The perfect metaphysical framework may be supplemented by what is at least pragmatically valid in the system of ~~(human)~~ knowledge. The perfect illuminates and guides the pragmatic and the pragmatic illustrates and is instrumental toward what is revealed in the perfect. The join is not perfectly faithful to the real. However, in terms of the value of ultimate realization, as our best instrument toward guaranteed realization it is perfect. The join is named real metaphysics or just (the) metaphysics.

While (the) real metaphysics has application in our world via, e.g., theories of science, how does it apply across the universe? It began in the ideal metaphysics, with the universe as the realization of possibility. It continues with dimensions and paradigms of being, below.

Argument

Introduction

The aims of this piece – or section if it is part of another article – are (i) to see perfect and less than perfect but reasonable establishment of conclusions as a continuum (ii) to find the common analogy between deductive inference and establishment of a theory in science, not as wrong, but as inappropriate and (iii) to show and analyze a better analogy.

The process of inference is either (i) deductive in which the conclusion is necessarily true if the premise is true (i.e., if the premise is true and the inference valid, the conclusion cannot be false) (ii) non-deductive in which the conclusion is reasonable but not necessary. Deductive inference is deductive logic, and non-deductive inference is ‘non-deductive reason’ or ‘logic’. Examples of non-deductive logic are induction (generalization, statistical), abduction (inference to the best explanation), and reasoning by analogy (e.g., if facial expressions are similar, the feelings they reflect are similar).

The reason for the certainty of deductive inference is that the conclusions are in some sense implicit in the premises, but that is not the case for non-deductive inference.

It will be effective to talk of argument rather than of logic. In the meaning used here, an argument is (i) establishment of facts (premises), e.g., by observation, and (ii) inference of further facts (conclusions) by inference.

An argument is called deductively valid if conclusion is inferred by deduction from the premise and a valid argument is called sound if the premise is (established as) true. In what follows, valid will mean deductively valid and ‘sound’ will refer to a valid inference with premise that is (established as) true.

How are premises established as true? The question is significant (i) because of the problem of error and (ii) because we want a conception of argument as general method for knowledge. Standard treatments have lesser role for argument and do not treat the question. Premises may be established as true (a) for discrete systems (e.g., there are ten pieces of licorice in the jar) or (b) by allowing imprecision (the sun is between ninety and a hundred million miles away from the earth, which is, after all, an introduction of discreteness. But another way to establish truth is via necessity, e.g., given experience, that there is being, or, given the conception of the void, it does (must) exist. Thus, necessary argument is a special and subcase of sound argument.

A non-deductive may be called strong, if the inference is sufficiently likely, and a strong argument is good if the premise is true or precise with sufficient reliability.

Premises may be established as true with sufficient reliability (i) establishing their truth as in the case of sound argument (ii) by experimental refinement and corroboration (iii) use of theory to establish or corroborate a result in terms of other observations.

Note that while the terms ‘valid’ and ‘sound’ are standard, the terms ‘necessary’, ‘strong’, and ‘good’ argument do not seem to be in common use.

We may think that there is a gulf between sound and good arguments, the former being necessary and the latter being just reasonable. However, there is a problem of application. That is, does a deductive argument refer to something in the world? That is, we often think of sound arguments as perfect because we think syntactically, but the application is also semantic. Consequently, even sound arguments apply imperfectly and the sound and the good constitute a continuum (and though some basic deductive logics are syntactically perfect, there are logics that we think are deductive but that may be syntactically imperfect).

The foregoing conclusion needs to be corrected. It is seen in (the) real metaphysics that some facts can be established of necessity (e.g., existence of the void, measurement in which precision is limited). Establishment of the necessity of the void shows that metaphysics must be done to establish its method.

Still, the conclusion that argument – deductive and non-deductive – constitutes a continuum remains true. This is emphatically true on the joint value-epistemic criterion for knowledge.

Argument vs Logic

In formal and technical use, logic is inference. In some informal use, conclusions—bare facts, desirability of courses of action—are established logically. The difference is that the informal use is what we call an argument.

There is a case to be made that we ought to use the term logic to cover both argument (establishment of fact, which includes inference) and logic (inference).

In other written works, I have used ‘logic’ in just that sense and to distinguish that use from logic as inference I have used the capitalized form ‘Logic’.

Science and logic

Let us now consider the analogy between (deductive) logic and science. The usual analogy is that logic is perfect but science imperfect. However, what is being compared is inference under a logic to inference to a scientific theory. On the other hand, if we compare (i) establishing a logic to establishing a theory (ii) inference under a logic to inference under a theory, the former is not certain, and the latter may be certain. “Science and logic form a continuum.”

Source or study topic 1. Category Theory (Stanford Encyclopedia of Philosophy), Bayes Theorem (Stanford Encyclopedia of Philosophy) – for study of Bayesian inference, Argument (Stanford Encyclopedia of Philosophy).