[PastorBiker3025]

heres your mathmatical equation you prolly wasnt lookin for but I aim to inform.. God blessCreationism defended Premise 1: Mathematics is real, at least as a real description of the universe. Mathematics has been used to model and describe countless phenomenon observed in business and scientific applications. For example, consider models of two variables x and y.sin( ( ))1ln...020 1 22 2y a b c x daecyy aby axy a b xy a a x a x a xAx Bxy Cy Dx Ey Fbxxbnn= + -+==== += + + + ++ + + + + =-These common “mathematical models” are referred to as second-degree, polynomial, logarithmic, power, exponential, logistic, and sinusoidal. These seven models have been used to describe and predict the accumulation of wealth, cost analysis, marketing strategies, radioactive decay, the earth’s mass distribution, the orbital paths of celestial bodies, and population fluctuations, just to name a few. What is so remarkable about this list is the simplicity of each equation. The only requirement is knowing the value of a small number of constants. The universe seems “hard-wired” with the laws of mathematics. The applications of mathematics draw one to conclude that mathematics must be real at least as a description of the physical universe.Premise 2: Mathematics exists independently from the physical/temporal universe. If one talks with mathematicians at any length one is left with the impression that mathematicians think that mathematics is of utmost importance. It is not just that mathematics is simply describing something. They treat mathematics as if it were a real entity, whose truth does not depend on the physical universe. Menzel (Howell & Bradley, 2001, p. 69) notes that even if there were not “pebbles and pomegranates and other countable sorts of things, there still would have been the number 11, as well as the proposition that it is prime.” Also implied is the independence of mathematics from time itself. The theorems of mathematics seem as if they were true even before time began and would continue to be true though time no longer existed. The practice of mathematics draws one to conclude that mathematics is true and exists independently from the physical/temporal universe. Premise 3: Mathematics is communicable between rational beings. First-order logic has been used as a foundation for almost all of mathematics. In particular, first-order logic includes the formalities needed to insure the effectiveness of formulas, axioms, and rules of inference.i) For a formula to be effective “there must be an effective procedure for deciding, for an arbitrary string of symbols, whether it is a formula.”ii) For an axiom to be effective “there must be an effective procedure for deciding, for an arbitrary formula, whether it is an axiom.”iii) For a finite sequence of formula, “there must be an effective procedure for deciding …whether each member of the sequence may be inferred from one or more of those preceding it by a rule of inference” (Stoll, 1963, p. 373).First-order logic is built up with a number of allowable symbols:i) variable symbols (like a1, a2, a3, …)ii) logical connectives: Ÿ, ⁄, ÿ, Æ, ´, etc.iii) quantifiers: ", $iv) equality: =v) parentheses: ( , ) vi) a set of constant symbols vii) a set of relation symbols viii) a set of functions symbols 0-ary relation symbols are allowed and are called propositional symbols. We specify a language in first-order logic by listing all other nonlogical symbols. For example arithmetic in the natural numbers can be specified using the language {0, s, +, *}, where s is the successor function: s(x) = x + 1.First-order logic also specifies the rules that guide the construction of proofs. The rules are called the set of proof axioms for a first-order language, where x and y are variables and p,q and r are formulas:i) p Æ (q Æ p) ii) (p Æ (q Æ r)) Æ ((p Æ q) Æ (p Æ r)) iii) ÿÿp Æ p iv) ("x) (p Æ q) Æ (p Æ ("x) q), where x is not free in q v) ("x) (p Æ p[t/x]), where x is free in p, and t is any term whose free variables are not bound in p vi) ("x) (x = x) vii) ("x "y) ((x = y) Æ (p Æ p[y/x])), where x is free in p, and y is not bound in p We are also allowed two rules of inference, commonly referred to as modus ponens and generalization:i) from p and (p Æ q) infer q, where q has a free variable or p is a sentence ii) from p infer ("x) (p), where x does not occur free in any premise which has been used in the proof of p These proof axioms require the notions of free and bound variables along with variable substitution. Informally, any occurrence of a variable in a formula in which " does not appear is free; and in ("x)p the quantifier ‘binds’ all occurrences of x in p which were not previously bound… Formally, if p is a formula, t a term and x a variable, we define p[t/x] (‘p with t for x’) to be the formula obtained from p on replacing each free occurrence of x by t, provided no free variable of t occurs bound in p; if it does, we must first replace each bound occurrence of such a variable by a bound occurrence of some new variable which didn’t occur previously in either p or t. (Johnstone, 1987, pp. 19-20, 22-23)Gödel and Henkin were able to show that even in the broad context of all first-order theories, there were conclusions that could be made. The following meta-theorems (theorems about mathematics itself) were established, where T is a set of sentences for some first-order language L and p is any formula.i) (Soundness Theorem) If p can be proven to be true, then p is true for every model of T with every assignment of variables.ii) (Completeness Theorem) If p is true for every model of T with every assignmentof variables, then p can be proven to be true.iii) (Extended Completeness Theorem) T is a consistent theory (never leading to contradictory theorems) if and only if T has a model. iv) (Compactness Theorem) T has a model if and only if every finite subset of T has a model.Barwise (1977, p. 41) describes the accomplishments of first-order logic:Many logicians would contend that there is no logic beyond first-order logic, in the sense that when one is forced to make all one’s mathematical (extra-logical) assumptions explicit, these axioms can always be expressed in first-order logic, and that the informal notion of provable used in mathematics is made precise by the formal notion provable in first-order logic. Barwise claims that expressibility is supported by empirical evidence, and provability is supported by the completeness theorem. This means that rational beings have a mechanism for expressing mathematical ideas and for checking each other’s proofs. Recent advances in logic draw one to conclude that mathematics is communicable between rational beings. Premise 4: Mathematics must be mediated by a time-independent intelligent being. Hilbert tried to go a step further. He attempted to demonstrate that logic could also verify that there were no contradictions in mathematics. Martin (1977, p. 825) translates Hilbert as saying:If the arbitrarily given axioms do not contradict each other through their consequences, then they are true, then the objects defined through the axioms exist. That, for me is the criterion of truth and existence. Hilbert attempted to define truth based solely on axioms, and hence to separate the truth of mathematics from rational beings, including God Himself. In others words, Hilbert is claiming that mathematics is created/sustained simply because it is non-contradictory, with no need for an intelligent creator. However, such a program could not be carried out, even on the natural numbers. Peano attempted to characterize the natural numbers with the following firstorder theory, known as Peano arithmetic.i) "x ÿ(s(x) = 0) (0 is not a successor)ii) "x"y (s(x) = s(y) Æ x = y) (unique successors)iii) "x (x + 0 = x) (0 is additive identity)iv) "x ((x + s(y)) = s(x + y) (distributivity of addition successor function)v) "x (x * 0 = 0) (multiplicative property of 0)vi) "x"y (x * s(y)) = (x * y) + x (distributivity of addition over successor function)vii) If f(x) is a formula with x free, then f(0) ^ "x (f(x) Æ f(s(x)) Æ "x f(x)(axioms of mathematical induction)Gödel and others were able to show the fallacy of Hilbert’s view of mathematics even when studying something as simple (?) as the natural numbers. The following theorems concern Peano arithmetic and can be used as evidence to support the necessity of a time-independent rational being.i) (First Incompleteness Theorem) Any formal theory which contains Peano arithmetic cannot prove some sentences which are known to be true. This seems to indicate that mathematical truth is ultimately not simply a logic consequence of a set of axioms, but must be decided by some external intelligence.ii) (Second Incompleteness Theorem) Peano arithmetic cannot prove a sentence that asserts the consistency (free from contradictions) of it own theory. This seems to indicate that the consistency of mathematics must be accepted on faith.iii) The set of true sentences of Peano arithmetic is not definable by a first-order formula. This seems to indicate that a time-dependent being could never know everything there is to know about mathematics and therefore mathematics must have been created by a being outside of time.iv) There is no effective procedure to determine whether an arbitrarily given statement is true or false. This seems to indicate that the verification of mathematics cannot be accomplished using only concrete methods. Since mathematics needs abstract methods, it also needs an intelligent being to use those methods.v) Using a Turing machine, there i