The fourth means of combining independent clauses relates them so as to allow the second to be inferred from the first.
We have not observed this combination as often in simple sentences as in more involved complex sentences.
In discussions of logical relationships, however, logicians hardly hesitate to use simple illative clauses where the second is a logical consequence of the first.
| (1) | Socrates is a man, therefore he is mortal. |
| a. | Socrates is a man. | |
| b. | Socrates is mortal. | Ill (CL) |
Logicians use this kind of illative conjoining when they derive a proof by means of a formal argument from a number of assumptions.
It is not always appreciated that this conjoining is distinct from material implication, which must be free of any conditional dependencies.
Material implication ( ) is equivalent to ( ) disjunction (v) provided we change the first clause to its negation (~), i.e., p q ~p v q.
What is naïvely strange about material implication is the fact that it may relate certain sentences which are fully independent and non-contingent.
We judge material implication as strange because it holds between a false protasis and a true apodosis.
The use of material implication allows anything to be proved from false premises. |
| (2) | (?)Points are three dimensional, therefore circles are round. |
| We may join the clauses of (1) using the disjunctive and negative relationships as in (3) or as in (4).
However, in English we interpret such clauses as condition-alternative (cf. ¶9-3-2). |
| (3) | Either Socrates is a mortal or he is not a man. |
| a. | Socrates is mortal. | |
| au. | (Socrates may not be mortal.) | |
| b. | Socrates is not a man (in this case). | cnDisj (CL) |
| (4) | Either Socrates is not a man or he is mortal. |
| a. | Socrates is not a man. | |
| au. | (Socrates may be a man.) | |
| b. | Socrates is mortal (in this case). | cnDisj (CL) |
| We know that the clauses in (3b) and (4a) do not hold under their normal interpretations, yet both clauses in (1) seemed fully acceptable as referring to some possible instance — Socrates.
The situation is that while the individual Socrates is a member of both the set of mortal things and the set of men, these two sets do not normally contain instances of things which fail being mortal and are yet men.
Conjoining clauses illatively seems to take situations or configurations of sets into consideration, not independent instances. |
|
Often the author expresses the relationship of logical consequence by use of a dependent adverb clause of cause (cf. §22-2) or an adverb clause of condition (cf. §22-3). |
| (1) | Socrates is mortal for he is a man. |
| (2) | If Socrates is a man, he is mortal. |
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![Illative Conjunction of Clauses [Ill(CL)]](gif/ri/gramri18.gif)
