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Arguments in Philosophy


An argument is a set of related propositions where some provide the basis for a conclusion. So propositions are the bricks with which arguments are made. Arguments are the central focus of Logic. According to Copi and Cohen, an Argument is any group of propositions of which one is claimed to follow from the others, which are regarded as the providing support or grounds for the truth of that one. The structure of an Argument is such that the propositions are related with one another and not just a mere collection of propositions. Propositions in an argument are related as premise(s) or a conclusion. The premises of an argument are the propositions which are affirmed (or assumed) as providing foundation or support or reasons for accepting (or the validity of) the other that is affirmed or supported. The proposition thus supported is called conclusion.


(a) No Nigerians are Americans
All Igbos are Nigerians
Therefore, no Igbo are Americans.

(b) Some films are not interesting
All films are instructive
Therefore, some instructive films are not interesting.

(c) All women are deceptive
No Christians are deceptive
Therefore, no Christian are women.

The examples given above are syllogistic. A syllogism is an argument which consists of three propositions (two premises and a conclusion), and it contains exactly three terms each of which must be used twice. For instance, the three terms in example I above are “Nigerian”, “Americans” and “Igbo”. An argument can also be deductive or inductive.


(a) Deductive Argument:
All the three examples given above are also examples of some Deductive Arguments. Deductive Arguments are arguments “whose premises make a claim to provide us with conclusive ground to assert their conclusion.” While a Deductive Argument can be from general to particular, it can also be from particular to particular as in
(i) The letter C comes after the letter B
(ii) The letter B comes after the letter A
(iii) Therefore, the letter C comes after the letter A.

(b) Inductive Argument:
Inductive Argument “are Arguments whose premises make a probable rather than conclusive claim to assert their conclusions.” An inductive Argument is probable because the premises do not give us enough grounds to ascertain the conclusion. An inductive argument can be from particular premises to particular conclusion as in

(i) Jane is a girl and she loves flowers
(ii) Bisi is a girl and she loves flowers
(iii) Mary is a girl
(iv) Therefore, she (probably) loves flowers.

It can also be from general premises to general conclusion as in

“All countries are societies and have structure
All churches are societies and have structure
All schools are societies and have structure
Therefore, probably all societies have structures.”

The major difference between Deductive and Inductive Arguments lies in the dative degree to which the conclusion can be drawn from the premises. In deductive reasoning, we start with some assumption or premise, and extract from its consequences that are concealed but implicit in it. But in deductive reasoning, on the basis of specific facts remake general assumptions, as in Theorems and Scientific Laws. Generally, Scientific Methodology is inductive with its sampling and experimentation. Induction is relevant to empirical and factual claims. The purpose of induction is either to establish the basis or ground of the very empirical proposition which is a fact, or to understand what that observation indicates or suggests as a more general, inclusive, or fundamental fact of nature.


An argument can be valid or invalid. An argument is valid where the conclusion is implied by the premise(s) or where the premises are supporting evidence for the conclusion. Inductive arguments are often invalid. Deductive arguments are invalid when we can infer there conclusion from the premises. The argument below is an example of a valid argument.

(a) All men are mortal
Jude is a man
Therefore, Jude is mortal

In addition, validity has nothing to do with the truth of the premises or conclusion. The argument below is valid (because we can deduce its conclusion from the premises), though one of its premise and its conclusion are false.

(b) All wild animals eat grass (false)
The lion is a wild animal (true)
Therefore, the lion eats grass (false)

However, the argument below, though deductive, is invalid because the conclusion cannot be inferred from the premises. In other words, the conclusion tells us something completely different from what can reasonably be deduced from the premises.

(c) All Ghanaians are hardworking and intelligent
Kofi is a Ghanaian
Therefore, Kofi is not hardworking and intelligent.


An argument is sound when its premises and conclusion are all true. The argument (a) above is an example of a valid and sound argument. Argument (b) above is an example of a valid and unsound argument because one of its premises is false and its conclusion is false as well. Argument (c) above is both invalid and unsound because the conclusion does not follow from the premises. So, all sound arguments are valid, but not all valid arguments (be they deductive or inductive) are sound.

However, it is pertinent to note that it is sometimes difficult to know whether a proposition is true or false. One reason for this difficulty is that some propositions are relative to some field in which one is not a specialist. This explains why Logic does not concern itself with the truth or veracity of propositions. It is only concerned with the state of arguments, stipulating grounds for valid inference, and investigating whether some valid rules have been correctly followed. In the next post, we will look at the four standard form categorical propositions.

At this point, we will look at the four standard form categorical propositions.