Refuting aristotelean logic

[robheus]

The base for logic for almost 2000 years has been the logic of aristotle, which works on the principle of logical identity.

 

"Classical reasoning assumes the principle of logical identity: A = A or A is not non-A".

 

When dealing with abstract things, like in mathematics or formal reasoning, this kind of logic works quite well. But it can be shown that for any real situation (examples will be given below) this identity just does not work right. The reason for that is that in the real world, everything develops and even things which seem (temporarily) to be static, at the micro level changes occur always and everywhere. So this means that any real thing we can think of, the identity A=A simply can not hold, because it would mean that A never changes, while we have to admit that change occur everywhere and all time. Atoms and molecules vibrate and in the nucleus the proton changes into a neutron and back into a proton trillions of times per second due to the strong force, etc.

 

At the deepest level, in quantum physics, we can simply deduce that it is even impossible to state that some thing is identical to itself at any given moment, because that would involve the impossibility of detecting all the properties of some microscopic system in all details at the same time, which the uncertainty relationship simply does not allow us. Which means, everything is always in a state of flux, at any moment in time.

 

At the other end of the spectum, at the most wide macroscopic level, it can be deduced also that what we get there is simply being, which is absolute, but then being is not more nor less then nothing, or put in other terms, the universe as a whole can not be distinguished from nothing.

 

For these reasons, and when we want to deal with the real world instead of the abstract world of formal reasoning and mathematics, a different kind of logic is needed, based on the identity of indentity and non-identity, which is dialectics, most profoundly developed by Hegel.

 

Some examples:

 

1. Living and non-living

 

In many cases we have no trouble in distinguishing living from dead or non-living, but then any medicist can tell you that the precise moment of death is less trivial. Should a virus be called a living organism or not? When is a living organism considered to be a living creature, and for example, at what stage in the development of a human being can we call it a human being?

All this cases show that the exact dividing line between living and non-living is less then trivial.

 

2. I and not-I

 

Where can we draw the line between I and not-I? Is my body part of the I? Does the air in my longues belong to I, and if not, where precisely do the air molecules or the food molecules digested become part of my body?

 

3. Human and non-human

 

Where is the dividing line between human and non-human. Suppose we set up a colony on Mars, which stay there permanently. After couple of thousand years, mutations caused them to be unable to interbread with humans from earth. Are they no longer human beings? Where exactly in our ancestry line did we become human?

 

Etc.

 

Hegel for beginners.

Edited July 6, 2012 by robheus

[Greg H.]

Actually we can still define a discrete A, even in the face of the idea that everything changes. The discrete line is that which changes separately from that things around it. If I remove the table from dining room, I can instantly see that it is a separate and discrete object from the chairs, because they are still there. If table = chairs, then they should all be in the same place. If I cut one in half, the others should suffer a similar fate - since they do not, I can rightly conclude that the one is separate from the others. Even at the atomic level, in order to say that these items form a single unit A they would need to undergo the same atomic changes at the same time.

 

The alive - not alive argument you presented makes no sense to me. On the one hand you are speaking of viruses, which are a kind of edge case to begin with, since they really can't even reproduce without other life to support it. For another thing, you talk about when is a human being considered to be a human being, which isn't the same argument. If you mean when is a human being considered alive, then the cells would be alive from the moment of conception - whether is counts as a person in the legal sense is a completely different matter.

 

 

Defining the idea of i is less concrete than it might seem, because it is inward facing, rather than outward. At the very least, I believe the concept of I can be said to include your consciousness and your physical body. After all, does not one think and the other do? And while there may be some debate of what happens to the consciousness after death, I think we can agree that the physical form, at least, ceases to function correctly once the consciousness has left it.

 

 

As for the argument of human and not human, human is only a stepping stone on the road from what we used to be towards what we will become. In another hundred thousand years we might not even be able to breed with our descendants, and they will have ceased being human. That does not mean we cannot define what it means to be human - genetically and morphologically.

 

In summary, I am failing to get how any of this refutes Aristotle's foundations of logic, and more specifically his syllogisms, which are as useful in discourse and philosophy as they are in math and the sciences.

[robheus]

Actually we can still define a discrete A, even in the face of the idea that everything changes. The discrete line is that which changes separately from that things around it. If I remove the table from dining room, I can instantly see that it is a separate and discrete object from the chairs, because they are still there. If table = chairs, then they should all be in the same place. If I cut one in half, the others should suffer a similar fate - since they do not, I can rightly conclude that the one is separate from the others. Even at the atomic level, in order to say that these items form a single unit A they would need to undergo the same atomic changes at the same time.

 

The alive - not alive argument you presented makes no sense to me. On the one hand you are speaking of viruses, which are a kind of edge case to begin with, since they really can't even reproduce without other life to support it. For another thing, you talk about when is a human being considered to be a human being, which isn't the same argument. If you mean when is a human being considered alive, then the cells would be alive from the moment of conception - whether is counts as a person in the legal sense is a completely different matter.

 

 

Defining the idea of i is less concrete than it might seem, because it is inward facing, rather than outward. At the very least, I believe the concept of I can be said to include your consciousness and your physical body. After all, does not one think and the other do? And while there may be some debate of what happens to the consciousness after death, I think we can agree that the physical form, at least, ceases to function correctly once the consciousness has left it.

 

 

As for the argument of human and not human, human is only a stepping stone on the road from what we used to be towards what we will become. In another hundred thousand years we might not even be able to breed with our descendants, and they will have ceased being human. That does not mean we cannot define what it means to be human - genetically and morphologically.

 

In summary, I am failing to get how any of this refutes Aristotle's foundations of logic, and more specifically his syllogisms, which are as useful in discourse and philosophy as they are in math and the sciences.

 

I do not disagree with the outlook that aristotelean logic has it's merits and field of application, which neither is denied by dialectics, since it does not realy replaces or refutes ordinary logic, but merely ammends it or complements it.

 

The examples I show, manifest that there are in reality no strict dividing lines between A and not-A. For example (although we have not yet a real model of how this process went on) a strict dividing line between non-living matter and the first living organism is impossible to make. Abiogenenesis supposes that before the first living cell was there, there were precursors to live, but where in that process from chemical tranformations and chemical evolution can we say that a living organism was formed?

[John Cuthber]

"The base for logic for almost 2000 years has been the logic of aristotle,"

Not entirely, it hasn't.

He got too many things wrong.

http://www.iep.utm.edu/aris-bio/#H8

[Greg H.]

"The base for logic for almost 2000 years has been the logic of aristotle,"

Not entirely, it hasn't.

He got too many things wrong.

http://www.iep.utm.edu/aris-bio/#H8

 

I'll admit Aristotle made some mistakes in his life, but then so did a lot of other people such as Einstein. That doesn't change the contributions Aristotle's propositions and his syllogisms made to modern logical thought, or that they served as an antidote to the sophistry so popular in his day.

[robheus]

In addition to this, below I have copied an article on this debate between formal logic and dialectics, which shows a more elaborated discussion on this topic.

 

Source: dialectics vs. formal logic

 

SOURCE: http://www.marco-learningsystems.com/pages/sawyer/dielectics.html

 

DIALECTIC AND LOGIC.

 

by W.W. Sawyer

 

The following is based on a talk given by me to a small philosophy discussion group in New Zealand. Arthur Prior, professor at Canterbury College, was the first New Zealand philosopher. He started a small group consisting of several philosophy students, a Catholic priest and a number of interested university lecturers, of which I was one.

 

What is dialectic? It does not seem satisfactory to take it as presented by Hegel or Engels or Heraclitus or any other single writer. In reading a philosopher, something in his approach strikes us as being sound. We should try to evaluate this sound element.

 

We had in this society an actual clash of two modes of thinking. When Garrett was told that "Unconscious Mind" was a contradiction in terms, he answered in the spirit of Walt Whitman, "I contradict myself: very well, I contradict myself."

 

Garrett's viewpoint coincides with that of most creative thinkers, whether in art or science, and I propose to call it dialectics, as against that of his opponents, formal logic.

 

If you are working towards a new theory, you discuss it with people and you divide their criticisms into two classes. Some comments, you feel, show real insight. Your critic seems to have a deeper understanding of the subject than you have yourself: if necessary you will have have to remodel your whole theory to fit in his (or her) ideas . Other criticisms strike you as purely verbal. They make no difference and you continue with your present line of thought. Perhaps you will add a footnote to explain your apparent inconsistency.

 

An example of this - William Bowyer Honey, in an essay on the nature of poetry, speaks of a poem evoking in the mind "a parallel or unwritten poem...the 'actual' poem to which the words with their meaning seem in the end the mere accompaniment."

 

All sorts of verbal criticisms could be made of the phrase "unwritten poem", but anyone who has any leaning towards poetry will recognize this as an accurate description of a real mental state.

 

Formal logic seems to assume that one can think quite satisfactorily with words. To the opposite faction it seems that words are very inconvenient and uncertain means for communicating the feelings and thoughts, the attitudes and experiences that are the stuff of reasoning.

 

First of all, we can concede that formal logic does deal quite adequately with many situations. The doorman at a cinema can argue "I have been told not to admit anyone without a ticket. You have no ticket. Therefore I will not admit you."

 

I believe supporters of dialectic, of every shade, will concede that classical logic has its sphere of usefulness. The spirit of orthodox logic seems to assume something like the following;-

 

1. That words can be exactly defined.

2. That one can then reason indefinitely on the basis of correct definitions.

3. "The interpenetration of opposites and the change of quantity into quality."

 

4. The protean character of matter: that the whole universe is made of one single substance, which is capable of assuming many forms.

 

Hegel's dialectic claimed to be a material logic: that is to say, not an abstract scheme but the logic needed for understanding the universe.

 

We should test the two approaches by seeing how they work out in practice : how they affect controversies in the past and present: how fruitful they are.

 

Certainly the idea of the universe being made out of one kind of stuff, so that anything can become anything else, does seem to have been a remarkable anticipation of the trend of science. The transmutation of elements, the conversion of matter into energy and energy into matter - certainly in physics and chemistry most of the things that were regarded as separate a century ago seem now to be regarded as interconvertible. Incidentally, physics and chemistry themselves have shown a tendency to fuse, with journals devoted to Physical Chemistry and Chemical Physics.

 

I would suggest one line of enquiry for the discussion to-night. Can any one produce a property A that in fact is capable of being exactly defined and separated from not-A? And if there are such properties, can one characterize the class they form?

 

A few suggestions:-

 

Sane and insane. Generally agreed no dividing line.

 

Biological species.Biologists generally agree that clear lines of demarcation cannot be drawn.

 

Living and not-living.The viruses, for instance, are described as having "some of the properties of living beings." I do not believe there is any real meaning in asking to which category they belong. In the medical profession there is great difficulty in saying at what moment a person becomes dead.

 

Male or female. 100% males and 100% females are rare. We have both sets of organs before birth and throw in our lot, more or less, with one side or the other. According to Coleridge the great mind is always androgynous.

 

I and not-I. People give the greatest variety of answers to this question - some regard only their minds as "I", others the whole of their bodies. Taking the latter view, where do we leave off? Is the air in my lungs "I"? I should soon cease to function without it.

 

Bertie Wooster attributed Jeeves' brainpower to the fact that Jeeves ate lashings of fish. At what point does the fish cease to be fish and become imperfectly organized Jeeves?

 

Human and not-human. At present the distinction seems a simple one. It might not be so simple if Neanderthals were still in existence. Again, it has been suggested that, if a number of nuclear bombs were exploded, the whole earth would become permeated with radioactive carbon, in sufficient quantities to upset the process of reproduction. Assuming monsters of all kinds to be born, by what test would one decide whether they were human or not? If this horrible situation actually arose, no doubt some ruling would be made on practical grounds, but whatever it was, there would be a considerable arbitrary element in it.

 

Pass and fail. No one yet seems to have produced a satisfactory procedure for separating "those who ought to pass" from "those who ought to fail".

 

Quantity and Quality.

An argument used some years ago by Lady Astor in the House of Commons may serve as an illustration of Hegel's dictum about quantity changing into quality.

 

Lady Astor had discovered that boys at Eton or Harrow -I forget which - had beer with their supper. She began by asking how, if boys of 14 were allowed to drink beer, you could stop boys of 13 drinking. From 13 she got to 12 and from 12 to 11, until she ended up with women taking babies into pubs for a drink. The weakness of the argument is that it proves far too much. You could apply it equally well to people having the vote at 21 - if so why not at 20, why not at birth? A representative of the brewers could argue that Lady Astor agreed to people drinking ginger-beer with 1%PC% or 2%PC% of alcohol; if why not ? - and so on up to vodka and absolute alcohol.

 

The dialectical thesis, as I understand it, is that any two contraries can be connected by a chain of imperceptible gradations. This does not mean that black is white. The existence of the intervening greys does not prevent us distinguishing black and white when they are direct neighbours.

 

The Appearance of New Qualities.

 

A question arising in many controversies is - can new qualities appear in the world?

 

This affects - among other topics - the theology of creation (since mind is in the world, the First Cause must have been a spirit); the origin of life (can living things arise from non-living?); the theory of evolution (can a new species arise?); the evolution of mind (can a conscious creature arise from unconscious forebears?)

 

The thesis of the static schools on all these questions is - things cannot develop; new qualities cannot appear. At each step forward - the appearance of life, for instance - something must be put into the world from outside the world. This means that the world, by itself, can only degenerate; qualities can disappear, they cannot appear.

 

Now obviously we do not want to discuss all these questions this evening; the only relevant point is - does some general principle exist which enables us to reject a priori all evolutionary theories?

 

My contention is that it is entirely gratuitous to invoke any such principle. If we see new qualities apparently evolving, there is no reason for questioning that it is actually happening, if all relevant experimental evidence points that way.

 

Connectedness.

 

One of the generating ideas of Hegel's philosophy is a sense of the connectedness of things, an idea I feel to be sound. This does not mean that every single fact is directly connected with every other, that the result of the Oxford and Cambridge boatrace depends on the climate of Mars or the colour of Sirius. But at least everything is connected with its immediate neighbours.

 

This is a much more vital aspect of the interpenetration of opposites than the possibility of a graded change from one to the other.

 

In the example of I and not-I, if you decide for example, to draw your barrier so that "I" includes my lungs but not the air in them - in what category do you put the forces acting between the molecules of my lungs and those of the air? They cross the barrier; should they count as I or not-I?

 

A similar difficulty arises in trying to make a clear distinction between mind and matter. It is beyond question that the mind and the body influence each other; that ill-health for instance can depress the mind and that a thought can lead to physical action.

 

To take the latter point - if the mind can cause the body to move, this means that the mind can exert a physical force, that the mind has physical properties. Equally, if the body has no mental properties, how does it hook onto the mind?

 

Any apparent contradiction in the question of mind and body seems to be the result of tearing apart things that are indissolubly connected together.

 

The union of opposites.

 

Earlier the objection was mentioned that the phrase "unconscious mind" combined logical incompatibles. Some time ago I read a book in which the author wrote, "I get no pleasure from having a soul. All my soul does is wake me up at two o'clock in the morning and pass votes of no-confidence in me." Such experiences, and phrases like "sleep on it" are evidence of a generally recognized activity of some kind, outside the conscious mind.

 

Nineteenth century mechanical materialism tended to regard all mental activity as a consequence of dead matter following determinate laws. For them the question of the human soul was simple enough - it was something purely physical. Freud's use of the term "unconscious mind" was an attempt to deal with the unknown activity in mental terms rather than in the language of biochemistry. In view of the kind of questions we feel the need "to sleep on", this seems essentially reasonable. (I am committing myself to the basic idea of the unconscious mind, not necessarily to Freud's account of its behaviour.)

 

Whichever end you approach it from, the appearance of paradoxes is inevitable if you cut off sharply "mental" from "non-mental". Either you have something that thinks but is unable to make the lips move and express thoughts in speech; or else you have something purely physical, a matter of chemical and electrical forces, and yet something that writes poetry,makes mathematical discoveries, regrets mistakes, repents for sins and passes votes of no-confidence in you.

 

This difficulty arises from the attempt to chop a single universe into separate pieces.

 

It may be asked - why is there no account of the answer given to this by the supporters of traditional logic? The reason is that no coherent answer was given. Professor Prior was away. Two graduate students were supposed to present the other viewpoint seemed completely disorientated by this attack from a completely unexpected direction.