Transcript of LOGICAL WAY OF EDUCTION
This term is defined as a logical way of re-expressing
the proposition by interchanging is subject and
predicate and in using or removing its negative to
retain its original meaning. Out of this nature, eduction
is sometimes called the logical process of re-expression.
DEFINITION OF EDUCTION
KINDS OF EDUCTION
There are four renowned
kinds of eduction these are:
defined as a logical way of re-expressing the proposition by interchanging its subject and predicate without changing its quality. There are two types of conversion namely: simple and partial conversion.
However, both types follow two fundamentals rules and these are the following:
1. Interchange the subject term and the predicate term.
2. Retain the original quality of the proposition.
SIMPLE CONVERSION is simply done by interchanging the subject and the predicate without affecting he quantity of both (subject and predicate) and the meaning of the original proposition or the convertend. This kind of conversion is viable only to propositions I and E. As a matter of consideration these two propositional symbols are taken from the very word known as SIMPLE where I and E are the only two vowels.
I to I:
Convertend: Many treasure hunters are successful businessmen.
Converse: Many successful businessmen are treasure hunters.
E to E:
Convertend: No Protestants are Catholics.
Converse: No Catholics are Protestants.
Note that A and O propositions are not indicated here, the reason for this is that they cannot be converted using the simple conversion. If A proposition will be converted using the simple conversion then he subject will become its predicate. This cannot be done for the quantity of the subject A is universal and its predicate’s quantity is particular. Now if the subject will be interchanged with the predicate then the quantity of the predicate will be extended and this will lead to a fallacy of illicit process of the major term. We shall know more about this fallacy the moment we get to the realm of the syllogistic interference and its rules.
In another perspective, O proposition cannot be converted using the same process for its subject is particular and its predicated is universal. Interchanging the subject with the predicate will mean an interchange also of their individual quantities. Hence, it will become another case of fallacy of illicit process.
PARTIAL CONVERSION is done when an original proposition or convertend is transformed
from universal to particular. Such type of conversion is applied to proposition A which is
transformed later into an I proposition and E which is to be converted to O proposition.
A to I:
Convertend: All Japanese are Asians.
Converse: Some Asians are Japanese.
E to O:
Convertend: No stars are galaxies.
Converse: Some galaxies are not stars.
The two examples above are conceived following the principle that “particulars” are contained in the extension o the ‘universals”. Therefore, they are all valid. It should be underscored that partial conversion cannot be used to convert a particular proposition into universal because by doing so will entail a fallacy of illicit process again. This will make converse to be invalid
done when only the quality of the original proposition or obvertend is changed without affecting its quantity.
Such logical way of re-expressing proposition follows three rules:
1. Retain the original subject and the quantity of the original proposition or obvertend
2. Change the quality of the obvertend either from affirmative to negative or negative to affirmative.
3. Present the contradictory of the original predicate
This case is applied to the universals; let’s say A proposition is re-expressed into E proposition or vice versa and also to the particulars thus I proposition is re-expressed into O proposition or vice versa.
Consider the following examples below:
A to E:
Obvertend: All dolphins are sea creatures.
Obverse: No dolphins are non-sea creatures.
E to A:
Obvertend: No patriots are secessionists.
Obverse: All patriots are non-secessionists.
I to O:
Obvertend: Some students are technologically inclined.
Obverse: Some students are not non-technologically inclined.
O to I:
Obvertend: Several foreign students in the Philippines are not Koreans.
Obverse: Several foreign students in the Philippines are non-Koreans.
logical way done by interchanging the subject and the predicate like in Conversion and presents the subject as the contradictory of the original predicate like in Obversion. There are two types of contraposition, the simple contraposition or the type 1 and the complete contraposition or the type 2. The original proposition in contraposition is known as contraponend and the new proposition is called as contraposit or contrapositve.
In SIMPLE CONTRAPOSITION OR TYPE 1, the subject is the contradictory of the original predicate, the quality is changed and the predicate is the former subject of the original proposition.
Here, two rules must be known and must be followed so that a correct form of re-expression will be attained.
1. Obvert the contraponend.
2. Convert it afterward.
These rules of contraposition are to be applied in A to E, E to I and O to I proposition.
A to E:
Contraponend: Every brain surgeon is a medical expert.
1. Obvert: No brain surgeon is a medical expert.
2. Convert: No non-medical expert is a brain surgeon.
Contrapositive: No non-medical expert is a brain surgeon.
A to E:
Contraponend: All painters are artists.
1. Obvert: No painters are non-artists.
2. Convert: No non-artists are painters.
Contrapositive: No non-artists are painters.
E to I:
Contraponend: No philosophers are morons.
1. Obvert: Some philosophers are non-morons.
2. Convert: Some non-morons are philosophers.
Contrapositive: Some non-morons are philosophers.
O to I:
Contraponend: Many saints are not medieval people.
1. Obvert: Many saints are non-medieval people.
2. Convert Many non-medieval people are saints.
Contrapositive: Many non-medieval people are saints.
In COMPLETE CONTRAPOSITION OR TYPE 2, the subject is the contradictory of the original predicate, the quality is unchanged and the predicate is the contradictory of the former subject of the original proposition.
Here, three rules must be followed:
1. Obvert the given contraponend.
2. Convert it afterward.
3. Obvert it again.
These rules are to be incorporated whenever A is to be expressed into A, E to O and O to O. Again I proposition has no contrapositive.
A to A:
Contraponend: All princes are of noble origins.
1. Obvert: All princes are of non-noble origins.
2. Convert: No non-noble origins are princes.
3. Obvert: All non-noble origins are non-princes.
Contrapositive: All non-noble origins are non-princes.
E to O:
Contraponend: No horses are three-legged creatures.
1. Obvert: All horses are non-three-legged creatures.
2. Convert: Some non-three-legged creatures are horses.
3. Obvert: Some none-three-legged creatures are not non-horses.
Contrapositive: Some none-three-legged creatures are not non-horses.
O to O:
Contraponend: Several overseas workers are not nurses.
1. Obvert: Several overseas workers are non-nurses.
2. Convert: Several non-nurses are overseas workers.
3. Obvert: Several non-nurses are not non-overseas workers.
Contrapositive: Several non-nurses are not non-overseas workers.
defined as a logical way of re-expressing the original proposition or invertend into a new proposition or inverse whereby the subject becomes the contradictory of the original subject. Like in contraposition, there are two types of inversion and these are simple inversion or type 1 and complete inversion or type 2.
SIMPLE INVERSION OR PARTIAL INVERSION OR TYPE 1, normally, happens if the quality of the invertend is changed but retaining the character of the original predicate. In this context, A proposition is re-expressed into an O proposition and E proposition is re-expressed to I porposition.
Simple Inversion is possible only if three simplified rules indicated here will be followed.
1. Present the contradictory form of the original subject.
2. Change the quality
3. Retain the predicate.
A to O:
Inverted: All creatures are organisms.
Inverse: Some non-creatures are not organisms.
This example presents the contradictory form of the original subject in which the subject “creature” has become “non-creature” and the quality is changed from affirmative to negative. Thus, the copula “are” becomes “are not” while the predicate remains the same.
E to I:
Invertend: No humans are naturally quadruped.
Inverse: Some non-humans are naturally quadruped.
This example is completely different from the first example but somehow the rules applied to re-express the proposition are the same. Hence, the subject “humans” is changed into “non-humans” which is actual contradictory form of the original subject and the quality is transformed from negative to affirmative while the predicate remains to be the same.
COMPLETE INVERSION happens if the quality of the invertend is unchanged yet the predicate is now the contradictory of the original predicate. It normally occurs when A proposition is transformed into I and E proposition to O.
This can be done by following the three simplified rules.
1. Retain the subject and predicate.
2. Present the contradictory form of both the subject and the predicate of the original proposition.
3. Never change the quality
A to I:
Invertend: All priests are evangelists.
Inverse: Some non-priests are non-evangelists.
The interchanging of the subject and predicate did not happen here and by presenting the contradictory form of the subject “priests” to “non-priests” and the predicate “evangelists” to “non-evangelists” without changing the quality of the proposition, we attained a complete inversion of this example.
E to O:
Invertend: No cancer patients are healthy people.
Inverse: Some non-cancer patients are not non-healthy people.
This example is simply the reiteration of the three rules which are applied in the first and second example. However, for the sake of clarification, the copulas “are not” attached in the inverse is not an expression that we violated the third rules which is “Never change the quality”. It should be clearly known that E proposition is by nature negative, therefore the copula “are not” attached to the inverse is, indeed, an application of the rules of inversion.