Logical Reasoning and Research


James W. Cornman and Keith Lehrer. Philosophical Problems and Arguments. New York: Macmillan. 1974.

William Poundstone. Labyrinths of Reason. New York: Doubleday. 1988.

The Encyclopedia of Philosophy. Vol. 5. "Logic, Traditional", by A.N. Prior. New York: Macmillan, pp. 35-45, 1967.

Milton D. Hunnex. Chronological and Thematic Charts of Philosophies and Philosophers. Grand Rapids: Zondervan, 1986.

I. The Problem of Knowledge

Proverbs 14:15

A simple man believes everything,

but a prudent man gives thought to his steps.

What is Logic? It is the study of the principles of reasoning, especially valid reasoning, as distinguished from invalid or irrational argumentation.

Logic is studied as a means of testing the validity of arguments -- specifically decutive arguments. An argument is a sequence of statements, one of which, the conclusion, is said to be logically deducible from, or a logical consequence of, the others, which are called premises.

Examples of arguments:

1. Sophocles was a philosopher or Socrates was a dramatist;

Sophocles was not a philosopher;

Therefore, Socrates was a dramatist.

2. Some philosophers are Platonists;

Some mathematicians are philosophers;

Therefore, some mathematicians are Platonists.

Arguments thus make claims, namely, that certain conclusions follow logically from, or are logical consequences of, certain premises. We count on logic to tell us just which arguments make valid claims and which do not.


What is a valid claim? Before this question can be answered, a distinction must be made between the validity of an argument and the truth of its conclusion. These are not the same: not all valid arguments yield true conclusions -- see 1 above. Conversely, not all arguments that yield true conclusions are valid -- see 2 above. Similarly, there are valid arguments with false premises, like 1 and there are invalid arguments with true premises, like 2. The question of the validity of an argument is therefore separate from that of the truth or falsity of its premises and conclusion. To say that an argument is therefore separate from the truth or falsity of its premises and conclusion. To say that an argument is valid is to say that its conclusion is a logical consequence of the premises, which is to say simply that if the premises are all true, then the conclusion must also be true. No claim is made with respect to the actual truth or falsity of any premise or conclusion; however, if the argument is valid, then it cannot be the case that the premises are all true and the conclusion false.

It is helpful to use another term, "sound", to refer to arguments that are both valid and contain true premises. Thus sound arguments satisfy two conditions a) they are valid and b) they proceed from true premises. Since the logical consequences of true premises must be true, sound arguments necessarily have true conclusions. An example is the following:

3. All human beings are mortal.

Socrates is a human being.

Therefore, Socrates is mortal.

Logic limits its concern strictly to problems of validity; the task of obtaining true or well-confirmed premises it leaves to other disciplines; however, the task of this class is to include some of those other disciplines.

So, we will also study the nature of induction, which covers all cases of nondemonstrative argument, in which the truth of the premises, while not entailing the truth of the conclusion, purports to be a good reason for belief in it. Under this category, we would include the scientific method.

The purpose of this study of course, is to help you discern the truth when you see it, and a lie when you see it.

A. Questions

1. What is mind?

This is also called the mind-body problem. Is the distinction between mind and body valid? It was Plato who was the first to make a sharp distinction between the mind and the body, holding that the mind could exist both before and after its residence in the body and could rule the body during that residence. St. Augustine further developed this distinction and theorized I more detail about the relation between the two. But it was Descartes who first developed a systematic theory of the natures and interrelationship of mind and body.

2. What is known?

That which is true.

3. What is knowing?

Discovering that which is true. The process of apprehending that which is true.

4. What is true?

It has been suggested that the requirement that what is known be true is excessively stringent. Complete certainty of a statement's truth is not to be had; the best we can achieve is very strong grounds for thinking it true. Thus, if knowledge entails truth, we can never attain knowledge or, at any rate, never know that we have done so.

This objection is misconceived.

If I firmly believe that something is true on what I take to be sufficient grounds, I am right to say that I know it. It may be that the grounds are, in fact, insufficient and that what I claim to know is false. In that case my claim is mistaken, but it does not follow that I was wrong to make it in the sense that I had no justification for doing so.

It has also been argued, with a view to showing that knowledge and belief are quite distinct and unrelated, that whereas beliefs can be true or false, knowledge is neither. The argument exploits the fact that we speak of a belief but not of knowledge. Furthermore, since all items or pieces of knowledge are by definition true, we never need to speak of them as true items or pieces in order to distinguish them from false ones.

5. What is valid?

A logical argument.

6. What is scientific?

The scientific method: questioning, redundancy, testing.

7. Is genuine knowledge possible?

Can we really know anything at all?

8. Is knowing innate or experienced or both?

Are we born with knowledge, or does it all come to us from outside sources? A priori vs. a posteriori. I think, therefore I am, vs. the sky is blue.

What are the answers? Are there any answers? Are any answers possible?

At first glance, these may sound like the sort of questions blitzed college students would be asking themselves at two in the morning. However, they actually have relevance and importance -- because they will help you form your grundstam, your basis, your foundation.

Socrates said that you must "know yourself", and "the life unknown is not worth living." It is a requirement for reasoned thinking that you know what you believe and why, and so it is necessary to begin at the very bottom, at the most basic presuppositions that you take so much for granted that you don't even know they could be questioned or that other points of view could even be possible.


Blue sky, sunshine, deja vu glazed with dread. Something horrible is going to happen about now. It is a perfect summer day in a meadow of tall grass. J.V. is following her brothers, lagging lazily behind. A shadow falls on the ground; something rustles the grass. J.V. turns -- she cannot help it, it is what happens next -- and sees a strange man. He has no face, like a minor character in a dream. The man holds something writhing and indistinct. He asks, "How would you like to get into this bag with the snakes."

J.V.'s encounter is an unlikely milestone in twentieth century thought. J.V., a fourteen year old girl, was not in a summer field but on an operating table in the Montreal Neurological Institute. Her physician, Wilder Penfield, was attempting an experimental operation to relieve her violent epileptic seizures. The operating team had removed the side of J.V.'s skull to expose the temporal lobe of the brain. In order to locate the site of the attacks, Penfield probed the brain with an electrode connected to an EEG machine. The surgery was a collaboration between physician and patient. J.V.had to remain conscious throughout and help locate the site of the seizures. When Penfield touched the probe to a certain spot on J.V.'s temporal lobe, she again found herself in the field of grass...

J.V.'s experience with the strange man had occurs seven years earlier, in Canada, in what we call the real world. She reported seeing herself as she was then, a seven year old girl. J.V. had been frightened but not physically harmed, and ran crying home to her mother. These few moments of terror were to haunt her over and over. The man with the bag of snakes entered her dreams, made them nightmares. The trauma became interwoven with her epileptic seizures. Like a madeleine, a fleeting recollection would trigger the whole memory, then an attack.

Under the EEG probe, J.V. not merely recalled, but relived the encounter. All the richness of detail, all the lucid horror of the original experience, came back. Penfield's probe caused the brain to replay past experiences like a movie. With bits of lettered or numbered paper, Penfield kept track of the sites on the cerebral cortex associated with the recollection. Touching nearby points produced different sensations. When the probe touched one point, J.V. remembered people scolding her for doing something wrong. Other sites produced only a phantasmagoria of colored stars. (pp. 3-4. Labyrinths of Reason, by William Poundstone. 1988. New York: Doubleday -- this is an incident that happened in the 1930's)


You think you're sitting there in that chair, when really you're a disembodied brain in a laboratory somewhere, soaking in a vat of nutrients. Electrodes are attached to the brain, and a mad scientist is feeding it a stream of electrical impulses that exactly simulates the experience of sitting in class.


"How do you know this isn't all a dream?"

The best known tale of this sort is the Chinese tale of Chuang-tzu, dating from the fourth century BC. Chuang-tzu was the man who dreamt he was a butterfly, then awoke and wondered if he was a butterfly dreaming he was a man.

The fable is unconvincing, however. It is true that we usually don't realize we're dreaming, but a waking person always knows he's not dreaming, right?

Opinions differ.

Rene Descartes in his "First Meditation" (1641) decided he couldn't be ABSOLUTELY sure he wasn't dreaming. Most people would probably disagree with Descartes. You're not dreaming now, and you know it because experiences in dreams are different from those in waking life.

Saying exactly HOW they're different is difficult.

1. Pain -- pinching yourself? But I've felt pain in dreams.

2. Few dreams are in color, so if you can see color -- but then again, maybe you dream in color.

3. Real life usually seems more detailed. If you can add a column of numbers then check the results on a calculator, then you're awake. Or if you examine a wall and can see all the little cracks, then you're awake.

Or, maybe you're dreaming you're doing those things, now that you've heard that such things can "prove" you're awake.

4. Some say the fact you wonder if you're dreaming or awake proves you're awake -- except then you could never dream in which you realize you're dreaming.

5. Keep a book of limericks by your bed. Don't read it. But whenever you want to know if you're dreaming, open it at random and read a limerick, making sure it is one you've never read or heard before. Most likely you cannot compose a bonafide limerick on a moments notice. (of course Samuel Taylor Coleridge composes his masterwork "Kubla Khan" in a dream. Of course, Coleridge was a poet in his waking life; the limerick test is only good for people who can't easily compose a limerick.)


Renes Descartes and his evil genius bent on deceiving him, a malicious demon of the utmost power.


BRAINS in VATS is the quintessential illustration of what philosophers call the "problem of knowledge". The point is not the remote possibility that we are all brains in vats but that we may be just as deluded in ways we cannot even imagine.


The whole of experience is a stream of nerve impulses. The roughness of a stone, the sound of a coin dropping on the floor, the odor of a fart. We have all IMAGINED a world that might account for the unique set of nerve impulses we have received since (and several months before) birth. The conventional picture of a real, external world is not the only possible explanation for the neural experience. We are forced to admit that an evil genius or a brains in vats experiment could explain the neural experience just as well. Experience is forever equivocal.

Science places great faith in the evidence of the senses.

Most people are skeptical about ghosts, the Loch Ness monster, and flying saucers, not because they are inherently stupid notions, but only because no one has produced unquestionable sensory evidence for them. Brains in vats turns this apparently reasonable skepticism inside out. How can you know, by the evidence of your senses, that you are not a brain in a vat? You can't!

The belief that you are NOT a brain in a vat can never be disproven empirically. In the jargon of philosophy it is "evidence transcendent."

This is a serious blow to the idea that "everything can be determined scientifically." At issue is not some bit of trivia such as the color of a tyrannosaurus. If we cannot even know whether the external world exists, then there are profound limitations on knowledge. Our conventional view of things might be outrageously wrong.


Descartes' evil genius was the starting point of an investigation into how we know what we know. Descartes wrote: "Some years ago I was struck by the large number of falsehoods that I had accepted as true in my childhood, and by the highly doubtful nature of the whole edifice that I had subsequently based on them. I realized that it was necessary, once in the course of my life, to demolish everything completely and start again right from the foundations if I wanted to establish anything at all in the sciences that was stable and likely to last."

Descartes wanted to address the problem of knowledge in much the same way that Euclid had treated geometry two thousand years earlier. All of Euclid's geometry is deduced from a set of five axioms. An axiom was, in Euclid's time, a statement so obviously true that one could not imagine a world in which it was false ( for instance: "A straight line can be drawn between any two points). All the theorems -- provably true statements -- of traditional geometry can be derived from Euclid's five axioms.

Descartes wanted to do the same thing with the facts of the real world. He needed to identify a set of facts known with utter certainty. These facts would be the axioms of his natural philosophy. Then he would establish valid rules of inference. Finally, Descartes would use those rules to deduce new facts from the original set of incontestable facts.

Unfortunately, almost any statement about the real world has some degree of doubt. Descartes found the ground floor of his natural philosophy vanishing beneath his feet.

This dizzying "whirlpool" aptly describes ONTOLOGY, the study of what is real. The first thing to realize in constructing an ontology is to realize that the accepted, everyday "facts" of the external world are disputable.

You can almost always come up with a scenario in which unquestioned beliefs can be wrong.

Is Paris the capital of France.


It's barely conceivable that our government is a totalitarian conspiracy that, for reasons of its own, does not want its citizens to know the REAL capital of France. They've rewritten all the history and geography books, and force teachers to indoctrinate each new generation of children with the Paris fiction. You say you went to Paris last summer and saw a bunch of official looking French government buildings there? That could have been a theme-park simulation maintained by our government to give its citizens the illusion of freedom of travel.

Wild fancies like this should not obscure the fact that some things are more disputable than others. By most people's standards, the Loch Ness monster is less real than a tyrannosaurus, and both are less real than the elephant you saw at the zoo last Sunday. What is most certain of all?

A popular answer is the truth of logic and mathematics. Even if your first grade teacher was the dupe of a conspiracy bent on teaching you falsehoods, you cannot doubt that 2 plus 2 is 4. Right now, you can picture two things, and put two more things beside them, and see that the total is four. The deduction seems obviously true in any possible world, be it the external world we believe exists, the brain in vats laboratory, or something stranger yet.

But there are two problems with these answer.

1. You can take the ultra-skeptical position that even logic and mathematics are an illusion. Just because you don't see how you could be wrong about 2 plus 2 is for doesn't guarantee it is right.

Your brain is evidently in a certain state when you come to a valid conclusion of logic or mathematics. What's to stop the brains in vats overlords from deluding you about arithmetic as well as the physical world? Maybe 2 and 2 equals 62,987, but by stimulating your brain in a precise way, the mad scientists have you thinking it is four, and even thinking that it's OBVIOUS that it's 4 and you can PROVE it is 4. Maybe somewhere they've got a whole row of brains in vats, each one believing in a different sum for 2 and 2 and immersed in a different "reality" consistent with that sum.

Philosophers rarely take skepticism so far.

2. The other, more pragmatic problem with restricting certainty to logic and mathematics is that it leaves us with no way of justifying beliefs about the physical world. Certainty about is not going to tell us what the capital of France is. So, are there any facts, aside from logic and mathematics, about which we can be certain?

We would prefer to think so; but belief in the possibility of knowledge is the consequence of our presuppositions -- and thus ultimately unprovable. But, we will propose that it is not unreasonable, though there are schools of thought which would argue just the opposite...