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Speaker 1: Chapter twenty four. Primary Laws of thought. In connection with

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this subject, we here with call the attention of the

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student to the well known primary laws of thought, which

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have been recognized as valid from the time of the

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ancient Greek logicians. These laws are self evident and are uncontradictible.

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They are axiomatic. Jevons says of them. Students are seldom

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able to see at first their full meaning and importance.

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All arguments may be explained when these self evident laws

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are granted, and it is not too much to say

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that the whole of logic will be plain to those

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who will constantly use these laws as their key. Here

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are the three primary laws of thought. One law of identity.

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Whatever is is. Two law of contradiction. Nothing can both

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be and not be. Three law of excluded middle. Everything

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must either be or not be. There is no middle course. One.

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The first of these laws, called the law of identity,

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informs us that a thing is always itself, no matter

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under what a guise or form it is perceived or

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may present itself. An animal is always a bird if

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it possesses the general characteristics of a bird, no matter

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whether it exhibits the minor characteristics of an eagle, a wren,

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a stalk, or a hummingbird. In the same way, a

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whale is a mammal because it possesses the general characteristics

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of a mammal, notwithstanding that it swims in the water

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like a fish. Also, sweetness is always sweetness, whether manifested

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in sugar, honey, flowers, or products of coal tar. If

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a thing is that thing, then it is, and it

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cannot be logically claimed that it is not. Two. The

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second of these laws, called the law of contradiction, informs

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us that the same quality or class cannot be both

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affirmed and denied of a thing at the same time

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and place. A sparrow cannot be said to be both

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bird and not bird at the same time. Neither can

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sugar be said to be sweet and not sweet at

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the same time. A piece of iron may be hot

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at one end and not hot at another, but it

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cannot be both hot and not hot at the same

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place at the same time. Three. The third of these laws,

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called the law of excluded middle, informs us that a

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given quality or class must be affirmed or denied to

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everything at any given time and place. Everything either must

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be of a certain class or not must possess a

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certain quality or not at a given time or place.

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There is no alternative or middle course. It is axiomatic

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that any statement must either be or not be true

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of any certain other thing at any certain time and place.

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There is no escape from this. Anything either must be

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black or not black, a bird or not a bird,

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alive or not alive at any certain time or place.

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There is nothing else that it can be. It cannot

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both be and not be at the same time and place,

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as we have seen. Therefore, it must either be or

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not be that which is asserted of it. The judgment

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must decide which alternative, but it has only two possible choices.

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But the student must not confuse opposite qualities or things

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with nottness. A thing may be black or not black,

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but it need not be white to be not black,

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For blue is likewise not black, just as it is

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not white. The neglect of this fact frequently caused error.

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We must always affirm either the existence or non existence

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of equality in a thing, but this is far different

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from affirming or denying the existence of the opposite quality.

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Thus a thing may be not hard, and yet it

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does not follow that it is soft. It may be

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neither hard nor soft fallacious application, there exists what are

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known as fallacies of application of these primary laws. A

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fallacy is an unsound argument or conclusion. For instance, because

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a particular man is found to be a liar, it

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is fallacious to assume that all men are liars, for

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lying is a particular quality of the individual man, are

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not a general quality of the family of men. In

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the same way, because a stork has long legs and

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a long bill, it does not follow that all birds

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must have these characteristics simply because the stalk is a bird.

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It is fallacious to extend an individual quality to a class,

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but it is sound judgment to assume that a class

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quality must be possessed by all individuals in that class.

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It is a far different proposition which asserts that some

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birds are black from that which asserts that all birds

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are black. The same rule, of course, is true regarding

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negative propositions. Another fallacy is that which assumes that because

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the affirmative or negative proposition has not been or cannot

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be proved, it follows that the opposite proposition must be true.

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The true judgment is simply not proven. Another fallacious judgment

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is that which is based on attributing absolute quality to

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that which is but relative or comparative. For instance, the

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terms hot and cold are relative and comparative and simply

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denote one's relative opinion regarding a fixed and certain degree

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of temperature. The certain thing is the degree of temperature,

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say seventy five degrees fahrenheit. Of this we may logically

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claim that it is or is not true at a

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certain time and place. It either is seventy five degrees

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fahrenheit or it is not. But to one man this

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may seem warm and to another cold. Both are right

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in their judgments as far as their own relative feelings

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are concerned. But neither can claim absolutely that it is

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warm or cold. Therefore, it is a fallacy to ascribe

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absolute quality to a relative one. The absolute fact comes

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under the law of excluded middle, but a personal opinion

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is not an absolute fact. There are other fallacies which

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will be considered in other chapters of this book under

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their appropriate heading. End of Chapter twenty four, Chapter twenty

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five Reasoning. Reasoning the third a great step it thinking

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may be said to consist of ascertaining new truths from

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old ones, new judgments from old ones, unknown facts from

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known ones. In short, are proceeding logically from the known

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to the unknown, using the known as a foundation for

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the unknown, which is sought to be known. Gordy gives

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us the following excellent definition of the term reasoning is

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the act of going from the known to the unknown

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through other beliefs. Are basing judgment upon judgments, reaching beliefs

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through beliefs. Reasoning then is seen to be a process

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of building a structure of judgments, one resting upon the other,

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the topmost point being the final judgment, but the whole

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constituting an edifice of judgment. This may be seen more

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clearly when the various forms of reasoning are considered immediate reasoning.

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The simplest form of reasoning is that known as immediate reasoning,

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by which is meant reasoning by directly comparing two judgments

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without the intervention of the third judgment, which is found

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in the more formal classes of reasoning. This form of

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reasoning depends largely upon the application of the three primary

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laws of thought to which we have referred in a

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previous chapter. It will be seen that if a a

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thing is always itself, then b all that is included

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in it must partake of its nature. Thus the bird

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family has certain class characteristics. Therefore, by intermediate reasoning, we

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know that any member of that family must possess those

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class characteristics, whatever particular characteristics it may have. In addition,

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and we likewise know that we cannot attribute these particular

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characteristics as a matter of course, to the other members

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of the class. Thus, though all sparrows are birds, it

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is not true that all birds are sparrows. All biscuits

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are bread, but all bread is not biscuit. In the

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same way, we know that a thing cannot be bird

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and mammal at the same time, for mammals form a

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not bird family, And likewise we know that everything must

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be either bird or not bird. But that being not

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bird does not mean being a mammal, for there are

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many other not bird things than mammals. In this form

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of reasoning, distinction is always made between the universal or

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general class, which is expressed by the word all, and

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the particular or individual, which is expressed by the word sum.

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Many persons fail to note this difference in their reasoning,

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and fallaciously reason, for instance, that because some swans are white,

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all swans must be so, which is a far different

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thing from reasoning that if all is so and so,

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then some must be so and so. Those who are

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interested in this subject are referred to some elementary textbook

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on logic, as the detailed consideration is too technical for

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conscuts iteration here. Reasoning by analogy. Reasoning by analogy is

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an elementary form of reasoning and is a particular kind

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of reasoning employed by the majority of persons in ordinary thought.

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It is based upon the unconscious recognition by the human

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mind of the principle, which is expressed by Jevons as

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if two or more things resemble each other in many points,

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they will probably resemble each other in more points. The

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same authority says, reasoning by analogy differs only in degree

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from that type of reasoning called generalization. When many things

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resemble each other in a few properties, we argue about

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them by generalization. When a few things resemble each other

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in many properties, it is a case of analogy. While

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this form of reasoning is frequently employed with more or

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less satisfactory results, it is always open to a large

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percentage of error. Thus, persons have been poisoned by toadstools

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by reason of the false analogous reason that because mushrooms

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are edible, then toadstools which resemble them must be also

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fit for food. Or in the same way, because certain

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berries resemble other edible berries, they must likewise be good food.

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As Brooks says, to infer that because John Smith has

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a red nose and is also a drunkard, than Henry Jones,

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who also has a red nose, is also a drunkard,

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would be dangerous inference. Conclusions of this kind drawn from

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analogy are frequently dangerous. Halleck says, many false analogies are manufactured,

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and it is excellent thought training to expose them. The

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majority people think so little that they swallow these false analogies,

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just as new fledged robins swallow small stones dropped into

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their mouths. Jevons, one of the best authorities on the subject, says,

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there is no way in which we can really assure

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ourselves that we are arguing safely by analogy. The only

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rule that can be given is this that the more

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closely two things resemble each other, the more likely it

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is that they are the same in other respects, especially

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in points closely connected with those observed. In order to

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be clear about our conclusions, we ought, in fact, never

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to rest satisfied with mere analogy, but ought to try

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to discover the general laws governing the case. We find

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that reasoning by analogy is not to be depended upon

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unless we make such an inquiry into the causes and

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laws of the things in question that we really employ

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Inductive and deductive reasoning higher forms of reasoning. The two

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higher forms of reasoning are known, respectively as one inductive

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reasoning or inference from particular facts to general laws, and

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two deductive reasoning, or inference from general truths to particular truths.

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While the class distinction is made for the purpose of

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clear consideration, it must not be forgotten that the two

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forms of reasoning are generally found in combination. Thus, in

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inductive reasoning, many steps are taken by the aid of

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deductive reasoning. And likewise, before we can reason deductively from

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general truths to particular ones, we must have discovered the

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general truths by inductive reasoning from particular facts. Thus there

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is a unity in all reasoning processes, as there is

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in all mental operations. Inductive reasoning is a synthetical process,

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deductive reasoning an analytical one. In the first, we combine

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and build up. In the latter, we dissect and separate

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end of Chapter twenty five Chapter twenty six. Inductive reasoning.

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Inductive reasoning is based upon the axiom what is true

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of the many is true of the whole. This axiom

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is based upon man's belief in the uniformity of nature.

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Inductive reasoning is a mental ladder by which we climb

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from particular facts to general laws, but the latter rests

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upon the belief that the universe is governed by law.

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The steps in inductive reasoning are as follows one observation, investigation,

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and examination of particular facts or things. If we wish

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to know the general characteristics of the bird family, we

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must first examine a sufficient number of birds of many kinds,

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so as to discover the comparatively few general characteristics possessed

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by all of the bird family, as distinct from a

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particular characteristics possessed by only some of that family. The

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greater the number of individuals examined, the narrower becomes our

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list of the general qualities common to all. In the

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same way, we must examine many kinds of flowers before

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we come to the few general qualities common to all flowers,

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which we combine in the general concept of flower. The same,

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of course, is true regarding the discovery of general laws

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from particular facts. We examine the facts and then work

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toward a general law which will explain them. For instance,

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the law of gravitation was discovered by the observation and

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investigation of the fact that all objects are attracted to

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the earth. Further investigation revealed the fact that all material

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objects are attracted to each other. Then the general law

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was discovered, or rather the hypothesis was advanced, was found

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to explain the facts, was verified by further experiments and

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observation two. The second step in inductive reasoning is the

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making of an hypothesis. And hypothesis is a pro opposition

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or principle assumed as a possible explanation for a set

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or class of facts. It is regarded as a working

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theory which must be examined and tested in connection with

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the facts before it is finally accepted. For instance, after

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the observation that a number of magnets attracted steel, it

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was found reasonable to advance the hypothesis that all magnets

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attract steel. In the same way was advanced the hypothesis

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that all birds are warm blooded, winged, feathered, oviparous vertebrates.

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Subsequent observation an experiment established the hypothesis regarding the magnet

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and regarding the general qualities of the bird family. If

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a single magnet had been found which did not attract steel,

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then the hypothesis would have fallen. If a single bird

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had been discovered which was not warm blooded, then that

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quality would have been stricken from the list of the

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necessary characteristics of all birds. A theory is merely an

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hypothesis which has been verified or established by continued and

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repeated observation, investigation, and experiment. Hypotheses and theories arise very

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generally from a subconscious similation of a number of particular

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facts and the conscious flashing of a great guess or

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a sacred suspicion of the truth into the conscious field

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of attention. The scientific imagination plays an important part in

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this process. There is, of course, a world of difference

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between a blind guess based upon insufficient data and a

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scientific guess resulting from the accumulation of a vast store

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of careful and accurate information. As Brooks says, the forming

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of an hypothesis requires a suggestive mind, a lively fancy,

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a philosophic imagination that catches a glimpse of the idea

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through the form, or sees the law standing behind the fact.

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But accepted theories in a majority of cases arise only

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by testing out and rejecting many promising hypotheses and finally

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setting upon the one which best answers all the requirements

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and best explains the facts. As an authority says, to

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try wrong guesses is with most persons the only way

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to hit upon right ones. Three. Testing the hypothesis by

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deductive reasoning is the third step in inductive reasoning. This

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test is made by applying a hypothetical principle to particular

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facts or things. That is, to follow out mentally the

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hypothetical principle to its logical conclusion. This may be done

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in this way. If so and so is correct, then

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it follows that thus and so is true, et cetera.

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If the conclusion agrees with reason, then the test is

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deemed satisfactory so far as it has gone. But for

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the result proves to be logical, absurdity, or inconsistent with

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natural facts, then the hypothesis is discredited. Four. Practical verification

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of the hypothesis is the fourth step in inductive reasoning.

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This step consists of the actual comparison of observed facts

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with the logical conclusions arising from applying deductive reasoning to

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the general principle assumed as a premise. The greater number

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of facts agreeing with the conclusions arising from the premise

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of the hypothesis. The greater is deemed the probability of

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the latter. The authorities generally assume an hypothesis to be

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verified when it accounts for all the facts which properly

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are related to it. Some extremists contend, however, that before

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an hypothesis may be considered as absolutely verified, it must

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not only account for all the associated facts, but that

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also there must be no other possible hypothesis to out

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for the same facts. The facts referred to in this

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connection may be either one observed phenomena or two the

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conclusions deductive reasoning arising from the assumption of the hypothesis,

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or three the agreement between the observed facts and the

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logical conclusions. The last combination is generally regarded as the

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most logical. The verification of an hypothesis must be an

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all around one, and there must be an agreement between

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the observed facts and the logical conclusions. In the case,

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the hypothesis must fit the facts, and the facts must

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fit the hypothesis. The facts are the glass slipper of

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the Cinderella legend. The several sisters of Cinderella were discarded

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hypotheses the slipper and the sisters not fitting. When Cinderella's

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foot was found to be the one foot upon which

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the glass slipper fitted, then the Cinderella hypothesis was considered

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to have been proved. The glacesterper was hers, and the

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prince claimed his bride