Logic

My more ambitious blog posts are in shambles, so let me start slowly.  Let me start with "logic". Specifically, let me start with an aspect of "logic" which is not widely or well enough understood for my liking.  It seems that the bulk of the curve, even those that regularly partake in discourse for their amusement and edification, do not seem to understand some simple characteristics of logic which are crucial if any real use it to be made of it in the determination of the affairs of mankind.

Perhaps the problem is that it is that logic lacks characteristics people attribute to it. Perhaps it would be easier to add a property to logic and than to ask people to understand its general meaning. People often thing that a "logical" argument has a conclusion.  In reality a logical argument says that IF some condition is met, THEN the conclusion is assured... IF some conditions are met. Or perhaps the problem is that a skeptical description of logic, while widely in use in science and engineering, is still not what is taught as the framework of logical analysis in the mainstream, so that even those educated in logic in mainstream universities will find it difficult to understand any very apt analysis of logic from a skeptical  point of view.  This is sad if true for this would preclude disscussing logic from  the level of abstraction necessary to understand the history of logic and the state of mankind's best understanding of rules of inference in general.

Put plainly, a "logic" is a system of inference.  The study of "logic" is the study of rules of inference. That there might be just one set of rules is clearly not an option, that is demonstrated. Study of various approaches to inference show sets of rules which cohere into separate, albeit related, systems of "logic". The rules of first order logic and second order logic are distinct and yet also bear a relationship. So too is it with modal logic, or fuzzy logic, or "logic" with any sort of qualifier meant to specify as least partially distinct characteristics.

At large with the so called natural languages of mankind one finds in use rules of inference which follow identifiable patterns, with some consistencies and some inconsistencies.  This holds true, it would seem, however lacking in formalization or however non-analytic the particular rules of inference may be, given enough people reason by said system of inferences.  Many such "logics" belong to categories of inference wholly held as fallacious by philosophers, which adopt sub-rules which logicians have tended to agree are unreliable and don't have a place in a proper "logic".  They may have gone overboard in such judgmentalism on the one hand, while on the other, it's clear they have a point considering how many bad rules of inference are still in use today which ought to be overcome.

This means that many rules of inference, which I would call a "logic" or "system of logic" are anathema to the traditions of philosophy.  These systems are anathema to them and generally we would call them illogical, which I can abide, and also prefer not to consider them as "logic" at all, which I cannot abide.  I understand some criteria upon a system of logic will over time be implied as a meta-logic develops by which one might measure and just a particular system of logic.  I understand calling some logics, illogic, but this can only refer to the incorporation of incoherency and irrationality, and cannot make us pretend that fallacious rules of inference are not inference at all.

An example of widely used systems of inference often considered illogic by philosophers are systems of inference which are purely heuristic systems, that is, they contain a set of arbitrary rules of thumb, learned by rote rather than by principle, as the latter are unknown.  A heuristic is not understood in principle, but is merely a matter of "if you see A happen, then B will happen".  These hueristics may be true, but not being understood, they are not very flexible, and tend to work for the bulk of cases and fail enigmatically as the edges of sets.  They are not themselves subject to the sort of reduction which allows exploration of subtle inferential details, a feature formal logic tends to intensify. An example of such a system of inference might be a persons ideas of what signifiers will reveal a person might be a good mate.  It may consist of lots of rules of thumb, this behavior implies that tendency, this physical characteristic or mannerism means that about their nature as lovers of home-makers. Given the context, where declarative statements cannot explain the conditions, first order logic is at a loss, and it may be only such crude systems can address the real human questions that afflict us in reality.

In a skeptical discussion of logic such systems are considered in addition to the formal systems which have the advantage of being technically defined and highly shareable.

Thus, the first thing to realize about "logic" is that it is not just one thing.  There is no one "logic".  When we say an argument is illogical we generally mean it apparently violates some of the known rules of first order logic, or possibly mathematical logic. While I myself am fond of making such criticisms, it is often forgotten that first order logic (indeed most logic) works only on a particular type of sentence, the declarative sentence, meaning it cannot be used to infer from question, exclamations, or imperative statements, all of which make frequent appearances in people's daily lives.  The theory that all sentances can be put in declarative form has never been satisfactorily demonstrated.

Equally important is to realize that the assertion of a logical system, as such, is that the inferences hold.  In formal logic this means that true statements entered into the argument as principles will never be contradicted, unless by another input statement, in which case the contradiction will be discoverable. The general notion of a logic as a system of inference in general does not yield logic that always has that property.  For most logic in actual use in human society, quite the opposite seems true, an perhaps the rules of inference are actually intended to hide certain types of troublesome contradictions.

No matter how well constructed some rules of inference may or may not be, there is still a fundamental difference between the conclusions logical argument from that system infer, and the claim they are so inferred. For example, the statement, "if life holds an ultimate purpose, then we ought to live by it" is not inferred by first order formal logic. Whatever one suspect of someone holding that inference as true, it does not, in an analysis of logic abstractly, mean the person believes we ought to live by lives ultimate purpose or that there is such a purpose.

Formal logic, especially traditional first order logic, attempts to make only undeniable analytic assertions about inference, based on AND, OR, and NOT.  In reality these are assertions, if widely palatable ones, and in other more natural and more widely used systems of inference the inferences themselves make statements... such as racist rules of inference which make predictions based on race.

One that I would consider a true logician by my own standard will not apply just one allegedly perfect logical system to a given set of facts and statement. The true logician is a collector of logical tools, and if at all competent will have encountered more than just one set of tools.  This logician will have access to many systems of logic, and will analyze any particular collection of  facts with as many systems of logic as can be applied based on context.  The "true logician" thereby also implicitly employs a still more abstract logic, a meta-logic, a characterization on inference itself, amd ways of combining distinct systems of logic, of averaging their results, of using one to judge the other in practical applications as well as academic ones.