On Possibility
And some beginnings of logic

Anil Mitra Copyright © January 2018—March 2018

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On Possibility

Given a conception of a being that does in fact specify a real being, its CONSTITUTION defines a range of states it may be in that are consistent with the conception. These are the POSSIBLE STATES for the being.

POSSIBILITY defines the states a being may be in. This is real possibility and since we will identify different kinds of possibility it is called REAL POSSIBILITY. When ‘possibility’ is not modified, it will generally mean ‘real possibility’.

An ACTUAL STATE of a being is a possible state. A possible state is not necessarily realized and so the range of actual states is included in (less than or equal to) the range of possible states.

An IMPOSSIBLE state for a being is defined by a variation of the conception that lies outside the possible—i.e., that lies outside the constitution.

UNIVERSAL POSSIBILITY is possibility for the universe. Universal possibility is real possibility for all beings as a compound being.

Given a PATTERN of form or behavior in the world, our conception of it is a NATURAL LAW or law of nature or, simply, LAW. While the term ‘natural law’ refers to a conception or reading, as long as it does not result in confusion, we use the term ‘natural law’ to refer to the pattern immanent in nature. Therefore we may say that such natural patterns and laws have Being. Note: there are other criteria that are generally required for the term ‘natural law’ is applied but they are not important to this discussion of possibility.

NATURAL POSSIBILITY defines the range of natural states. That is inherently vague but the intent is that natural possibility is what is consistent with natural law. Examples of natural possibility are given by our sciences of physics, biology, and psychology. Typically, natural possibility refers to our cosmos.

SENTIENT POSSIBILITY is what can be realized by sentient beings and their capacities of psyche, foresight, creativity, choice, design, will, and realization. If we make the restriction to nature as we know it in our cosmos, sentient possibility is an example of natural possibility.

Other kinds of possibility may be considered, e.g. cosmological, human, and animal. We may also consider possibility subject to certain constraints on beings but this is not fundamentally different than a ‘kind’ of possibility.

The following relations obtain among the above kinds of possibility: universal > natural; natural > physical / biological / of psyche / sentient (> means includes or is the same as; and, for later use, >> means includes and is far large than, and => means implies). However if we do not restrict consideration to our cosmos, the sentient may exceed the natural may equal the universal.

The foregoing kinds are all real—which means that though we invoke the concept the possibility lies in the object side of the concept-object.

Logical impossibility is a property of a conception such that it is cannot be realized. That is, logical impossibility is not a property of the world but of concepts. LOGICAL POSSIBILITY is defined as follows—it is a property of a conception such that it is not logically impossible. We may state this in the following way, ‘logical possibility is realized in some conceivable world.

In principle, there are logical possibilities that are never realized. Thus we know that logical possibility > universal possibility (the universal may equal the logical).

Note that the conception of logical possibility above need not depend on a prior conception of ‘logic’. What are conceptions that ‘cannot be realized’. Let us begin with examples. Can a black object be blue? That depends on the definitions of ‘black’ and ‘blue’. Can a black object be not black? Only (a) if blackness specifies nothing at all—and in this case, blackness is not a concept; or (b) in an empty ‘universe’, all black objects are not black (but they are also blue and green and are also sheep and not sheep and so on). That is, if black is a concept and in a non-empty universe all real black objects cannot be not black. What about the real universe in which we only know objects by experiencing them directly or indirectly or perhaps hypothesizing them but which again is a form of (shadow) knowledge? That is, an object that is black cannot be not black; but an object that is black only-to-the-best-of-all-knowledge can be non-black. We deal with that situation by saying that in an ideal universe in which knowledge is perfect—or with sufficient abstraction—a black object cannot be not black and that fits the real universe to the extent that our knowledge may be true. That is, we are separating our thinking here, into logic and fact. The fact is empirical but logic is ideal. And in logic so conceived, a black object cannot be not black; note, importantly, that while facts are empirical, they can also be necessary if there is sufficient abstraction (and similarly there are conditions under which hypothetical generalizations can be necessary—e.g. with abstraction or with restriction of the domain of application). That generalizes to the logical principle known as the law of non-contradiction. It also gives us insight into the nature of logic and how it can be certain—its certainty comes from idealization andor abstraction (and is therefore not a mere property of grammar). Along these lines we can arrive at other laws of logic, especially the law of the excluded middle and the law of identity, and any limits on conditions even for ideal / abstract as well as real application. Similarly, we can arrive at the propositional and predicate calculi as well as other systems such as the Syllogisms and analysis of the categorical propositions.

Generally for the above possibilities, if kind-A > kind-B, then B-possibility => A-possibility but not vice versa. Thus a physically possible being must be universally possible which in turn must be logically possible.

Now suppose that we want to experiment conceptually with a logically possible being to explore the limit of the realizable. This kind of exploration could be informative for physics, life, mind, AI and more. However, we find the logical too permissive and the natural too restricted. We may imagine constraints on the concept that are greater than the logical but, instead of the empirical, are formal. Suppose we ask whether a thought—the thought, not the content—must be immanent in or be a form. That kind of constraint may be labeled ‘metaphysical’ and the resulting possibility may be called METAPHYSICAL POSSIBILITY—which (1) is Í logical possibility, (2) is usually for conceptual application but may also be real, (3) in metaphysical systems usually >> the common real systems. Consider the question whether thought itself, not content, must have or be a form (body). Logically, thought could have no body; but we may wish to consider and define minimal formal requirements for embodiment. In a formal but different use, metaphysical possibility may refer to (a) possibility of any existing being, which cannot be known perfectly without a final metaphysics as in essential metaphysics or (b) possibility in terms of some system of categories of being—perhaps falling under a rational or final metaphysics.

A FACT is usually statement or conception of situational or contingent a restriction on the states of a being to a subset of its possible states (the number of facts has no particular importance for we can think of many single statements as a compound statement and a single statement may often be broken down into a set of simpler statements). A set of situational facts and the constitution of the being may be equivalent to a further situational fact (facts). Showing such equivalence is called INFERENCE. Inference will typically deploy constitution. The original and the inferred facts are called premise and conclusion respectively. In arriving at a conclusion, we may first wish to determine a premise and the compound process is called ARGUMENT. While fact and constitution may be distinguished, they may be counted among the facts and, with sufficient conceptual freedom, the distinction between argument and fact may be seen as null—as in tautology. Since the real possible cannot be logically impossible, argument regarding real systems may naturally deploy logical (deductive) inference. However, inference deploying logic alone, called deductive or logical inference, employs only logic and rules, derived or postulated, regarding particular systems of logic. An inference would result in a CONDITIONALLY NECESSARY conclusion—one that is true if the premises are true. A NECESSARY conclusion, then, is one that requires no ‘premises’ except rules of inference. In some cases the rules of inference themselves may be counted as given—e.g. when sufficiently abstract to be transparently given. In this case no premise is required for a necessary conclusion.

This leads to the important idea of METAPHYSICAL ARGUMENT. A METAPHYSICAL FACT could, for example, be that thought must have body at least as complex as the form of thought; other such facts could be that thoughts are represented as symbols and the process of thought by elementary operations; a metaphysical inference might then concern the simplest body capable of realizing a system of symbolic thought. This is an example of METAPHYSICAL NECESSITY.