COLLEGE OF
SOUTHEASTERN
EUROPE
PHI 3120
"Introduction to Logic"
Instructor: Dr. Pontikos
Essay 1
"A discussion of the laws of thought"
Tuesday, 15 July 2003
Fotios Bassayiannis
Student #: 88395
Logic and the laws of thought
Traditional logic states three laws of thought. Specifically these laws are the following:
1. Law of identity
2. Law of non-contradiction
3. Law of the excluded middle
These laws cannot be proved or disproved. In order to demonstrate them, they must be axiomatically assumed and hence to deny them is a self-contradictory act. They are presupposed in all rational -- that is, consistent -- thought and discourse. In fact it is fair to say that without these laws no rational thought is possible and thus language as a form of communication of propositional truth ceases altogether or is at least reduced to animalistic groans and moans.
In criticising or at least discussing these laws one has to consider two very serious, and it seems to me unavoidable, questions. Specifically:
· Do the laws of thought apply to all of reality?
· Are they the basic rules of reality, or of thought[1] only?
Before we entangle these questions on each of pre-mentioned traditional laws of Logic, it would be useful to briefly mention the positions held by two major philosophical schools or trends on this matter.
Rationalism holds that the laws of thought apply to everything[2] because they are the most general truths of reality. They apply not only to what we think and say but also to what we think and talk about.
Empiricism, on the other hand, holds that the laws of thought are useful verbal conventions applying only to the way we think or talk, not necessarily to what we think and talk about or even necessarily how we must think or talk.
a) The Principle of Identity
Simply stated, the first of the fundamental laws is a tautology. If any statement is true, then it is true. Some have criticised this first principle on the basis that things change. For instance, in 1790 one could make the statement: "The United States of America is made up of 13 states." But obviously such a statement is not true today. However, the fact of change in human affairs does not negate this principle of logic. Statements that change over time are said to be "elliptical", or incomplete statements. Thus, the statement "The United States of America is made up of 13 states" is a partial formulation of the statement, "The United States of America was made up of 13 states in 1790." Such a statement is as true today as it was in 1790. Thus, when we confine our attention to complete or non-elliptical formulations, the Principle of Identity seems to be perfectly true and unobjectionable in all possible worlds[3].
b) The Principle of Non-contradiction
Simply proposed, this principle asserts that "no statement can be both true and false." Or to take it a step further, "a given thing cannot be and not be in the same way and to the same extent at the same time." This is possibly the most vital principle of the three, since it seems that without it reasoned thinking is not possible at all. While it may seem obvious, for instance, that a given object cannot be both an apple and a peach, this principle is often ignored or twisted out of shape by various philosophical schools or treatises.
The word "paradox" is used sometimes to describe contradictions -- contradictions that, some would say, must be accepted. For instance, the famous experiments with light, which indicate that under certain experimental conditions, light can be demonstrated absolutely to be made of particles, while under other experimental conditions, light can be demonstrated absolutely to be made of waves. A pure contradiction, to say the least! In some scientific circles it has been concluded that light is both and neither and that consequently we must live or learn to live with this blatant contradiction. In my opinion a more educated or "logical" if you like approach is to say that the experiments, so far conducted, have settled nothing and that further study is needed before we grant existence to this contradiction. We can't just throw up our hands and say, "oh well, it's both; lets say light is made of 'wavicles'." What, in the name of logos, is a 'wavicle'?
The same thing arises in theology in attempts to explain the Trinity, the relationship of free will to divine sovereignty, or how a good, all-powerful God could permit sin. Too often, theologians are satisfied with the paradox -- "the apparent contradiction" -- and leave it at that. I cannot bring myself to accept such a treatment of occurring "paradoxes" or logical inconsistencies, as I prefer to address them, for I think that if a single instance of failure of the laws of logic is permitted then eventually the whole discipline will gradually collapse.
I believe that this last argument is best expressed in the following quotation: "Nature poses many riddles but contains no contradictions. By solving one of her puzzles, therefore, we are guaranteed to learn something -- and the weirder, the more impossible the paradox seems at first, the more mind-expanding will be its ultimate resolution." [F. Wilczek and B. Devine. Longing for the Harmonies: Themes and Variations From Modern Physics, New York: W.W. Norton, 1988, p. 218]
What all this means then, is that contradictions cannot be real. Such a conclusion is a very hopeful and useful tool, and has been of immense impetus to scientific research, because its implicitly stated principle of non-contradiction assures the researcher, in whatever field, that there is, indeed, an answer to any conundrum. And if there is an answer, then it is possible to find it. What could be better motivation for research than the assurance of the existence of a final result.
On a personal or ethical level, this principle of non-contradiction has some serious implications. Every day, we discover people who, within their lives, are not living up to the principle, that is they explicitly contradict themselves. George Orwell described the problem with the term "doublethink". An older word for this sort of person is simply "hypocrite". The Bible calls such a person a "double-minded man" and of course Nietzsche calls him a "priest"[4].
Of course what is in our heads rarely matches our practice, and often even contradicts other ideas in our mind, but this is only a problem when logic and its laws are treated psychologically - that is non-objectively. The psychological treatment of the laws of thought is in my opinion wrong because logic is a discipline developed to state in a formal way how we ought to think and not how we tend or have grown accustomed to think. Humans are strange that way.
Still, contradiction and life as we know it are probably
much more related than one would like to think since for objective truth to be
reached a "valid inference" formalised mechanism[5] has to be fed with true
premises. Characteristic to this fact is the following quote from George
Orwell's "1984": "The Party said that Oceania had never been in
alliance with Eurasia. He, Winston Smith, knew that Oceania had been in
alliance with Eurasia as short a time as four years ago. But where did that
knowledge exist? Only in his own consciousness, which in any case must soon be
annihilated. And if all others accepted the lie which the Party imposed -- if
all records told the same tale -- then the lie passed into history and became
truth. 'Who controls the past,' ran the Party slogan, 'controls the future: who
controls the present controls the past.' And yet the past, though of its nature
alterable, never had been altered. Whatever was true now was true from
everlasting to everlasting. It was quite simple. All that was needed was an
unending series of victories over your own memory. 'Reality control,' they
called it; in Newspeak, 'doublethink.'
'Stand easy!' barked the instructress, a little more genially. Winston sank his
arms to his sides and slowly refilled his lungs with air. His mind slid away
into the labyrinthine world of doublethink. To know and not to know, to be
conscious of complete truthfulness while telling carefully constructed lies, to
hold simultaneously two opinions which cancelled out, knowing them to be
contradictory and believing in both of them, to use logic against logic,
to repudiate morality while laying claim to it, to believe that democracy was
impossible and that the Party was the guardian of democracy, to forget whatever
it was necessary to forget, then to draw it back into memory again at the
moment when it was needed, and then promptly to forget it again, and above all,
to apply the same process to the process itself -- that was the ultimate
subtlety: consciously to induce unconsciousness, and then, once again, to
become unconscious of the act of hypnosis you had just performed. Even to
understand the word "doublethink" involved the use of doublethink.
[George Orwell, 1984, pp. 35-36]
c) The Principle of the Excluded Middle
The principle of the excluded middle asserts that "any statement is either true or false". Some have objected that if this principle is accepted one is forced into a "two-valued orientation"[6] which implies that everything is "either this or that", with no middle ground possible. Such an objection results from a misunderstanding of the principle. If you have something that is grey, for instance, the statements "this is black" or "this is white" are both false. When faced with a situation where one is given such statements, "this is white" or "this is black", while both statements cannot be true, they very easily might both be false, for "this is white" being false does not mean that "it is then black"; it merely means that "it is not white and it could therefore be anything else". Once again, when one restricts oneself to statements that are unambiguous and precise, then the principle of excluded middle[7] is perfectly valid. In other words, what this principle asserts is that a REAL paradox is not possible, only an APPARENT paradox is, and that usually is the result of language limitations or insufficient data[8]. By the principle of excluded middle, when faced with the question of whether light is made of waves or particles, since the experiments contradict each other, it is best to assume that light is neither wave nor particle, but something else: GRAY[9].
Concluding, I would like to say that logic can be very powerful if properly implemented to any problem - that is to a given set of premises - but for it to work properly great precision is needed and the sad fact is that precision is not one of the defining properties of the human being. One could generalise here and say that the whole - corporeal at least - world is not precise at all and that then the whole discipline of logic wholly belongs to some other realm of reality, comparable to the mathematical or number realm of the Pythagoreans.
These are crucial points that in no case should be taken lightly, but on the other hand logic is not necessarily something non-adaptable to real world although it bears strong mathematical roots. One thing is sure, logic has worked fairly well up to now.
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The main problem with the discovery of truth though is not to be found in the essence of logic - that is in the science of valid inference - but in the following question: How can one be sure that the premises fed to any logic formula are true to begin with?
BIBLIOGRAPHY:
Cohen, M.R. & Nagel, E., , An Introduction to Logic and Scientific Method , London 1934
Stebbing, S., A Modern Elementary Logic, London 1952
Friend, A., Help for my Friend Fotis, Athens 1998