NECESSITY VS TRUTH

(This post is a prerequisite to understanding most of the posts on this blog)

Truth is commonly defined as "that which corresponds with reality", proposing that it describes and aligns with a state of manifestation. For example, "the tree exists is true because the properties that make up what we call a tree manifests as a coherent distinct entity". If "the tree exists" is true then it is the case and its manifestation is part of a container we call reality, as we can define reality as the set of all manifestations, or all that is the case. However, it is not just truths that correspond with reality, as there are what we can call necessities that also correspond with reality. Necessities are not equivalent to truths, yet they are part of what make up all that is the case.

A Necessity is defined here as "a coherent condition that manifests in reality, where the contrary is a contradiction (incoherent)", or "must be the coherent case". A truth is "a coherent condition that manifests in reality, where the contrary is not a contradiction (coherent)". All truth values (true/false) are non-necessary, or "can be the coherent case otherwise", and as such are in contrast with that which is necessary. That the contrary is coherent in truths allow us to be out of accord with our beliefs. One can not be out of accord with necessities, as the contrary is incoherent. It is common to use the term "incoherent" as either meaning "not understood" or "not understandable". In this case, we are using the latter definition. It is not that we can not currently comprehend a contradiction, it is that contradictions are incomprehensible.

We should make clear that "truths" are representations of the state of reality. "Reality" is an ontological state that is independent of a mind. "Truths" are epistemological states that are representations created by a mind, intending to map to ontological states. Ontologically, there are no truths. If a truth correctly maps to an ontological state, then in "reality", it is a necessity. For example, when we claim that a particular ball is red, we could be wrong, as the ball could have an ontological state of being blue (or yellow, or green etc.). If the ontological state is in fact red, then the contrary that it is not red would be a contradiction. Therefore, ontologically, the ball would be necessarily red. All necessities are ontological states (and all ontological states are necessities) and are the case, and all "truths" are non-necessary, mental (epistemological) states that may be the case.

It is common to refer to that which is the case as true or necessarily true. This is understood in a colloquial sense, however, in a strict sense, adding necessarily, which follows a distinct condition to be met (incoherent contrary), to the term true, that follows an opposite distinct condition (coherent contrary), contradicts the truth condition. When we speak of truths, we associate it with terms like justification and beliefs, which we can be in accord or out of accord with, and then qualify those states incorrectly with necessarily, a state that we can not be out of accord with. We must separate the terms, necessary and true, in order to maintain coherency. That which is necessary is not a truth, or a subset of truth. Necessities and truths are subsets of that which is the coherent case. It can be the case that A is necessary or it can be the case that A is true, however, it can not be the case that A is necessary and true, or necessarily true. That is a contradiction and incoherent, for it is to propose that A has a coherent contrary and an incoherent contrary at the same time in the same sense.

All necessities and truth values are composed of a subject and at least one condition regarding the subject to evaluate (predicate). For example, "All swans are white" has the subject of "All swans" and a condition to evaluate "are white". It is unintelligible to state, "Swans are true". However, if by "swans" we mean "swans exist", then we have a condition ("exist") to evaluate.

We determine a necessity or a truth value by evaluating the two horns of a strict dichotomy, "it is the case that A OR it is not the case that A". All coherent cases are either necessary or true or false (unnecessary). We can not refer to a necessity as true, as there is no coherent value to contrast with. If both horns of the dichotomy are coherent, we can have justification for believing which horn is true, as there will be a coherent contrary to evaluate.

An example of a necessity is "A=A". "A" is a variable (place holder) for anything, such as a chair or a planet or an atom, etc. A chair must equal itself, a planet must equal itself. It is the fundamental principle in logic. The contrary to "A=A" is "A ≠ A", which is a contradiction and incoherent. One can not  justify a necessity, as justification implies there is a reason A is the case over other options. The concept of justification applies only to truths, where the contrary options are coherent, and can be evaluated. An example of a truth value is "The grass is green". The contrary is "The grass is not green". This is coherent, as the grass could be red, or blue etc. One could have justification for this claim, as one would have other coherent options that need discounting.

When we determine that 2+2=4, we are not expressing a truth, but a necessity. The math is merely a reformulation of "A=A" (4=4). Similarly, suggesting 2+2=5 is not a falsity, it is a contradiction and thus incoherent. We say we have "proofs" in math due to the necessity of the answer. One could ask, "What is 2+2?" and the response could be "5". While, out of context, the number "5" is coherent, it is the relationship between the expression asked (2+2) and the answer (5) that is incoherent. It demonstrates that the respondent does not understand the concept of "2+2". It is like asking if a square triangle has 8 sides. One could say, "Of course it doesn't!", feigning to understand what is being asked. As the concept of a square triangle is incoherent, one could not coherently answer the question one way or another without understanding what a square triangle is.

There are three types of necessities presented here, a simple necessity (non-contingent), which we concentrate on in this article, a conditional necessity (contingent), and a relative necessity (contingent). A=A would be a simple necessity, as there is no condition in which it is not the case. That,  "I cannot fly by flapping my arms" can be a conditional necessity (see: nomological) if certain conditions must prevent me from flying. The conditions could be: if gravity is of a certain strength, and I am of a certain mass, and my arms are of a certain shape, etc., then if I flap my arms, all things being equal, it is impossible for me to fly. If I could fly, it would contradict the conditions that are assumed to be true.  An example of a relative necessity (see: performative) would be, "I exist". It is only a necessity to the mind that thinks it, and is contingent upon the mind to think it. To all other minds, it is a truth value.

When contemplating "possible worlds", what we mean is that reality could be different based on one or more contrary truth values, as they are coherent otherwise. For example, "The Statue of Liberty exists in one possible world and it does not exist in another possible world" is coherent. We do not mean that necessities could be different, as necessities "must be the case" in all variations of a possible world.

When one declares that a particular entity necessarily exists, what is being referenced is an entity where all of it's properties have contraries that are contradictions. If one property, within the set that describes the entity, is a truth value (contrary is coherent), or relies on a truth value, then the entity in question is a contradiction, as the entity as a whole would be described as being necessary yet not necessary at the same time in the same sense. A particular entity that is referenced as contingent (non-necessary) is coherent as long as at least one property is a truth value (non-necessary) and does not contradict another truth value within the set. In this case, one's belief in the existence of the entity in question would be based on some form of justification, with the inescapable possibility that one is incorrect regarding this belief.

Declaring any thing (or entity) as logically necessary would require a demonstration of a contradiction. One could say that something isn't contingent just because we cannot readily find the contradiction of the contrary. However, this defense changes the original declaration, "it is necessary" to "it could be necessary, as there might be a contradiction". This implies the admitted possibility that there might not be a contradiction to the contrary, which in turn concedes that the thing or entity can only be assumed to be contingent (non-necessary), until demonstrated otherwise.

It is possible that we, and the universe that surrounds us, have been created and/or controlled by a coherent, contingent entity (or entities) that exists "outside" of our universe. One can imagine a "brain in a vat" or "computer matrix" scenario, as it can be accomplished without contradiction. This does not entail that we may not really exist, just that we may not exist in the way, shape, or form that we believe ourselves to exist. The way, shape, or form that we exist is a truth value, and is coherent (possible) otherwise. However, if we exist in some way, shape, or form, then we must be something, and that something must equal itself (A=A). All distinct "things", however arbitrary they are defined, are contingent on necessities that are absolute, infinite, and non-contingent, such as A=A.

August 2019