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Hence, it is said, the meaning and the truth of, for instance, "2 + 2 = 4" are bound up with the meaning and the truth of all the other statements in the arithmetical system and our knowledge of its meaning and its truth is bound up with our knowledge of their meaning and their truth.

Thus, 2 would not be the number we associate with the numeral 2 if it were the third of 4 instead of the half of 4 or the cube root of 27 instead of the cube root of 8. It is characteristic of the parts of a logical system like that of pure mathematics that no part would be what it is if its relations to the other parts were different from what they are. Further, this coherence is what we mean by calling such a proposition true. In this test, which is not merely a practical one, for a proposition to cohere with other propositions is for it to be logically deducible from them. In the exact and reputable science of pure mathematics, the logical test for the truth or acceptability of any proposition is whether it coheres with some of the other propositions, and ultimately with the axioms, of its system. In practice, we sometimes reject as false an ordinary person's assertions -for instance, that he saw a ghost -or even a scientist's results -for instance, in experiments on extrasensory perception -on the ground that they do not cohere with the other commonsense or scientific views that we also hold as true.

It is not altogether possible to give a plausible exposition of the theory independently of its close historical links with rationalist and idealist metaphysics, but the account might go something like this. In either case, no statement can be known to be true until it is known to cohere with every other statement of the system where the system consists of all true statements, such knowledge is unattainable. The metaphysical supporters of coherence, on the other hand, insist that a statement cannot properly be called true unless it fits into the one comprehensive account of the universe or reality, which itself forms a coherent system. The system with which all true statements must cohere is said by its logical positivist supporters to be that accepted by the scientists of the contemporary culture. To test whether a statement is true is to test it for coherence with a system of statements. Many proponents of the theory hold, indeed, that each member of the system implies every other member. According to the coherence theory, to say that a statement (usually called a judgment) is true or false is to say that it coheres or fails to cohere with a system of other statements that it is a member of a system whose elements are related to each other by ties of logical implication as the elements in a system of pure mathematics are related. Hegel, and Francis Herbert Bradley but it has also had a vogue with several members of the logical positivist school, notably Otto Neurath and Carl Gustav Hempel, who were much influenced by the systems of pure mathematics and theoretical physics. The coherence theory is characteristic of the great rationalist system-building metaphysicians Gottfried Wilhelm Leibniz, Benedict (Baruch) de Spinoza, G. For concreteness, we report the form of decoherence time τ d in a finite Heisenberg model with respect to the number of particles N, density n ρ, spatial dimension D and ϵ in a η/r ϵ-type of potential.The coherence theory is one of the two traditional theories of truth, the other being the correspondence theory. However, in most cases, the decay of off-diagonal elements differs from the usual exp(-t/τ d) behaviour. Moreover, the concept of decoherence time is applicable in closed and finite systems. It appears that coherence is an important measure that helps to understand quantum properties of a system, e.g., the decoherence time can be derived from the coherence function Ξ(t), but not from the entropy dynamics. As expected, decoherence is understood as a statistical process that is caused by the dynamics of the system, similar to the growth of entropy. For this purpose, we present a quantifiable definition to quantum coherence Ξ, and discuss in some detail a general coherence theory and its elementary results. A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems.