Speaker 1: Chapter twenty four. Primary Laws of thought. In connection with
this subject, we here with call the attention of the
student to the well known primary laws of thought, which
have been recognized as valid from the time of the
ancient Greek logicians. These laws are self evident and are uncontradictible.
They are axiomatic. Jevons says of them. Students are seldom
able to see at first their full meaning and importance.
All arguments may be explained when these self evident laws
are granted, and it is not too much to say
that the whole of logic will be plain to those
who will constantly use these laws as their key. Here
are the three primary laws of thought. One law of identity.
Whatever is is. Two law of contradiction. Nothing can both
be and not be. Three law of excluded middle. Everything
must either be or not be. There is no middle course. One.
The first of these laws, called the law of identity,
informs us that a thing is always itself, no matter
under what a guise or form it is perceived or
may present itself. An animal is always a bird if
it possesses the general characteristics of a bird, no matter
whether it exhibits the minor characteristics of an eagle, a wren,
a stalk, or a hummingbird. In the same way, a
whale is a mammal because it possesses the general characteristics
of a mammal, notwithstanding that it swims in the water
like a fish. Also, sweetness is always sweetness, whether manifested
in sugar, honey, flowers, or products of coal tar. If
a thing is that thing, then it is, and it
cannot be logically claimed that it is not. Two. The
second of these laws, called the law of contradiction, informs
us that the same quality or class cannot be both
affirmed and denied of a thing at the same time
and place. A sparrow cannot be said to be both
bird and not bird at the same time. Neither can
sugar be said to be sweet and not sweet at
the same time. A piece of iron may be hot
at one end and not hot at another, but it
cannot be both hot and not hot at the same
place at the same time. Three. The third of these laws,
called the law of excluded middle, informs us that a
given quality or class must be affirmed or denied to
everything at any given time and place. Everything either must
be of a certain class or not must possess a
certain quality or not at a given time or place.
There is no alternative or middle course. It is axiomatic
that any statement must either be or not be true
of any certain other thing at any certain time and place.
There is no escape from this. Anything either must be
black or not black, a bird or not a bird,
alive or not alive at any certain time or place.
There is nothing else that it can be. It cannot
both be and not be at the same time and place,
as we have seen. Therefore, it must either be or
not be that which is asserted of it. The judgment
must decide which alternative, but it has only two possible choices.
But the student must not confuse opposite qualities or things
with nottness. A thing may be black or not black,
but it need not be white to be not black,
For blue is likewise not black, just as it is
not white. The neglect of this fact frequently caused error.
We must always affirm either the existence or non existence
of equality in a thing, but this is far different
from affirming or denying the existence of the opposite quality.
Thus a thing may be not hard, and yet it
does not follow that it is soft. It may be
neither hard nor soft fallacious application, there exists what are
known as fallacies of application of these primary laws. A
fallacy is an unsound argument or conclusion. For instance, because
a particular man is found to be a liar, it
is fallacious to assume that all men are liars, for
lying is a particular quality of the individual man, are
not a general quality of the family of men. In
the same way, because a stork has long legs and
a long bill, it does not follow that all birds
must have these characteristics simply because the stalk is a bird.
It is fallacious to extend an individual quality to a class,
but it is sound judgment to assume that a class
quality must be possessed by all individuals in that class.
It is a far different proposition which asserts that some
birds are black from that which asserts that all birds
are black. The same rule, of course, is true regarding
negative propositions. Another fallacy is that which assumes that because
the affirmative or negative proposition has not been or cannot
be proved, it follows that the opposite proposition must be true.
The true judgment is simply not proven. Another fallacious judgment
is that which is based on attributing absolute quality to
that which is but relative or comparative. For instance, the
terms hot and cold are relative and comparative and simply
denote one's relative opinion regarding a fixed and certain degree
of temperature. The certain thing is the degree of temperature,
say seventy five degrees fahrenheit. Of this we may logically
claim that it is or is not true at a
certain time and place. It either is seventy five degrees
fahrenheit or it is not. But to one man this
may seem warm and to another cold. Both are right
in their judgments as far as their own relative feelings
are concerned. But neither can claim absolutely that it is
warm or cold. Therefore, it is a fallacy to ascribe
absolute quality to a relative one. The absolute fact comes
under the law of excluded middle, but a personal opinion
is not an absolute fact. There are other fallacies which
will be considered in other chapters of this book under
their appropriate heading. End of Chapter twenty four, Chapter twenty
five Reasoning. Reasoning the third a great step it thinking
may be said to consist of ascertaining new truths from
old ones, new judgments from old ones, unknown facts from
known ones. In short, are proceeding logically from the known
to the unknown, using the known as a foundation for
the unknown, which is sought to be known. Gordy gives
us the following excellent definition of the term reasoning is
the act of going from the known to the unknown
through other beliefs. Are basing judgment upon judgments, reaching beliefs
through beliefs. Reasoning then is seen to be a process
of building a structure of judgments, one resting upon the other,
the topmost point being the final judgment, but the whole
constituting an edifice of judgment. This may be seen more
clearly when the various forms of reasoning are considered immediate reasoning.
The simplest form of reasoning is that known as immediate reasoning,
by which is meant reasoning by directly comparing two judgments
without the intervention of the third judgment, which is found
in the more formal classes of reasoning. This form of
reasoning depends largely upon the application of the three primary
laws of thought to which we have referred in a
previous chapter. It will be seen that if a a
thing is always itself, then b all that is included
in it must partake of its nature. Thus the bird
family has certain class characteristics. Therefore, by intermediate reasoning, we
know that any member of that family must possess those
class characteristics, whatever particular characteristics it may have. In addition,
and we likewise know that we cannot attribute these particular
characteristics as a matter of course, to the other members
of the class. Thus, though all sparrows are birds, it
is not true that all birds are sparrows. All biscuits
are bread, but all bread is not biscuit. In the
same way, we know that a thing cannot be bird
and mammal at the same time, for mammals form a
not bird family, And likewise we know that everything must
be either bird or not bird. But that being not
bird does not mean being a mammal, for there are
many other not bird things than mammals. In this form
of reasoning, distinction is always made between the universal or
general class, which is expressed by the word all, and
the particular or individual, which is expressed by the word sum.
Many persons fail to note this difference in their reasoning,
and fallaciously reason, for instance, that because some swans are white,
all swans must be so, which is a far different
thing from reasoning that if all is so and so,
then some must be so and so. Those who are
interested in this subject are referred to some elementary textbook
on logic, as the detailed consideration is too technical for
conscuts iteration here. Reasoning by analogy. Reasoning by analogy is
an elementary form of reasoning and is a particular kind
of reasoning employed by the majority of persons in ordinary thought.
It is based upon the unconscious recognition by the human
mind of the principle, which is expressed by Jevons as
if two or more things resemble each other in many points,
they will probably resemble each other in more points. The
same authority says, reasoning by analogy differs only in degree
from that type of reasoning called generalization. When many things
resemble each other in a few properties, we argue about
them by generalization. When a few things resemble each other
in many properties, it is a case of analogy. While
this form of reasoning is frequently employed with more or
less satisfactory results, it is always open to a large
percentage of error. Thus, persons have been poisoned by toadstools
by reason of the false analogous reason that because mushrooms
are edible, then toadstools which resemble them must be also
fit for food. Or in the same way, because certain
berries resemble other edible berries, they must likewise be good food.
As Brooks says, to infer that because John Smith has
a red nose and is also a drunkard, than Henry Jones,
who also has a red nose, is also a drunkard,
would be dangerous inference. Conclusions of this kind drawn from
analogy are frequently dangerous. Halleck says, many false analogies are manufactured,
and it is excellent thought training to expose them. The
majority people think so little that they swallow these false analogies,
just as new fledged robins swallow small stones dropped into
their mouths. Jevons, one of the best authorities on the subject, says,
there is no way in which we can really assure
ourselves that we are arguing safely by analogy. The only
rule that can be given is this that the more
closely two things resemble each other, the more likely it
is that they are the same in other respects, especially
in points closely connected with those observed. In order to
be clear about our conclusions, we ought, in fact, never
to rest satisfied with mere analogy, but ought to try
to discover the general laws governing the case. We find
that reasoning by analogy is not to be depended upon
unless we make such an inquiry into the causes and
laws of the things in question that we really employ
Inductive and deductive reasoning higher forms of reasoning. The two
higher forms of reasoning are known, respectively as one inductive
reasoning or inference from particular facts to general laws, and
two deductive reasoning, or inference from general truths to particular truths.
While the class distinction is made for the purpose of
clear consideration, it must not be forgotten that the two
forms of reasoning are generally found in combination. Thus, in
inductive reasoning, many steps are taken by the aid of
deductive reasoning. And likewise, before we can reason deductively from
general truths to particular ones, we must have discovered the
general truths by inductive reasoning from particular facts. Thus there
is a unity in all reasoning processes, as there is
in all mental operations. Inductive reasoning is a synthetical process,
deductive reasoning an analytical one. In the first, we combine
and build up. In the latter, we dissect and separate
end of Chapter twenty five Chapter twenty six. Inductive reasoning.
Inductive reasoning is based upon the axiom what is true
of the many is true of the whole. This axiom
is based upon man's belief in the uniformity of nature.
Inductive reasoning is a mental ladder by which we climb
from particular facts to general laws, but the latter rests
upon the belief that the universe is governed by law.
The steps in inductive reasoning are as follows one observation, investigation,
and examination of particular facts or things. If we wish
to know the general characteristics of the bird family, we
must first examine a sufficient number of birds of many kinds,
so as to discover the comparatively few general characteristics possessed
by all of the bird family, as distinct from a
particular characteristics possessed by only some of that family. The
greater the number of individuals examined, the narrower becomes our
list of the general qualities common to all. In the
same way, we must examine many kinds of flowers before
we come to the few general qualities common to all flowers,
which we combine in the general concept of flower. The same,
of course, is true regarding the discovery of general laws
from particular facts. We examine the facts and then work
toward a general law which will explain them. For instance,
the law of gravitation was discovered by the observation and
investigation of the fact that all objects are attracted to
the earth. Further investigation revealed the fact that all material
objects are attracted to each other. Then the general law
was discovered, or rather the hypothesis was advanced, was found
to explain the facts, was verified by further experiments and
observation two. The second step in inductive reasoning is the
making of an hypothesis. And hypothesis is a pro opposition
or principle assumed as a possible explanation for a set
or class of facts. It is regarded as a working
theory which must be examined and tested in connection with
the facts before it is finally accepted. For instance, after
the observation that a number of magnets attracted steel, it
was found reasonable to advance the hypothesis that all magnets
attract steel. In the same way was advanced the hypothesis
that all birds are warm blooded, winged, feathered, oviparous vertebrates.
Subsequent observation an experiment established the hypothesis regarding the magnet
and regarding the general qualities of the bird family. If
a single magnet had been found which did not attract steel,
then the hypothesis would have fallen. If a single bird
had been discovered which was not warm blooded, then that
quality would have been stricken from the list of the
necessary characteristics of all birds. A theory is merely an
hypothesis which has been verified or established by continued and
repeated observation, investigation, and experiment. Hypotheses and theories arise very
generally from a subconscious similation of a number of particular
facts and the conscious flashing of a great guess or
a sacred suspicion of the truth into the conscious field
of attention. The scientific imagination plays an important part in
this process. There is, of course, a world of difference
between a blind guess based upon insufficient data and a
scientific guess resulting from the accumulation of a vast store
of careful and accurate information. As Brooks says, the forming
of an hypothesis requires a suggestive mind, a lively fancy,
a philosophic imagination that catches a glimpse of the idea
through the form, or sees the law standing behind the fact.
But accepted theories in a majority of cases arise only
by testing out and rejecting many promising hypotheses and finally
setting upon the one which best answers all the requirements
and best explains the facts. As an authority says, to
try wrong guesses is with most persons the only way
to hit upon right ones. Three. Testing the hypothesis by
deductive reasoning is the third step in inductive reasoning. This
test is made by applying a hypothetical principle to particular
facts or things. That is, to follow out mentally the
hypothetical principle to its logical conclusion. This may be done
in this way. If so and so is correct, then
it follows that thus and so is true, et cetera.
If the conclusion agrees with reason, then the test is
deemed satisfactory so far as it has gone. But for
the result proves to be logical, absurdity, or inconsistent with
natural facts, then the hypothesis is discredited. Four. Practical verification
of the hypothesis is the fourth step in inductive reasoning.
This step consists of the actual comparison of observed facts
with the logical conclusions arising from applying deductive reasoning to
the general principle assumed as a premise. The greater number
of facts agreeing with the conclusions arising from the premise
of the hypothesis. The greater is deemed the probability of
the latter. The authorities generally assume an hypothesis to be
verified when it accounts for all the facts which properly
are related to it. Some extremists contend, however, that before
an hypothesis may be considered as absolutely verified, it must
not only account for all the associated facts, but that
also there must be no other possible hypothesis to out
for the same facts. The facts referred to in this
connection may be either one observed phenomena or two the
conclusions deductive reasoning arising from the assumption of the hypothesis,
or three the agreement between the observed facts and the
logical conclusions. The last combination is generally regarded as the
most logical. The verification of an hypothesis must be an
all around one, and there must be an agreement between
the observed facts and the logical conclusions. In the case,
the hypothesis must fit the facts, and the facts must
fit the hypothesis. The facts are the glass slipper of
the Cinderella legend. The several sisters of Cinderella were discarded
hypotheses the slipper and the sisters not fitting. When Cinderella's
foot was found to be the one foot upon which
the glass slipper fitted, then the Cinderella hypothesis was considered
to have been proved. The glacesterper was hers, and the
prince claimed his bride