George A. Blair
Copyright © 1988
by George A. Blair
0.1. The subject-matter
0.2. Plan of the book
Chapter 1: Doubt and Skepticism
1.1. How to appear wise
1.1.1. The prevailing "wisdom"
1.2.1. Descartes' methodic doubt
1.2.2. Something that can't be doubted
Chapter 2: Opinion and Absolute Knowledge
2.1. Modern-day closed mindedness
2.2.1. Something that is absolutely true
2.3.1. Opinion, faith, and testimony
188.8.131.52. Religious faith
Chapter 3: The Basic Laws of Thought
3.1. The Principle of Contradiction
3.1.1. Its self-evidence
3.1.2. The Principle of Identity
3.1.3. The Principle of the Excluded Middle
3.2. The Principle of Causality
3.2.1. History of the Principle
3.2.2. Causality and evidence
Chapter 4: Certainty, Probability, and Induction
4.1. The kinds of certainty
4.1.1. Certainty and evidence
4.1.2. Opinions and certainty
4.2.1. The "law of averages"
Chapter 5: Subjectivity and Objectivity
5.1. The Kantian problem
5.4. Objective knowledge
5.4.1. Toward a solution
5.4.2. Why we can agree
184.108.40.206. Science to the rescue
Chapter 6: Concepts, truth, and goodness
6.1. Sensations and concepts
6.3.1. Goodness/badness and humor
6.3.2. Pragmatism's criterion of truth
Chapter 7: Language
7.1.1. Its social arbitrariness
7.1.2. Meaning in language
Chapter 8: Logic I: Propositions
8.1.1. Kinds of sciences
8.3.1. The proposition
8.3.2. The "quantity" of terms
8.3.3. The pseudo-quantity of the predicate
8.3.4. Some notes on translation
Chapter 9: Logic II: The Lesser Operations
9.1. Single-proposition operations
9.1.3. Multiple conversions and obversions
9.2. Compounding propositions
Chapter 10: Logic III: The Major Operations
10.2.1. "Material implication"
10.2.2. Some English compounders
10.3. The "square of opposition"
10.3.1. The great "some" controversy
10.3.2. Makeup of the square
10.4. The categorical syllogism
10.4.1. Rules of the categorical syllogism
10.4.3. A Blairian addition
INTRODUCTION0.1. The subject-matter
This is not, really, a book on how to think, because there are no rules on how to think.
Thinking, as I have tried to show in my book Living Bodies, is a spiritual act, one that is "transparent" to itself, or one that knows what it is doing while it does it. If you are a human being, you have the same power to think that every other human being does. You may not have the same data available (because of lack of information or lesser or greater brain-power to be able to hold data in your consciousness at one time); but, given the data, your capacity to think about it is the same as anyone else's. Spiritual acts have nothing by which one could be said to be greater or less than another.
Nor is it a book, exactly, on what thinking is. That again is something you find out about in the philosophy of man.
What the first part of it is is a book on the relation between our acts of thinking and the object we are thinking about. When we think about an object, is what we are thinking about "in our mind" or "outside" it; do we think accurately about it, so that what we think it is is what it actually is, or is thinking about the object distorted, and if so how?
That is, the first part of the book deals with truth, and whether our knowledge of things is objective and accurate, or whether we don't know things as they truly are.
DEFINITION: The name of the science that investigates knowledge from the point of view of its relation to what is known is EPISTEMOLOGY.
Then, once we have settled, so far as it can be settled, in what sense or to what extent our knowledge is objective, accurate, and truthful, we will take up the relation of our knowledge to the expression of our knowledge in such a way that it can be communicated to others: in other words, language as an expression and communication of knowledge.
Once we have looked at what language does as an expression of (factual) knowledge, we will then take up ways in which our language can be manipulated so as to give us new knowledge that we didn't have before.
DEFINITION: The name of the science that gives the rules for manipulating statements to get new statements is FORMAL LOGIC.
It might seem that when we get to logic, we are then giving lessons in how to think. But this is not really true either. When we reason, we are using logic and thinking, so that we see what we are doing, why we are doing it, and why the new statement emerges from our manipulations, as well as what the new statement means.
For instance, if you put together the statements, "Every human being is something that begins to exist," and "everything that begins to exist is something that is not master over its own existence," you see how you have to say, "every human being is something that is not master over its own existence." Either that, or you have to disagree with one or the other of the two statements.
That is reasoning; when you do logic and see how the conclusion follows from what you have said. It involves thinking.
But logic itself is just the manipulation of the statements, and good logic is the manipulation of the statements in such a way that a new statement is forced (that is, good logic follows certain rules whose purpose is to force new statements). And you don't need to think to do logic, even good logic. Machines can do it--in fact, sometimes better than we can, because thinking sometimes gets in the way of doing logic accurately (if the statements are confusing).
Anyone who can read this book can actually do much more complicated logic that it will talk about; just as anyone who can speak English can "do" more complicated grammar than the kind of thing people study in English classes. What the book will try to do is what grammar courses do with the language in another respect: this book will try to show what the structure of logic is, and why the various manipulations work.
The practical usefulness of the logic section of this book, then, is more or less the same as the practical value of studying grammar: when unusual cases come up, a person can fall back on the rules and find out what is the correct procedure. Thus, in grammar, you might wonder whether "between you and I" is correct, or whether it should be "between you and me." If you know that prepositions take the objective case, then it has to be "between you and me," however "vulgar" this might sound. Similarly, when you see "Every German Shepherd is a dog, and nothing that whinnies is a German Shepherd; and so--what?" you will be able to figure out that the correct conclusion is, "Some dogs do not whinny."
Of course, we aren't usually vitally interested in non-whinnying dogs, but it's nice to know logic to be able to spot what are called "fallacies" that are foisted upon us by everyone from politicians to salesmen.
0.2. Plan of the book
So we will first take up the relation of our knowledge to its object.
The first topic under this heading will be whether we are ever absolutely certain of anything at all: that is, whether it is ever the case that it is absolutely impossible for us to be mistaken. It turns out that it is. We are absolutely certain of some facts, and to deny this is to assert it.
Next we will deal with the issue of whether what is true and certain for you is true just for you or whether there are things that are known to be true that are true for everyone. And again, it turns out that there are some facts that do not depend on a person's point of view--and the assertion that everything depends on your point of view is an assertion that some things (the assertion itself) don't depend on your point of view.
We will then discuss the basic law of all knowledge: the Principle of Contradiction: something that is known for certain by everyone, no matter what his point of view.
This will lead us into a discussion of certainty, and we will discover that there are different sorts of certainty, each of which is a kind of certainty and not probability or likelihood, but that not everything that is known for certain is known with absolute certainty. But the facts that can be known with absolute certainty are generally facts that deal with our knowledge of our own knowledge; and at this point, we will bring up the question of how we know about things outside us, if our knowledge is based on reactions to things, and reactions are subjective and not objective.
Having set up the problem, we will try to solve it by discovering the objectivity of relationships among our reactions to things; and these relations (concepts) are parallel to the relations among the things "out there": and those relations are called "facts." Hence, our objective knowledge is that of facts.
We will have to say something about abstraction at this point, and why, though abstraction leaves something out, it does not of itself distort our knowledge, so that we actually can know facts about the world outside our minds.
We will then discuss what truth is, as the relationship of agreement between what we think the fact is and what the fact actually is. We will find that it is possible to make mistakes, and how, having made them, we can set about discovering that a mistake was made and correcting it.
This relation between the fact and our knowledge of it will be explored a bit, showing that that same relation, from one point of view, is the truth/error relation, from another is the good/bad relation, and from another is the relation we call "humor." We will not spend much time on the latter two ways of considering the relation, however, since this is a book on knowledge or truth.
Truth will then be investigated more fully, in its various senses: the truth opposed to error, that opposed to lying, and that opposed to falseness. We will see how something can be true (in one sense) and not true (in another) at the same time, with no contradiction.
The truth/lie and truth/false relations will lead us into an investigation of the expression of our factual knowledge in perceptible form, or in language in general.
After an initial discussion of what language is about, we will get into the type of language that expresses factual knowledge: what statements (or propositions) are, and what their parts correspond to in our knowledge of the facts. We will learn what the subject of a statement is and why there are such things, and what the predicate is, and why it is different from the subject.
That will then allow us to start manipulating language, and doing logic.
First, we will learn logical operations dealing with a single proposition: how you can "convert" it and "obvert" it and get new propositions from it.
Then we will learn what you can do with terms by manipulating their "quantity" and "quality," so that from the same two terms, you can get whole sets of propositions, which have various truth-relations with each other. After that, logic will take up combinations of propositions; what is the meaning of "and," and "or" in its various senses, and "if-then"; and we will develop "syllogisms" dealing with these.
Then we will take up what has traditionally been called the "categorical syllogism," showing how combinations of two propositions with three terms can yield new propositions.
There will follow a listing of some common fallacies, and how to avoid making them, as well as how to spot them and refute them when someone else has made them.
Having been through all this, you should have a better acquaintance with this tool you have that is almost the same as your very reality: your mind; and you should have a better idea how it connects with your world.