Lecture Summary I: Basic Logical Concepts
Michael Jhon M. Tamayao
Subject: Philo1 (Logic 1)
June 21, 2007
Logic is defined as the science of correct reasoning. As a science, it provides methods and
principles for distinguishing good (correct) from bad (incorrect) reasoning.1 But why do we exactly need
to know these methods and principles? It is for the simple reason that we care to be correct. The human
mind always strives for the “truth.” It is precisely this “truth” that correct reasoning aims for. But what
exactly is “truth”?
We say that something or a statement is true if it coincides with reality. If I saw a poodle, for
example, and it is for a fact that it eats meat, then a true statement basing from what I perceive would
be “The poodle is a carnivore.” Truth then is defined as the correspondence of the mind to reality. Thus,
if what is thought in the mind does not coincide with the reality, then it is said to be false.
The simplest act of the mind to attain truth is judgment. When I affirm (or deny) an attribute
to a subject, I am making a judgment. When I “think” for example that “The poodle is a carnivore” I am
affirming the attribute “carnivore” to the subject “poodle.” My act of affirming this description to the
house is a judgment. Now this judgment can be true or false. In this case (given the condition is indeed
followed) it is true.
Even before the mind makes a judgment it has already done a simple comprehension. Taking
the same example above, even before I made the judgment “The poodle is a carnivore” I already
conceived individually the notions of “carnivore” and “poodle.” Thus my simple apprehension of the
notions “carnivore” and “poodle” is a more elementary act of my mind than my judgment. It is only
when I affirm the attribute carnivore to the subject poodle that I will actually make a judgment.
Now if I make a series of judgments following an orderly structure and flow, then I make an
inference. For example,
All dogs are carnivores
All poodles are dogs
Therefore, all poodles are carnivores.
In other words, inference is the process of deducing or extracting a judgment from previous judgments.
Looking now at the whole process of reasoning, we first have simple apprehension, then
judgment and lastly inference. Nevertheless, these are only “acts” of the mind. Unless they are verbally
expressed, they cannot be evaluated through the logical methods and principles. The end products or
verbal expressions of the three acts are term/name (for the notion conceived in simple apprehension),
proposition (for judgment), and argument (for inference). In Traditional Logic, syllogism is the typical
format of the arguments (as seen in the example above). It is composed of three propositions.
One of the fundamental principles of traditional logic is that “a proposition is always
composed of two terms, the subject and the predicate.” In the proposition “All poodles are carnivores”,
carnivore is the predicate because it is that which is predicated (affirmed/denied) to the subject poodle.
The poodle is said to be the subject because it is the object being affirmed (or denied) of the attribute
“carnivore.”
Arguments always have two parts, the conclusion and the premises. Otherwise, it is not an
argument. The conclusion is the statement supported by previous statements. Premises, on the other,
are the statements that support the conclusion. Referring to the example above, the conclusion is “All
poodles are carnivores” and the premises are “All dogs are carnivores” and “All poodles are dogs.”
Arguments are central concepts in logic inasmuch as they support our claim to truth. There
are two factors to assess the worth of an argument, its truth and validity. Truth has already been
elucidated, but what is validity? We say that an argument is valid, like in the example above, when its
premises give conclusive grounds to its conclusion. In other words, the premises give 100% support to
the conclusion, otherwise it is said to be invalid. Moreover, validity is anchored on the rules of inference
so that once these rules are broken an argument becomes invalid. However, it must be well noted that
truth is properly used for propositions and validity for arguments. Thus we say “propositions are
true/false not valid/invalid” and “arguments are valid/invalid not true/false.”
The first principle in logic is the independence of truth from validity. An argument may be
valid but has one or more false propositions, or an argument may be invalid but has true propositions.
For example,
All priests are humans
All angels are priests
Therefore, all angels are humans.
Although the second and third propositions are false, the entire argument is still valid because it does
not break any rule for making a valid argument.
Inasmuch as truth and validity are the basis of making a good argument, we say that an
argument is good or “sound” when all of its propositions are true and the entire process of reasoning is
valid. Consider the following example of a “sound argument”:
All priests are humans (True)
All Popes are priests (True)
Valid
Therefore, all Popes are humans. (True)
But if one or more propositions are false and/or the reasoning is invalid, then the argument is said to be
unsound or fallacious. Fallacies usually commit these errors because of their ambiguous or vague
language. Consider the following example:
God is love
Love is blind
Therefore, God is blind.
The argument seems to be valid but, in close inspection, it is fallacious. Not only is its
language ambiguous, it also has an invalid argument considering its form and figure. The explanation for
the second point will be elaborated in later lectures. The meaning of the word “blind” in the second
statement is a metaphor for “does not seek for any specific answer” while the word “blind” in the third
statement is understood as “physical blindness.” It sounds persuasive but it is fallacious.
Moreover, there are two kinds of arguments: the Deductive and the Inductive. An argument
is said to be deductive if is necessitates validity, that is to say, its premises must claim to support the
conclusion with necessity. An Inductive argument, on the other hand, also have premises that support its
conclusion but do not guarantee its necessity. The example of the sound argument above is a deductive
argument because the premises guarantee the necessity of the conclusion. An example of an inductive
argument, on the other hand, is “Of all the 50 million swans I saw, nothing is black. Therefore, No swan is
black.” Although the argument provides support to the conclusion, it does not give a 100% support to
the conclusion because there is still a possibility of error. Seeing fifty million swans which are colored
black does not entitle you to say with “100% correctness” that “all” swans are black. “Fifty million swans”
is not the sane with “all swans.” Although the premise gives support, it is only done out of “probability.”
Gathering therefore all the basic concepts we have: LOGIC, SIMPLE APPREHENSION,
JUDGMENT, INFERENCE, TERM, PROPOSITION, ARGUMENT, SYLLOGISM, SUBJECT, PREDICATE, TRUTH,
VALIDITY, SOUND ARGUMENT, FALLACY, DEDUCTIVE ARGUMENT, and INDUCTIVE ARGUMENT. *****
1 Irving M. Copi, “Introduction to Logic” ( New York: Macmillan Publishing Co., Inc., 1972) p. 3.