About the Author: Peter Kreeft, Ph. His many bestselling books cover a vast array of topics in spirituality, theology, and philosophy. All rights reserved. The two logics P This section can be omitted without losing anything you will need later on in the book.
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An excerpt from chapter 1: Section 3. The two logics P This section can be omitted without losing anything you will need later on in the book.
Inductive reasoning could be very roughly and inadequately defined as reasoning from concrete particular instances, known by experience, while deduction reasons from general principles. Induction yields only probability, while deduction yields certainty. Today nearly all logic textbooks use the new mathematical, or symbolic, logic as a kind of new language system for deductive logic. It is not a new logic; logical principles are unchangeable, like the principles of algebra.
It is more like changing from Roman numerals to Arabic numerals. There are at least three reasons for this change: 1 The first and most important one is that the new logic really is superior to the old in efficiency for expressing many long and complex arguments, as Arabic numerals are to Roman numerals, or a digital computer to an analog computer, or writing in shorthand to writing in longhand.
However, longhand is superior to shorthand in other ways: e. That is why most people prefer longhand most of the time — as most beginners prefer simpler computers or even pens.
That is why Aristotelian logic is more practical for beginners. Even though symbolic language is superior in sophistication, it depends on commonsense logic as its foundation and root. Thus you will have a firmer foundation for all advanced logics if you first master this most basic logic.
Strong roots are the key to healthy branches and leaves for any tree. Any farmer knows that the way to get better fruit is to tend the roots, not the fruits. This is only an analogy. Analogies do not prove anything — that is a common fallacy — they only illuminate and illustrate. But it is an illuminating analogy. Modern symbolic logic is mathematical logic. Bayerly, in A Primer of Logic. Mathematics is a wonderful invention for saving time and empowering science, but it is not very useful in most ordinary conversations, especially philosophical conversations.
The more important the subject matter, the less relevant mathematics seems. Its forte is quantity, not quality. Mathematics is the only totally clear, utterly unambiguous language in the world; yet it cannot say anything very interesting about anything very important. Compare the exercises in a symbolic logic text with those in this text. How many are taken from the Great Books? How many are from conversations you could have had in real life?
The very artificiality of its language is a plus for its defenders. But it is a minus for ordinary people. Philosophy aims at insight into principles and into the relationship of conclusions to the principles from which they are derived.
The old, Aristotelian logic was often scorned by 20th century philosophers because it rests on two commonsensical but unfashionable philosophical presuppositions. The following summary should not scare off beginners; it is much more abstract and theoretical than most of the rest of this book. Hume inherited from his predecessor Locke the fatal assumption that the immediate object of human knowledge is our own ideas rather than objective reality.
Thus they were always particular e. Common sense says that we can be certain of some universal truths, e. Hume argued that particular facts deduced from these only-probable general principles could never be known or predicted with certainty.
If it is only probably true that all men are mortal, then it is only probably true that Socrates is mortal. The fact that we have seen the sun rise millions of times does not prove that it will necessarily rise tomorrow. We have only probable knowledge of objective reality. Even scientific knowledge, Hume thought, was only probable, not certain, because science assumes the principle of causality, and this principle, according to Hume, is only a subjective association of ideas in our minds.
But we do not see causality itself, the causal relation itself between the bird and the egg. We must be skeptics, if we are only Humean beings. Rather, knowledge constructs or forms reality as an artist constructs or forms a work of art. The knowing subject determines the known object rather than vice versa. Human knowledge does its job very well, but its job is not to learn what is, but to make what is, to form it and structure it and impose meanings on it.
Thus the world of experience is formed by our knowing it rather than our knowledge being formed by the world. I am predicting the effect from the cause. But symbolic logic does not allow this commonsensical, realistic interpretation.
Besides epistemological realism, Aristotelian logic also implicitly assumes metaphysical realism. Metaphysics is that division of philosophy which investigates what reality is; epistemology is that division of philosophy which investigates what knowing is.
Epistemological realism contends that the object of intelligence is reality. Metaphysical realism naturally goes with epistemological realism.
There are two forms of metaphysical realism: Plato thought that these universals were real things in themselves, while Aristotle thought, more commonsensically, that they were real aspects of things which we mentally abstracted from things. William of Ockham — is the philosopher who is usually credited or debited with being the founder of nominalism. It is quantitative digital , not qualitative.
It is reducible to mathematics. The new logic has no means of saying, and even prevents us from saying, what anything is! And if we cease to say it, we will soon cease to think it, for there will be no holding-places in our language for the thought.
Language is the house of thought, and homelessness is as life-threatening for thoughts as it is for people. If we should begin to speak and think only in nominalist terms, this would be a monumental historic change. It would reverse the evolutionary event by which man rose above the animal in gaining the ability to know abstract universals. It would be the mental equivalent of going naked on all fours, living in trees, and eating bugs and bananas.
Could monkeys have evolved by natural selection from nominalists? And changes in logic are not wholly unrelated to it. To most modern minds, those last seven words sound almost as archaic as alchemy or feudalism. Many criticize them as ideologically dangerous.
Not only our logicians but also our society no longer thinks primarily about the fundamental metaphysical question, the question of what things are, the question of the nature of things. Instead, we think about how we feel about things, about how we can use them, how we see them behave, how they work, how we can change them, or how we can predict and control their behavior by technology. But all this does not raise us above the animal level in kind, only in degree.
The higher animals too have feelings, and things to use, and sight, and action, and even a kind of technology of behavior prediction and control. For the art of hunting is an art of predicting and controlling the behavior of other animals. What do we have that no mere animal has? The thing that many modern philosophers vilify: abstraction.
We have the power to abstract and understand universals. This is the thing traditional logic is founded on, and this is the thing symbolic logic ignores or denies. Logic is deeply related to moral and ethical changes in both thought and practice. It is not an unthinkable suspicion that one of the most powerful forces driving the new logic is more social than philosophical, and more sexual than logical. Symbolic logic naturally fosters utilitarian ethics, which is essentially an ethic of consequences.
The very nature of reason itself is understood differently by the new symbolic logic than it was by the traditional Aristotelian logic. Having met some of these people at MIT, I must admit that their self-description sometimes seems quite accurate.
Aristotelian logic is not exact enough for the nominalistic mathematical logician, and it is too exact for the pop psychology subjectivist or New Age mystic. Out at sea there between Scylla and Charybdis, it reveals by contrast the double tragedy of modern thought in its alienation between form and matter, structure and content, validity and meaning. This alienated mind was described memorably by C.
On the one hand, a glib and shallow rationalism. On the other, a many-islanded sea of myth and poetry. Nearly all that I loved, I believed subjective.
Aristotelian logic is also easier, simpler, and therefore time-saving. I have found that students who are well trained in Aristotelian logic are much better at arguing, and at understanding arguments, than students who are trained only in symbolic logic.
For Aristotelian logic is the logic of the four most basic verbal communication arts: reading, writing, listening, and speaking. It is the logic of Socrates. If you want to be a Socrates, this is the logic you should begin with. The old logic is like the old classic movies: strong on substance rather than sophistication.
But logic should be a human instrument; logic was made for man, not man for logic. For a fuller treatment of the new logic see the Appendix, p. Logic is most especially about reasoning, or inference: the process of thinking by which we draw conclusions from evidence, moving from one proposition to another.
But we can also use false propositions in good reasoning. Since a false conclusion cannot be logically proved from true premises, we can know that if the conclusion is false then one of the premises must also be false, in a logically valid argument. A logically valid argument is one in which the conclusion necessarily follows from its premises. In a logically valid argument, if the premises are true, then the conclusion must be true.
Socratic Logic (textbook)
An excerpt from chapter 1: Section 3. The two logics P This section can be omitted without losing anything you will need later on in the book. Inductive reasoning could be very roughly and inadequately defined as reasoning from concrete particular instances, known by experience, while deduction reasons from general principles. Induction yields only probability, while deduction yields certainty. Today nearly all logic textbooks use the new mathematical, or symbolic, logic as a kind of new language system for deductive logic. It is not a new logic; logical principles are unchangeable, like the principles of algebra. It is more like changing from Roman numerals to Arabic numerals.
Peter Kreeft’s Recommended Philosophy Books
These three sections are based upon the three main functions of any argument. First, one must define the terms to see whether they are clear or ambiguous. Then, one must evaluate the Peter Kreeft provides an introductory textbook on the argumentative logic of Socrates in his book Socratic Logic. Then, one must evaluate the premises to determine whether they are true or false. Finally, one must test the argument to see whether the argument is valid or invalid.
ISBN 13: 9781587318085
Mar 17, Brian Chilton rated it it was amazing Peter Kreeft provides an introductory textbook on the argumentative logic of Socrates in his book Socratic Logic. These three sections are based upon the three main functions of any argument. First, one must define the terms to see whether they are clear or ambiguous. Then, one must evaluate the Peter Kreeft provides an introductory textbook on the argumentative logic of Socrates in his book Socratic Logic. Then, one must evaluate the premises to determine whether they are true or false.