The S5 System of Epistemology

The analysis of information is known as epistemology. The logic of understanding and belief is known as epistemic logic. Its primary purpose is to shed light on the flaws in the transfer of knowledge and the truth value of propositions. It is based on the properties of truth as a constant and aims to ensure that the actual value and logic laws are implemented logically. This paper will present and defend the S5 epistemological logic system, one of many approaches (S4, S4.2, S4.3, S4.4, S5) suitable for current use.
The S5 system is one of the provisions of modal logic as were proposed by Clarence Irving Lewis and Cooper Harold Langford (Lewis 25). It is one of the oldest systems of Modal logic and the most basic one. It bases its logic on the application of truth values to its axioms and uses them to dispel any epistemic errors inherent in any proposition or epistemic argument. However, to do this, it mostly uses the modal operator; ‘necessarily; ◻ and; dual possibly’ ◊.
To begin with, epistemology relies on the value of truth as stated previously. Therefore it is incumbent that it relies on the principles of truth for it to have its propositions right and truthful. Therefore the first value of truth that we will be looking at is the immutability. The Axioms of S5 are K: (A B) ( A B). ‘K’ is to be adopted as the necessary constant. Therefore the immutability of the S5 axiom that defines that it is unchangeable. It uses conditional clauses such as ‘ : ‘It is necessary’, and ‘if … then’. Hence, it is necessary that, if ‘A’ therefore ‘B’. To expand the formulae is to apply that; if it is necessary ‘A’, then it is necessary B( A B). That necessary clause is predetermining that the causality that ‘A’ is needed for the effect ‘B’ to occur and that is unchangeable (Horne 30). Moreover that ‘B’ only comes to exist as a proposition or inference only precede by ‘A’ is indicative of an unchangeable cause-effect relationship. That level of dependability that isn’t changeable and is highly connective makes this logical system stronger in its truth value than any other.
Secondly, the other attribute of truth that this epistemological system relies on, is the universal character (Anderson 20). Truth is that quality that is bound to be universal in its application and its essence, such to say that, it is universally accepted as such everywhere and holds its dignity around the globe. Therefore if the S5 epistemological system is to derive its truth value from the universality of Truth as a virtue, then it has to have its predication placed on the universal principles or inferences. Such to mean that if ‘A’ necessitates ‘B’ then it implies that in every situation that ‘B’ occurs then ‘A’ must have preceded it. Or on the contrary to mean that there cannot be any ‘B’ without an ‘A’. Such a level of indisputability of the fact that, if ‘A’ then ‘B’, or if it is necessary ‘A’ then it is necessary ‘B’, would mean that the necessity of ‘B’ is based on the provision of ‘A’. And therefore being no other way to arrive at ‘B’ without first presenting ‘A’ means that it is universal and that such an effect (B) is only predicated as a consequence of ‘A’. Such clarity means that the system S5 is self-revolving and evident and thus the apt system to be adopted than the others as mentioned in the introduction.
Thirdly, the S5 system bases its predication of prepositions on a realistic platform and its consequents are based on a realistic antecedent (Weyl 10). Using the previous illustrated Axiom; if it is necessary ‘A’ then it is necessary ‘B’, one can infer the following truth value; that ‘B’ is based on the ontological aspect of what ‘A’ represents. If the former ‘A’ is not present, then the latter ‘B’ is absent. ‘B’ is predicated on the reality of ‘A’. As much as the effects of ‘B’ are realized only at after the realization of ‘A’; such a relationship that is based on the existence of the antecedent makes such a system complete in its reference of causality. It cannot therefore be confused that ‘B’ would ever be present without ‘A’ or that if ‘A’ occurs then ‘B’ would not follow.
Fourthly, the value of the S5 axioms is based on correspondence and not on any contradiction (Wang 35). Correspondence is the value that causes truth not to be contradictory to itself and to have all its inferences straight forward. The axioms in the S5 system as provided for previously indicate that the inference and flow of logical progression are not contradictory. Such to say that; if ‘A’ therefore ‘B’ or if it is necessary that ‘B’ then it is necessary ‘A’ is to entail a congruence. The insistence here is that; the axioms make complete logical sense even when reversed in meaning or order. If one is to state ‘A’ then ‘B’, then it is correct as to state; if ‘B’ therefore ‘A’, that the two variables are cause and effect. If one is to desire the ‘B’ effect then they must initiate the ‘A’ causality (reversed logic), or if one is to cause ‘A’ to exist, then they must have in mind that ‘B’ follows. This is because the relationship of both the variables is based on a necessary clause as opposed to a possibility.
Fifthly, the S5 system is based on constancy (Nebel 12). Truth is constant. This is to be distinguished from the universal and immutability aspects as mentioned previously. Constancy means that truth is predicated on itself, on a value that doesn’t change no matter what the variables ‘A’ or ‘B’ represent. Such to say that ‘A’ could represent the proposition that; If you cut yourself with a knife on the wrist, then ‘B’ – you are going to bleed. The variables could be changed to represent any another conditional clause (If you punch a concrete wall with bare hands then expect to feel pain). Both the variables (the former and the latter) predicate themselves on a constant truth that never changes. Therefore it is held as constant that one will bleed if they cut themselves on the wrist and they will feel pain if they punch the wall with a bare fist. Such truth is constant regardless which variables are used. That constancy is evident in the S5 epistemological system; it is based on the constant that; If ‘A’ then ‘B’, then regardless whatever the variables represent, the constant remains that whatever ‘B’ is, then it must be dependent on whatever ‘A’ is. Such an aspect (Constancy) brings to place the value of verification. The S5 axioms need not be verified simply because they are self-evident; they derive a single consequence from a single antecedent and cannot be subject to contradiction as mentioned previously. Hence they are superior to the other epistemological systems because they are self-contained.
The other value of the S5 system that is laudable is its simplicity. The S5 axioms are simple in themselves; they do not derive a multiplicity of meanings and consequences. They are simply a single antecedent that obtains a unique effect (Nebel et al. 18). That direct inference means that the propositions drafted using this system cannot bear contradictions in themselves. As long as there is one interpretation of the antecedent, then there is already cause enough not to misconstrue the meaning of the preposition. That simplicity goes hand in hand with what Truth is. It is simple (Nebel et al. 19). One antecedent derives only one logical consequence. That one to one ratio is what has held the value of truth as indisputable. To derive more than one conclusion is to entail a complication. Complications are in essence weak disjoints that can predispose a logical argument to infer different meanings. A simple, composed proposition is far stronger than a disjointed proposition. And that is what the S5 system provides for, a singularity in cause and effect.
Finally, having elaborated the aspects that make the S5 epistemology system efficient, it is, therefore, the findings that such stability is drawn from the fact that such a system (S5) is self-explanatory and self-evident just as Truth is in itself. The other systems (S4, S4.2, S4.3, and S4.4) bear in themselves contradictions that cannot suffice the test of truth and validity. Hence cannot be the best system to adopt. S5 is therefore the most superior epistemological platform and the apt one to be adopted in the 21st century.

Works Cited
Anderson, Alan Ross, Nuel D. Belnap Jr, and J. Michael Dunn. Entailment, Vol. II: The Logic of Relevance and Necessity. Vol. 2. Princeton University Press, 2017.

Lewis, Clarence Irving. Essays on the Foundations of Ethics. SUNY Press, 2017.

Horne, Jeremy. “The Core of Logics.” Philosophical Perceptions on Logic and Order (2017): 1.

Nebel, Bernhard, C. Becker-Asano, and S. Wöl. “Multiagent Systems.” (2014).

Wang, Yanjing. “Beyond knowing that: a new generation of epistemic logics.” arXiv preprint arXiv:1605.01 995 (2016).

Weyl, Hermann. “Similarity and congruence: a chapter in the epistemology of science.” Symmetrie. Springer Berlin Heidelberg, 2017. 153-166.

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