From the strong response in letters received after the recent editorial on logic, I gather you like questioning the whole subject. Obviously, I do too. So... let's try another approach, and see if we can't find something somewhat different from either the A or non-A business.
Let's define logic as "one of the methods of rational thinking". Conventionally, "logical" and "rational" have been considered synonymous; evidently that's stretching the meaning of logic quite a bit, or else using an exceedingly peculiar definition that's based on the individual's viewpoint on the matter at a particular time and/or place. I suggest that there are several other methods of rational thinking, and that neither Aristotelian nor non-A is adequate - that, in other words, logic is necessary but not sufficient.
You can get some most peculiar effects from considering data that is true, and nothing but the truth. For instance, it is perfectly true that I habitually come from my suburban home into New York City floating about four feet off the ground. I don't come down to Earth - and that's a true statement.
The fact that there's a train between me and the ground is, however, the rest of the truth. Frequently the truth and nothing but the truth is a particularly vicious kind of he, because it can not be disproven or attacked in any way. I could, for instance, get twenty or thirty witnesses to confirm my statement that I came into New York without once touching Earth, and no witness could be found who could testify otherwise.
Logic has been based on the use of high-probability data; actually, the concept "true" and "false" can be interpreted as "probability of truth equals 1.000" and "probability of truth equals zero". It's mighty easy to evaluate data when the data can be classified in that nice, easy, put-up-or-shut-up manner. A relay is either open or closed - provided the contacts aren't dirty, and haven't welded together. A man is either alive or dead - until we find out how to suspend animation. A star either is visible out there in space, or it isn't - unless it's one of an eclipsing binary pair.
The unfortunate fact of the Universe is that, as Information Theory shows, the real physical Universe contains noise, and always will contain noise. There is no statement of Probability 1.000, and no statement of Probability Zero - save in the non-physical system of theoretical discussion.
The interesting and necessary conclusion from that fact is that mathematics, like Euclidean geometry, does not apply to the real Universe; mathematics is a noise-free system, and therefore cannot be congruent with the real, noise-containing Universe. And there cannot ever be any exact science that is congruent with the real Universe. No computing machine can ever be built which is both constructed of real physical components, and is congruent with the system of mathematics; the machine can only be tangential to the field of mathematics, because it, being physical, must contain noise, while the system of mathematics does not.
One consequence of that is that any real physical computer will, inevitably, have breakdowns. The observed fact is that they do!
Now I have done a great deal of my thinking on the basis of inadequate data, inaccurate data, using as data the fact that there was a lack-of-data, and that the data-is-inadequate. In the field of logic, which has been confined to high-probability data, that sounds like a prescription for "How to think in a sloppy and improper manner". It isn't. But it will get you into some highly frustrating arguments, since the method of thinking involved is not accepted generally.
Consider this: an ordinary silk thread cannot support the weight of an automobile. This is an easily demonstrated fact. I can prove, then, that this specific thread, #1, cannot do it. Neither can thread #2, which I can test and prove inadequate. Neither can thread #3, which likewise fails under test. Nor thread #4, #5, #6... #n. You see, I have proven that there is not one single bit of evidence which you can show me that silk thread will support an automobile. I can break down every single piece of evidence you bring up. Not one of those one hundred thousand threads you brought up as evidence that silk could support an automobile would actually stand up on examination, and that proves that you cannot lift an automobile with a silk cable.
I suggest that, in addition to the standard, conventional logical argument, there is also a quite different thing - the gestalt argument. The argument in which there is not one single argument of any useful strength - but in which there are many, many lines of argument which, as a gestalt, are more powerful than any single argument could be!
This is argument based on barely significant data, improbable data, inaccurate or inadequate data - which is, none the less, a completely sound argument. In terms of probability, it can be put this way.
Suppose there are ten steps, a sequence of ten dependent events. Each individual step has a probability of 0.1. We can represent this as "if A, then (0.1 B):: if B, then (0.1 C):: if..." et cetera.
Now in such an event sequence of ten steps, the product probability of the tenth step will be 10^-10 - one chance in ten billion.
The above argument is a logical argument - i. e., a one-line-of-development argument. But let's consider a gestalt argument on the same subject.
It's true that the probabilities are such that "if A, 0.1 B" applies on one line of development. But it happens that there is also "if A, then (0.05 A1)" and also "if A, then (0.08 A2) and "if A1 or A2, then (0.5 B)" applies. And in addition, there are several other sequences involving A-to-A1-A2-to-B and a lot of other routes. In addition, there are various crossovers from B to side-chains that also lead to C. In fact, careful investigation reveals that there are, actually, ten trillion different possible lines down the whole ten-event sequence, no one of them having a probability higher than 10^-10th - but the summated probability products turn out to have a value of 0.99!
Now a chain is as strong as its weakest link - because it's a single-line development. Logic operates on that principle, and a logical argument can be completely shattered by breaking any one link in the sequence.
But a cable doesn't have links; breaking any one strand does not break the cable. And a gestalt argument doesn't depend on any single link, or any single line of development. Like the fibrous construction so typical of the strength of living things, each line of development is independent, but interactive; it will not shatter under stress, but is capable of elasticity. It can't be handled very easily by a mathematical process, because it's a noise-filled system; it's so interactive that breaking one line of development interacts to put more stress on the other fines of development. Many times blocking of one fine of development simply increases the probability of another, while at other times, blocking one decreases adjoining and subsequent probabilities.
Gestalt argument methods simply haven't been formulated, and can't, at present, be described in detail. We're stuck with that. But we must, also, recognize that logic is the truth, and nothing but the truth - but a lie, if we don't recognize that it is not the whole truth.
In addition to gestalt arguments based on multiple-channel low-probability developments, there is a third method of rational thinking that has not been adequately formulated, but evidently does exist; let's call it analogic. Since I can't formulate either gestalt rationality, nor analogic rationality, I can't derive a sharp distinction between them, and show where the boundaries are such that they do not overlap. But that there are two distinct non-logical rationalities I think can be shown.
When aeronautical engineers work with models in wind tunnels they have to do some very tricky mathematics, based on some rather largely empirical formulas called the Laws of Models. If you build a full-size fuselage and wing system having exactly the form of the model that tested successfully - you'll have a Grade A flop. The engineers are forced, by practical considerations, to experiment with models - which are analogous to the full-scale ship they want to build, but not similar to it. The full-scale ship will not work right if its form is similar in the sense the term "similar" is used in geometry - having the same angles and length-ratios.
In making the transformation of dimension ratios, the engineer is using analogic; he is reasoning by analogy, in one of the very few areas where analogical reasoning has been sufficiently formulated to be acceptable.
Any logician will throw out as not legitimate logic an effort to use reasoning by analogy; it has been held for many years that analogic reasoning is not logical reasoning. But analogic is rational! The Navy researchers towing test hulls in the Navy's tow tank depend on the rationality of analogic. In actual everyday living and thinking we must depend on analogic - yet we cannot defend our analogic in debate because there has never been an adequate formulation of the Laws of Analogic. This doesn't mean that no such laws exist; it simply means that we haven't found them yet.
Yet all science is, actually, based on the use of gestalt rationality and analogic rationality, far more than on logic, when the matter is investigated. Logic is the result finally achieved by the preliminary use of analogic and gestalt thinking.
Cosmologists are studying turbulence in a small laboratory pool of water in an effort to better understand the interactions of spiral nebulae. They find that galaxies collide, sometimes, and show viscous characteristics. How can that be? If we could formulate analogic, we could study better the pool of water, the swirl of gas in a near-vacuum, the eddy-in-space that is an atom.
Stellar mechanics has been greatly helped by the study of a large pool of mercury metal in a strong magnetic field. But if we just knew the Laws of Analogic, we could do a lot better.
Logic is only one of the methods of rational thinking!

March 1954

END