gödel is out. "The true reason for the incompleteness that is inherent in all formal systems of mathematics lies in the fact that the generation of higher and higher types can be continued into the transfinite whereas every formal system contains at most countably many." [Kurt Gödel: "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I", Monatshefte für Mathematik und Physik 38 (1931) p. 191] Since transfinity has been contradicted (see e.g.philosophy.stackexchange.com/questions/51038/…), there is no problem with Gödel. – Wilhelm Apr 25 '18 at 9:08
• @BlowMaMind Your comment is correct, the people talking about Gödel are incorrect and should be ignored. Gödel's theorems have absolutely nothing to do with the "fallibility" of logic. – Not_Here Apr 25 '18 at 18:53

• Does infallible logic even as a concept, imply the existence of God?

I take "infallible logic" as the assumption: By logical reasoning we do not arrive at false conclusions when departing from true assumptions.

Taken in this sense, logic does not imply the existence of god.

Logical reasoning draws conclusion from assumptions. Logic does not support any assumptions about the world or about our experience in the world. Therefore logic cannot draw any conclusion about the world or about our experiences.

• Is the truth [and reality] of mathematics inconsistent with materialism?

I take "truth of mathematics" as the property, that one can prove mathematical statements. And as soon they are proved they hold forever.

Mathematics is useful to design and formalize theories about the world. But mathematis is neutral with respect to the philosophical approach taken by the theory. Therefore

Mathematics is consistent with materialism.

Note: Mathematics does not support a materialistic approach more than other philosophical approaches. And mathematics does not make any assumptions about the world. Therefore I would like to skip the term "reality of mathematics".

• If an entirely mathematical description of the entire universe is possible, does that mean God exists?

Like logic also mathematics does not make any a priori assumption about the world. Mathematics is a formal discipline alike logic. Both consider the structure and the relations between statements. They are not doing the job of natural sciences, which aim at true statements about the world and an explanation of our experiences. Therefore:

Even if a mathematical formalization of a correct theory of the entire universe were possible, that does not mean that god exists.

In this hypothetical case, the question on the existence of god has to be adressed not to mathematics. First, the questioner has to clarify his concept of god. Then he should address the question of god's existence to the primary theory.

Note. The fact that deterministic chaos exists, shows the limits for making mathematical predictions on the base of observed initial conditions.

• Your answer seems to only describe mathematical logic. I want to note that when I create a syllogism I do not use any assumptions or axioms. Secondly, if one doesn't know the rules of the logic you refer to one can start with all true premises & still deceive the wrong conclusion. One who knows the rules will not likely get the conclusion wrong from true premises. So I would say math teaches that logic is logic which is far from reality. Logic does not HAVE TO have any assumptions as you indicate. I can begin with factual propositions.There are no axioms and no assumptions in classical logic. – Logikal Apr 25 '18 at 18:09
• @Logikal Classical logic does assume the so-called Laws of Thought - i.e., the laws of identity, excluded middle and non-contradiction. I'm not reading Jo's answer as being only relating to mathematical logic, at least no more than the OP describes. – Nick Apr 25 '18 at 18:35
• @NickR, do you think one must know the three laws of thought to evaluate a syllogism? I would say the law never even come up. The rules of classical logic so not require knowing the three famous rules. They are thrown in as a bonus. – Logikal Apr 25 '18 at 18:38
• @JoWehler Thnx for your answer. But, what I meant is: If logic is infallible, does it mean that it is more than just a human created thing? That something in the real world makes possible the infallibility of logic? Does it have to originate from a being such as God – BlowMaMind Apr 27 '18 at 3:40
• @BlowMaMind What about making an edit to your original question and adding the comment as additional subquestion no. 4? – Jo Wehler Apr 27 '18 at 5:30