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PHILOSOPHY AS A NECESSARY CONDITION OF MATHEMATICS

Using fundamental relationships in mathematics such as necessary conditions to root out fundamental relationships in mathematics such as foundations of set theory.

PHILOSOPHY AS A NECESSARY CONDITION OF MATHEMATICS 1+1=2. Let's just break the rules. We could conclude this means: “2=+”. So, in this case + := 2. (:= means 'necessary condition that’). We could also find other cases where: +:=3 or, +:= 45, etc. We might conclude that + just means ' the means to reach 45' or ' the means to reach 3'. Similarly, we could write originally 2 - 2 = 0. This could mean “2 not= -”. And we would conclude: -not := 2. We could conclude - just means := not reach 2. Similarly, - could be := not reach 45, or not reach 3. Now there is a direct relation through: - not := + to: 2 not := -2 and 43 not := -43. This is different and more specific than traditional math. Traditional math assumes numbers have similarity. Here, the closest opposite relationship is not subtraction OR addition, but the opposite sign. In other words, we have a direct choice about what operators do as far as solving a problem, unless negation is just a process of reaching an opposite equation. And just as easily, negation could be any other process. Because if all negation is is a direct cancellation of a concept, then it depends on the concept, and the concept can define the rules. If negation is a process of finding the opposite, what makes it mathematical? And, how can it exist without a concept of things that can be directly opposed? It is one thing to say that negatives are opposite, and another to say that -0 doesn't exist, or that equations don't work equally with -=. The simple solution seems to be that negation is an operation more than a number, just as equals is an operation more than a number, and so just as = and -= are directly correlated, +2 and -2 are directly correlated. But the implication of this is more interesting. We now know that in terms of sign, +2 and -2 are merely operators, and so if -= and = are about finding solutions, the entire expression reduces to operators. It is now possible to put +2 or -2 on one side of the equals sign without an equation and get a solution. For example, -= -2 = 2, just as = -2 -= 2 or -2 = -2, etc. However, we would also conclude 2 -= 2 UNLESS negation is an operation with equal value to the equals sign. If -2 -= 2, and -2 = -2, we are led to believe -2 -= =-2, and so we are led to believe that 2 -= 2. The solution to this is that negation is radically equal to equals, and also can only be used once per operation. However, we might also conclude that numbers can only be used once per operation, and then we must conclude that operations are always uni-directional if they involve equals. Now the only means to quantify sums of OPERATIONS is to do permutations, or introduce a different sum of operators. The only way to be efficient in the case of permutation would be to logically reduce the number of combinations, or apply an irrational rule. The only way to have the correct sum of operators is to be coherent or incoherent. A linear permutation must be recursive to be coherent, and if it is incoherent it must either be finite or capable of infinite expansion. We have concluded that if basic math is representative, then it involves linear permutation. Such a permutation we have concluded must be recursive, finite, or be capable of infinite expansion. Infinite expansion = dimensions. Finite =not absolutely significant, so unprovable unless perfect. Recursive = either continuously circular, or self-proving. Therefore, the options for proofs are most obviously, Linear permutation involving self-proving dimensions. Linear permutation involving perfection. Thus the options are really: Exponential Efficiency, and: Completeness. In a roundabout way I have proved that basic math really aspires to be objective philosophy. I have also proved math amounts to logical operators, specifically those that follow after necessary conditions. For, if 2 came before equals we would just get := 2. If - came before = we would get := -. And there is no point of forming an equation, since that begs the question that it is not a necessary condition, or that -= cannot imply -2. REFERENCES ---. “4 Critiques of Mathematics”. ACADEMIA. ---. “Arbitrary Mathematics: Seminal Paper on Mathematics Expanded for Larger Formal Systems”. ACADEMIA. ---. “Calculus Paradoxes”. ACADEMIA. ---. Coherent Calculus. ACADEMIA. ---. “The Fundamental Critique of Mathematics”. ACADEMIA. ---. THE INTUITIVE CALCULUS. ACADEMIA. ---. “Logical Solution to the Abraham-Minkowski Problem in Physics”. ACADEMIA. ---. “Logical Solution to the Von Neumann Paradox in Mathematics”. ACADEMIA. ---. “Logical Solutions to Mathematical Incompleteness”. ACADEMIA. ---. “Logics”. ACADEMIA. ---. “The Perversity of Zero”. ACADEMIA. ---. “Philosophy of the Decimal System”. ACADEMIA. ---. PROGRAMMABLE HEURISTICS. ACADEMIA. ---. The Structure of Probability. ACADEMIA. ---. “What I Call Fermat”. ACADEMIA Coppedge, Nathan / SCSU 2017/04/11, p.
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