Lecture on Eduction

IMMEDIATE INFERENCES:EDUCTION
Jamil Adrian L. Matalam

There are generally two kinds of immediate inferences, eduction and oppositional inferences. They are said to be inferences because they have the nature of being a derivative, a taken from or drawn out. In this case, there are presuppositions, that which is something prior to which we draw out; for instance, in the act of taking there must be some object that is taken or the object from which we take something which comes first. Thus, Sirs Ryan Maboloc and Jet Pascua tells us that “inference is the way by which the mind acquires new knowledge from a set of facts that is already known” (Maboloc and Pascua, 32). To infer, then, is to draw conclusions from something given through thinking, or through the operation of the intellect (logic) in the mind. Conversely, in the act of concluding, or thinking, we infer. Truly, inference is (logical) thinking, and not simply the exercise of realigning or rearranging the subject and the predicate of propositions.

They are said to be immediate because they do not have essentially a middle term, a mediator. They are not borne out of combinations or comparisons, synthesis; they are what are called implied. Meaning, the ideas we infer from them are intrinsically part of the meaning of a given idea or proposition. The conclusions that we draw are from the object alone and not through the mediation or intervention of another matter. Thus the conclusion that Socrates is mortal cannot be an immediate inference because it is done through an act of combinations or comparisons. In such a conclusion the ideas of mortality and Socrates are combined and compared. We cannot infer that Socrates is mortal from the idea alone of what is mortal; we must also have an idea of what Socrates is before we could have such conclusion. Immediate inferences therefore, unlike mediated inferences, are conclusions drawn from one idea alone without comparing or combining it with another. They essentially belong to the same given idea or proposition but are not expressed, they are implied. Thus to have knowledge about them we use inferences (logical thinking), we make them express, or expose them from their being implied or hidden. Let us take for example the idea or proposition ‘All human beings are mortal creatures’. From it alone we could infer that some mortal creatures are human beings; or infer the opposite that all human beings are not immortal.

This lecture shall be essentially limited with the discussion of eduction as a mode of immediate inference. Eductions could be conversion, obversion, contraposition, and inversion. Further, we shall deal only with the first two since the knowledge of them is generally essential in proceeding with the last two, and because of energy and time constraint. We shall deal with the other two next time.

CONVERSION

We converse when we infer a new conclusion or idea by interchanging (conversing) the subject with its predicates. Thus, the converse of the idea or proposition that ‘life is unfair’ is ‘some unfair thing is life’. Note that the new conclusion, we call it converse, is implied in the given idea or proposition, we call convertend. We have arrived at a new idea, meaning, or an insight, not outside the meaning or extension of the given idea or proposition, it is derived from the nature of that idea alone. (If life is unfair then some unfair thing is life). Since it is not something outside the given idea it is in a certain sense not something new; no synthesis of ideas resulted. Conversion is simply the reversals, flip-flopping, of ideas or propositions, of course with the intention of discovering further the nature or truth of an idea. It is therefore an action of the intellect in the mind, of thinking, and thus a subject proper of logic.

One of our tasks in the Philo 102 course is the analysis of ideas or propositions. The course is also a study of the rules of formal logic. Therefore in our analysis of propositions we must observe these rules of formal logic. It is essential that we understand these rules lest we may not apply it correctly, and ultimately we end up having illogical and false ideas.

Sirs Ryan and Jet has provided as a good discussions of these rules. Let us review the contents of their book on logic entitled Elements of Logic, and review the rules in conversion of propositions. We shall just simplify our discussion of the rules. Afterwards, have some examples of its application.

The rules that are generally observed in conversions of propositions are the following:
1. Interchange subject and predicate of the given proposition
(convertend);
2. the quality of the proposition retained; and lastly
3. no term must be extended.
But we shall keep in mind of these following matters:
1.Only an (A) proposition can be partially converted, meaning an (A)
proposition can be converted to an (I) proposition and no other proposition.
2. Complete or total conversion can only be done and only with (E) and (I)
propositions.
3. Thus, an (O) proposition cannot be converted.

Let us see some examples of the application of these rules of conversion. Let us analyze these propositions.
1. (A) Every p is a q (convertend), let us converse this proposition.
1. (I) Some q is p. (converse)

Note that in this example we observed the three rules. First, we interchange the subject and predicate; then we retained the quality of the proposition which is affirmative; and lastly we did not extend any term. The last rule explains why in the converse the term some is used instead of every. Since the quantity of the predicate in the given proposition is particular we cannot extend it to universal, thus we cannot retain the term every. Moreover, we must keep in mind that an (A) proposition can only be partially converted, it can only be converted to an (I) proposition.

This time let us analyze these examples of conversion:
2. (E)Every p is not a q. (convertend)
2. (E) Every q is not a p. (converse)
3. (I) Some x is a y. (convertend)
3. (I) Some y is an x. (converse)

In the following examples the quantity of the propositions are retained, unlike the number 1 example. This is so because an (E) and an (I) proposition can be completely converted. Note that we have observed the three general rules of conversion; subjects and predicates were interchanged, quality retained, and we did not extend any term.

This time let us try to convert this idea or proposition.
4. (O) Some x is not a y. (convertend)
4. (O) Some y is not an x. (converse)

The conversion in this example is erroneous, wrong. The answer or converse was not mindful that (O) propositions cannot be converted. Formally, it violated the set rules of conversion and therefore wrong and illogical. Substantially, (O) propositions or ideas cannot be converted since they result to wrong inferences, they result to conclusions that are not implied in the given proposition or idea, and absurd or illogical conclusions. Take for example the proposition ‘some animals are not human’ and converse it to ‘some humans are not animals’. In this case, we end up with a wrong immediate inference and absurd conclusions. To infer that some humans are not animals is to extend the term human. There is therefore a violation of the third rule of conversion. Moreover, it leads to illogical and absurd conclusions. To infer that some humans are not animals is to reverse the order of things, and thus it is logically impossible or invalid. This is so because the idea animals is broader or superior than the idea human; thus the idea or term human is an example, particular, or inferior to the term animals. To say that some humans are not animal is obviously wrong, absurd and illogical idea.

A further question was asked by a student concerning conversions. May an (E) proposition be converted to an (O) proposition? Could there be a conversion from an (I) proposition to an (O) proposition?

The answer to question is no. No to the first question because only (A) proposition can be partially converted. Moreover, (E) are negative propositions and thus generally it is an exclusion of ideas; meaning it separates ideas. Converting it then to (O) proposition would lead to an extension of terms. No to the second question because the second rule of conversion is violated, the quality of the given proposition is not retained. An (I) proposition is an affirmative proposition, and converting it an (O) proposition would change its quality to a negative proposition.

OBVERSION

Another mode of eduction is obversion. In obversion we change the quality of ideas without changing its meaning. We turn around the same idea inside to out, or front to back, to see it in an opposite way, from positively looking at ideas to negatively looking at it or vice versa. We infer the opposite perspective of the same idea or proposition in terms of its quality. Thus, if the proposition ‘life is unfair’ is obversed we yield the inference ‘life is not fair’. Note that idea or meaning of the proposition is not changed but its quality changed by the use of the negative copula not. What we usually do in obversion is to think about or restate the idea or proposition by changing its quality and by providing the contradiction of its predicate.

Like conversion, obversion has formal rules that must be observed in arriving at a correct inference. They usually involve changing the quality and the predicate of the given proposition. Here is a more detailed account of the rules.
1. The subject and quantity of the proposition must be retained;
2. the quality of the proposition is changed by removing or adding
negatives copulas; lastly
3. use the contradictory of the predicate of the given proposition or
obvertend.
In this case we should be mindful of the following:
1. Only an (A) proposition can be obversed to an (E) proposition and vice versa.
2. Only an (I) proposition can be obversed to an (O propositiom and vice versa.
3. Therefore all obversion are by nature complete or total. No obversion may happen
from (A) to (O) or from (E) to (I). Moreover, there could be no obversion from (A) to
(I) or from (E) to (O) obviously because the second rule will not be observed, the
qualities of said propositions are the same.

Let us see some examples of the application of these rules. Let us try to analyze these propositions:
1. (A) Every man is homo economicus. (obvertend)
1. (E) Every man is not non-homo economicus. (obverse)
2. (E) All non-p is not a non-q. (obvertend)
2. (A) All non-p is a q. (obverse)
3. (O) Love is not a thing. (obvertend)
3. (I) Love is a non-thing. (obverse)
4. (I) Some games are non-violent. (obvertend)
4. (O) Some games are not violent. (obverse)
Clearly, the rules of obversion have been observed by the examples provided. Number 1 example for instance, reveals to us that the quantity and the subject of the proposition are retained, but the quality of the proposition is changed, and the contradictory of the predicate of the overtend is used, it was changed from homo economicus to non-homo economicus. The rest of the examples observed the same rule. Note that there are no examples of partial obversions like from (A) to (I) or from (E) to (I) since doing so is a clear violation of the first rule, the quantity of the proposition must not be changed. Thus, if one insists on partial obversion one may end up having wrong inferences or absurd and illogical ideas.

Perhaps athis point we could end the dicussion on the first two modes of eduction. We shall just proceed with the other two at another opportune time. Therefore the coverage of the preliminary examinations would begin with chapter 3 of your textbook and end with the idea of obversion.

I have some important reminders for the examination. Please do not forget to bring the following materials on the examination schedule:
1. Textliner or highlighter.
2. Legal sized (long) bond papers.
3. Either blue or black pens. Pencils will not be allowed in answering
the examination.


Reference
Maboloc, Christopher Ryan and Pascua, Edgar III. 2008. Elements of Logic: An
Integrative Approach. Quezon City, Philippines: Rex Bookstore.