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Give the two definitions of the syllogism. Comment elaborately on the definitions. |
The word Syllogism comes from the Greek word, syllogismos which originally meant a reckoning up and which later came to mean reasoning in general. To syllogize is thus by derivation and usage to put two and two together in regulated discourse and to gather from them something other. It Is composed of propositions which in turn are composed of terms, and its structure should be considered and described as made up of both propositions and of terms.
Syllogism however, has been described in two ways:
The Simpler and easier description: is a triad of connected propositions so related that one of them called the Conclusion necessarily follows from the other two which are called premisses.
All boys are footballers. Adamu is a boy. Therefore, Adamu is a footballer. Footballers are related to boys. Adamu is also related to boys. Therefore, Adamu is related to footballers.
The More penetrating and more instructive description: is an argument to prove that two terms which are each related as subject or as predicate to the same third term are necessarily related as subject or as predicate to one another.
The Syllogism must have three subject-predicate propositions,Two to join terms 1 and 2 to the same third term, and one to join them to one another. Thus suppose we wish to construct an argument to prove that the two terms unselfish and happy, which are each related as subject or as predicate to the same third term, good, are necessarily related as subject or as predicate to one another, three propositions suggest themselves at once, and together constitute a syllogism, the first two propositions which relate the two terms to the same third term, being the premisses, and the third proposition which relates the two terms to one another being the conclusion:
The good are happy The unselfish are good Therefore, the unselfish are happy.
All things bright are beautiful. All Chandeliers are bright. All Chandeliers are beautiful. The two premisses join Beautiful and Chandeliers to the same third term, Bright. And the conclusion joins Chandeliers and Beautiful to one another.
In summary, in a syllogism we so unite in thought two premisses, or propositions put forward that we are enabled to draw from them or infer, by means of the middle term they contain, a third proposition called the conclusion. |
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Aristotle's definition of syllogism |
"Discourse in which certain things being stated, something other than what is stated follows of necessity from their being so." The mesh of the definition is too wide and would let in non-syllogistic inferences. In other respects it well describes the three essentials of a Syllogism: 1. The data, the 'things stated' I.e the premisses
2. The result or conclusion, the 'something other'.
3. The necessity of the consequence. |
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Discuss the virtues of syllogistic method of reasoning. |
Syllogism has been described in two ways: the simpler and easier description; and the more penetrating description. The simpler and easier description describes syllogism as a triad of connected propositions, so related that one of them called the conclusion, necessarily follows from the other two which are called premisses. And the more penetrating description describes syllogism as an argument to prove that two terms which are each related, as subject or as predicate to the same third are necessarily related as subject or as predicate to one another. All that glitters is gold. All Irons glitter. All Irons are gold.
The word Syllogism comes from the Greek word, syllogismos which originally meant a reckoning up and which later came to men reasoning in general. To syllogize is thus by derivation and usage to put two and two together in regulated discourse and to gather from them something other. It Is composed of propositions which in turn are composed of terms, and its structure should be considered and described as made up of both propositions and of terms.
All boys are footballers. Adamu is a boy. Therefore, Adamu is a footballer. Footballers are related to boys. Adamu is also related to boys. Therefore, Adamu is related to footballers.
The Syllogism must have three subject-predicate propositions,Two to join terms 1 and 2 to the same third term e.gAll lawyers are good Guy is a lawyer And one to join them to one another e.g.•. Guy is good.
Virtues of syllogistic method of reasoning: there are other ways of reasoning but men do syllogize and reason in syllogism, and the logic of the syllogism is to the average man of education a gymnasium in which to study and practice the finer points of reasoning. It benefits thus in different ways:
1. The syllogism is a test for consistency; it can furnish proof for propositions, accepted or disputed, and it can be an instrument for ascertaining new truth.
2. Syllogizing helps a man to seek and find truth for conscious syllogizing, conducted in a liberal spirit, is a general tonic for the mind.
3. A knowledge of syllogistic technique curbs hasty inference, disciplines slovenly thought, promotes precise statement, clears up ambiguities, and corrects fallacies.
4. Syllogizing encourages a man to seek premisses, to examine them, and to value good premisses.
5. It is a first-class training in drawing conclusions and testing them.
6. Disguised syllogisms occur in ordinary discourse.
In conclusion, syllogism is a form of discourse and the Latin derivative of Logic, 'logos' means discourse; therefore, syllogizing does to the mind exactly what Logic does to the mind. It works on the mind and gives it precision, firmness, consistency; it drills the mind into exactitude, helps it in weighing the pros and cons and in sifting evidence; it trains the mind to draw the right conclusion and to avoid the wrong, make true inference and not the false. It leaves one with a mature and critical faculty. |
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Highlight and comment on the structural conditions for three connected propositions to make a syllogism. |
Syllogism is an act of thought by which from two given propositions we proceed to a third proposition, the truth of which necessarily follows from the truth of these given propositions. The three connected propositions to make a syllogism must comply with the following structural conditions for the syllogism to be valid:
A. Their terms, numerically six, must be in fact three terms, each occurring twice.
B. The subject of the conclusion must occur in one of the premisses.
C. The predicate of the conclusion must occur in the other premiss.
D. The third term, known as the middle term must occur in both premisses, but not in the conclusion.
With the above disposition of terms, the syllogism is a connected whole, for the middle term joins the two premisses together and the two other terms join the premisses to the conclusion. Example, All men are footballers. Hassan is a man. Therefore, Hassan is a footballer. From the above example, the three terms are: Man(men), Hassan, and Footballer(footballers); they all occur twice in the syllogism. The subject of the conclusion (which is ‘Hassan’ called the Minor term) occurs in the second premise (called the Minor premise because it contains the Minor term, ‘Hassan’). The predicate of the conclusion (which is ‘Footballer’ called the Major term) occurs in the first premise (called the Major premise because it contains the Major term, ‘Footballer/Footballers’). The third term known as the Middle term (which is ‘Man/Men’) occurs in the first and the second premises (it joins the two premises together) but not in the conclusion.
In summary, the syllogism necessarily consists of a premiss called the major premiss, in which the major and the middle terms are compared together; of a minor premiss which similarly compares the minor and the middle term; and of a conclusion, which contains the major and minor terms only. |
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Technical terms |
The subject of the conclusion is called the minor term. And the premiss that contains it is the minor premiss. The predicate of the conclusion is called the major term. And the premiss that contains it is the major premiss. The major and minor terms when spoken of together, are called the Extremes. The conclusion before it is proved is known as the Question. The accepted order of a syllogism is: Major premiss, minor premiss, conclusion. |
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Second general rule |
The second general rule of syllogism states “No term undistributed in the premises may be distributed in the conclusion”. A term is said to be distributed if it covers the entire members of its class, while a term is said to be undistributed if it doesn’t cover the entire members of its class. For example: All books are educative. From the given example, “All books” is distributed because it covers the entire members of its class, as no other books are left out. The predicate “educative” is undistributed because it does not cover the entire members of its class as there are other things that are educative. By this rule, if a term is not distributed in either of the two premises, it cannot be distributed in the conclusion. In logic, one must not take from the given, more than is given. That a statement about a term is true in parts of its extension, doesn’t necessarily makes it true in the other parts of its extension. For instance; “Some lawyers are liars” doesn’t mean that “All lawyers are liars or lie”. For example: All dogs are carnivores Bingo is a dog Therefore Bingo is a carnivore
The breach of this rule is called Fallacy of Illicit Process; it refers to a situation where an undistributed term in the premiss becomes distributed in the conclusion.
The Fallacy of Illicit Process is divided into two: Illicit major and Illicit minor Fallacy of Illicit major occurs when the predicate of a conclusion is distributed in the conclusion and undistributed in the major premiss. For example: All fishes are cold blooded All crocodiles are not cold blooded All crocodiles are not cold blooded In the example above, the major term which is “cold blooded” is undistributed in the major premiss but distributed in the conclusion thereby making it an invalid syllogism.
Fallacy of Illicit minor occurs when the subject of the conclusion is undistributed in the minor premiss and distributed in the conclusion. For example: All dogs are carnivores All dogs are mammals All mammals are carnivores In the example above, the minor term which “mammals” is undistributed in the minor premiss but distributed in the conclusion thereby making it an invalid syllogism.
NOTE: In logic one cannot take more than what is given. The rule does not require a term to have the same quantity in the premiss and conclusion. There is nothing against a term, distributed in its premiss, being distributed in the conclusion, except that in such cases one is generally entitled to conclude about all; and if one is entitled to conclude about all, it is usually (but not always)pointless to conclude about some.
COROLLARY: the Oxford advanced learners dictionary defines corollary as a proposition which follows easily from the proof of another proposition, Something given beyond what is actually due, something added or superfluous. From rule 1(the middle term must be distributed at least once) and rule 2(no term undistributed in the premiss may be distributed in the conclusion) taken together, it follows that there must be at least one more distributed term in the premises than in the conclusion. This goes to show that the number of terms in the premiss should be more than the number of terms in the conclusion. For example: All girls are pretty Amina is a girl Amina is pretty In the example above, the number of terms distributed in the premiss is 2, while the conclusion has just 1.
EXAMPLES OF SYLLOGISMS THAT CONFORM TO RULE 2 All dogs are carnivores Bingo is a dog Bingo is a carnivore
No boys are tall Simon is a boy
All president are corrupt Buhari is a president Buhari is corrupt
In conclusion, it should be noted that a syllogism must conform to the 7 general rules of syllogism with no rule omitted. It should also be noted that there is nothing wrong with a term, distributed in its premiss, being undistributed in the conclusion. |
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First general rule |
The seven general rules of syllogism are divided into distribution of terms, quality and quantity of the premisses. The first two relate to distribution of terms, 3, 4 and 5 relate to quality and 6 and 7 relate to quantity.
THE FIRST RULE OF SYLLOGISTIC INFERENCE THE MIDDLE TERM MUST BE DISTRIBUTED AT LEAST ONCE (Aut semel aut iterum medius generaliter esto): A term is said to be Distributed when the reference is to all the individuals denoted by the term. The Distribution of the subject of a proposition is determined by the quantity of the proposition. If the proposition is Universal, affirmative or negative (A or E), the subject is Distributed; if the proposition is Particular, affirmative or negative (I or O), the subject is Undistributed. The Distributed of the predicate is determined by the quality of the proposition, and is not affected by the Distribution of the subject: if the proposition is affirmative (A and I), the predicate is Undistributed; if the proposition is negative (E and O), the predicate is Distributed.
A Middle term is a term that is common to both Premises of a Syllogism but does not appear in the Conclusion.
In the syllogism below, ‘bad’ is the Middle term and it is Distributed in the first premise; therefore, the syllogism is valid.
The bad are unhappy. The selfish are bad. Therefore, the selfish are unhappy.
The rule states, if the middle term is not distributed at least once, it cannot serve the purpose of a middle term; it cannot bring the extremes (the Major and Minor terms spoken of together) together: for it might be taken in one part of its extension in one premise, and in a different part of its extension in the other premise; and then the premises would fall asunder. Example: Tall men can sing. Juan can sing. Therefore, Juan is a tall man.
There are tall and short men, and there is nothing in the premises to show to which part of the extension of ‘singers’ Juan belongs.
All Frenchmen are Europeans All Russians are Europeans
The two propositions above do not distribute the middle term at all because that are both affirmative propositions which have undistributed predicates. It is apparent that Frenchmen are one part of Europeans and Russians are another part.
The fallacy for this invalidity is called Undistributed Middle. The Undistributed Middle is a formal fallacy in which the middle term of a syllogism is not distributed at least once. The middle term ‘sing’ in the syllogism above is undistributed in both premises; therefore, the conclusion does not follow from the premises. The syllogism is fallacious and invalid. Examples of valid syllogisms that comply with the first rule:
1. All law students are wise. John is a law student. Therefore, John is wise.
2. All lecturers are awesome. Prof. Oche is a lecturer. Therefore, Prof. Oche is awesome.
3. All lecturers are wise. Mr John Bull is a lecturer. Therefore, Mr John Bull is wise.
In conclusion, in a valid syllogism, the middle term must be distributed in at least one premise for the two terms of the conclusion to be connected through the third; at least one term must be related to the whole of the class designated by the middle term otherwise, the connection might be with different parts of the middle term.(philosophy.lander.edu). One should be careful to judge by the rules when making syllogistic inference so as not to go overboard and fall prey of committing logical fallacies. |
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Third general rule |
From two negative premisses nothing follows: If one man says, A is not B, and another adds, B is not C, no advance is registered. Nothing has been affirmed. A and C have been exclude from B, but that does not include A in C or exclude A from C. The data do not relate A and C positively or negatively.
No law students are liars Hassan is not a law students .•. Nothing follows Because liars are excluded from the middle term law students. And Hassan is also excluded from the middle term law students. So, there's no connection. The middle term is meant to link or connect the terms together so that a conclusion can follow but both terms are excluded from the middle term, therefore, no conclusion can follow. The premisses are not connected, it is first of all against the definition of syllogism itself- a triad of connected propositions so related that one of them called the conclusion necessarily follows from the other two which are called premisses.
The gist of these discussions is that where cases occur of two negative premisses apparently yielding a valid conclusion, either one of them is a disguised affirmation or there are four terms, or in some other way the inference is non-syllogistic. Exception: What is not compound is an element. Gild is not compound. Gold is an element. |
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Make a syllogism using the syllogistic mood contained in each of the following mood names: Celarent Camestres Felapton Camenes
Explain the general rule or rules you considered in each of the syllogisms. |
Mood is derived from the Latin word, modus which is the determination of the syllogism according to the quality and quantity of its constituent propositions. Each of the three propositions is designated by its appropriate vowels, written consecutively in the conventional syllogistic order-major premiss, minor premiss, conclusion-designate the Mood of the syllogism. Thus an AAA syllogism is one with three universal affirmative propositions. An EAE is one with a universal negative major, a universal affirmative minor, and a universal negative conclusion. An AAA syllogism can occur only in the first figure; an EAE syllogism can occur in the first or second figures. An EIO syllogism can occur in any of the four figures.
Celarent: No books are smart. All novels are books. No novels are smart.
Camestres: All law students are pirates. No natives are pirates. No natives are law students.
Felapton: No houses are burned. All houses are mansions. Some mansions are not burned.
Camenes: All Housa men are rude. No rude people are wise. No wise people are Housa men. |
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Do an elaborate discussion on the rule of rules. |
The rule of rules is discussed under conversion. Conversion Is the interchange of the subject and the predicate, so that the original subject becomes the predicate and the original predicate becomes the subject. The original proposition is called the convertend.The derived proposition is called the converse. The convertend and the converse have the same quality. They may or may not differ in quantity depending on the mode of conversion.
The rule of rules states that, No term undistributed in the convertend may be distributed in the converse. In inference, we must not take from the given more than is there to take. This is a fundamental principle of all inference, mediate or immediate. We must take the distribution of terms into cognizance. For instance, in some circles where Logic is undervalued, it is a short step in argument to go from, 'All learned men are wise' to 'All wise men are learned'. It is a short step but an utterly false one; and what is wrong is that the derived/inference goes beyond the given. In the given, the term wise is undistributed (being the predicate of an affirmative proposition); whereas in the inference it is distributed; from a proposition given true, connecting the 'learned' with 'some wise men', we have deduced a proposition connecting the learned with all wise men; we have no ground for the deduction, and the supposed inference proves to be a fallacy. If we convert "All metals are elements" to "All elements are metals," we imply a certain knowledge about all elements whereas the predicate of an A proposition is undistributed, and that the convertend does not really give us any information concerning all elements. All that we can infer is that "Some elements are metals;" this converse proposition agrees with the rule and the process by which we thus pass from A to I is called conversion per accidens. When the converse is a proposition of exactly the same form as the convertend the process is called simple conversion. Thus from "Some metals are brittle substances," we can infer "Some brittle substances are metals" as all the terms are here undistributed. Thus I is simply converted into I. Again from "No metals are compounds," we can pass directly to "No compounds are metals", because these propositions are both in E, and all the terms are therefore, distributed. The proposition E is then simply converted into E. The rule does not state that terms must have the same quantity in convertend and converse; and there is nothing against a term distributed in the convertend and being undistributed in the converse. What we take out of the given may be less than is given but must not be more.
In conclusion, as logicians, we must be cautious to always stick to the rules of Logic because making fallacious statements is only a slip away. |
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Distinguish between immediate inference and mediate inference. |
Inference is the bringing in of a proposition from one or more propositions. It is derived from the Latin word, infere which means to bring in. It is the mental activity that involves having to move from the affirmation or denial of a proposition to the affirmation or denial of another proposition on the basis of an insight into their necessary conclusion. Sir W. Hamilton defines inference as the carrying out into the last proposition what was virtually contained in the antecedent judgment. We are said to infer whenever we draw one truth from another truth or pass from one proposition to another.
Inference has two aspects; it is both in the mind and in the facts. Inference is an activity of the mind; it is something we do and know that we do, and do well or ill. We could not draw out the inference unless it were already there in the facts; we find it, not make it. If we are to infer validly, our inferring must be controlled by the facts, and the facts are propositions to which the mind responds, and which tend to carry the mind forward by their own momentum. Inference in the facts is often called Implication. Implication is a metaphor from folding. The logical inference is viewed as enfolded in the facts and unfolded by the activity of the inferring mind. Immediate Inference: Immediate here does not mean quick but without a middle term. Im-not mediate. In immediate inference, we start from the two terms of a proposition given true or false, and without the intervention of any other term we go straight to a second proposition called the conclusion which employs the same two terms. E.g All lawyers are liars. Some lawyers are liars.
All philosophers are wise. Some philosophers are not wise.
All A is B. No A is B.
Some A is B. Some A is not B.
All learned are wise. No learned are unwise.
No principal is wicked. No wicked is principal.
Some lawyers are wise. Some wise people are lawyers.
All lawyers are strange. Some strange people are lawyers.
All philosophers are wise. No unwise people are philosophers.
In Mediate inference on the other hand, we start from two propositions which have one term in common, called the middle term, and proceed to a third proposition called the conclusion which employs the other two terms.
All intelligent people are wise. All girls are intelligent. All girls are wise.
The two propositions: All intelligent people are wise.All girls are intelligent; are called premisses. The one common term they have, intelligent is called the middle term. The third proposition, All girls are wise; called the conclusion, employs the other two terms.
In conclusion, the validity of inference depends on the form of argument and these forms are immediate and mediate as discussed above. One must be careful to adhere to the rules these forms so as to escape making fallacious statements in argument. |
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Figures of syllogism |
The major determinant of the figures of syllogism is the varying position of the middle term. It can be the subject of both premisses, predicate of both premisses, subject of the major and predicate of the minor, or predicate of the major and subject of the minor.
The schemata of the four figures are as follows: 1.) M P 2.) P M 3.) M P 4.) P M S M S M M S M S S P S P S P S P
1) M P S M: the minor premiss must be affirmative The major premiss must be universal. Barbara, Celarent, Darii, Ferioque.
2) P M S M : one of the premisses must be negative The major premiss must be universal. Cesare, Camestres, Festino, Baroco,
3) M P M S: the minor premiss must be affirmative The conclusion must be particular Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison
4) P M M P: If the major is affirmative, the minor premiss is universal
If the minor premiss is affirmative, the conclusion is particular
If a premiss is negative, the major is premiss is universal.
Bramantip, Camenes, Dimaris, Fesapo, Fesison It is evident that the several figures of syllogism possess different characters and logicians have thought that each figure was best suited for certain special purposes. A German Logician, Lambert, stated these purposes concisely as follows: "the first figure is suited to the discovery or proof of the properties of a thing; the second figure to the discovery or proof of the distinction between things; the third to the discovery or proof of instances and exceptions; the fourth to the discovery or exclusion of the different species of genus. " |
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Sixth general rule |
From two particular premisses nothing follows. Suppose it is possible that there could be two particular premisses. These must be II, IO, OI, OO. II contains no distributed term and is excluded by rule 1. IO, OI contain only one distributed term apiece, and are excluded by rule 5 the conclusions of which must be negative, and their predicates distributed, and therefore by the corollary of rules 1 and 2 two distributed terms apiece in the premisses would be required. OO is excluded by rule 3. |
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Differences between contradiction and contrariety |
1. In contradiction, the two propositions differ in both quality and quantity. While in contrariety, they only differ in quality. E.g 2. The two propositions cannot both be true nor can they both be false. While they may be both false but they cannot both be true. 3. One of them must be true and the other must be false. They may both be false and cannot be both true. 4. We can argue from falsity to truth and vice versa. While we cannot argue from falsity to truth. 5. Contradiction denies in part while contrary deny in its whole extent. 6. Symbols from A-O, E-I,. While A and E. |
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Contraposition |
Consists in first obverting, and then converting the obverse. The chief use of the process is to alter the quality of a negative convertend, it transfers the negation to the predicate, and thus enables the converse to admit an undistributed predicate. In this way, it does for O propositions what conversion proper cannot do. A is contraposed simply; for its obverse is E. E is contraposed per accidens; for its obverse is A. I cannot be contraposed; for its obverse is O. O can be contraposed simply; for its obverse is I. Examples: All S is P No not-P is S. All mistakes are excusable. Nothing inexcusable is a mistake. Some remedies are not pleasant Some unpleasant things are remedies. No S is P Some not-P is S Some S is not P Some not-P is S No Arabs are inhospitable Some hospitable people are Arabs. No legends are historical. Some unhistorical tales are legends. In conclusion, in all these cases the original subject is the predicate of the contrapositive and the contradictory of the original predicate is its subject. No further process is required in syllogistic logic. |
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Show the rules of inference in contradiction. |
Contradiction is a mode of inference that state by opposition. Opposition is the relation between two propositions which have the same terms as subject and predicate, respectively, but which differ in quality. In Contradiction, there are two contradictory propositions in which one affirms what the other denies. They differ both in quality and in quantity. They cannot both be true nor can they both be false. One of them must be true and the other must be false. According to Aristotle, in his Metaphysics, book iv, part 4, translated by W. D Ross: "it will not be possible to be and not be the same thing". Following the rule, let's see some examples: All poets try to please. Some poets do not try to please. Differ both in quantity and quality. No poets try to please. Some poets try to please. Some books are not worth binding. All books are worth binding. In symbols, the contradictory pairs are: A to O, E to I, I to E, O to A. The rules of inference: 1) from the truth of either contradictory we may infer the falsity of the other. 2) from the falsity of either contradictory we may infer the truth of the other. Therefore, If A is true, O is false. If E is true, I is false. If I is true, E is false. If O is true, A is false. If A is false, O is true. If E is false, I is true. If I is false, E is true. If O is false, A is true. The rules however, is between propositions with a common term as subject; where the subject is a singular term, contradiction is irregular. For example, Jack loves Jill is adequately contradicted by Jack does not love Jill. As we know, all singular terms are universal. The quantity does not change and the rule of Contradiction is not strictly followed. That is why it becomes irregular because you cannot say Some Jack does not love Jill. In conclusion, Contradiction in practice: Contradiction is a precise thing and not just any form of verbal opposition. If you think that a statement needs contradicting then contradict it but know the rules and keep them. Contradict the statement rather than the man who made it. Attacking the man is the wrong approach, that is the spirit of all-out opposition, the club and not the rapier. You'll fall prey of committing the fallacy of ad hominem. Attacking the person rather than the argument. If it suffices to contradict a statement, it is a bad tactics to do more. You will go beyond your brief and expose yourself to a damaging counter attack. Supposing someone says, No corporal punishment is justifiable, and you feel the proposition should be contradicted, begin systematically. It is an E proposition; therefore, its contradictory is I. Some corporal punishment is justifiable. If you know your justifiable types, then you have sufficiently disproved the statement to which you took exception. If you go to the opposite extreme and say, All corporal punishment is justifiable, you are playing into your opponent's hands and he will upset your statement by producing some harsh statute of former days that no one today could defend. |
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Subcontrariety |
Of two subcontrary propositions the one affirms particularly what the other denies particularly. They may both be true, they cannot both be false. Being both particular and differing in quality, they are in symbols, I and O. E.g Some rivers are alkaline. Some rivers are not alkaline. Some slow driving is not good driving. Some slow driving is good driving. The rule of inference: from the falsity of either subcontrary we may infer the truth of the other. Since both subcontraries may be true, we cannot argue from truth to falsity as in Contrariety. T-T F-T T-there cannot be falsity. The rules of inference and non-inference can be deduced from those of Subalternation and contradiction. If I is false, E is true (by c), therefore, O is true (by s). If O is false, A is true (by c), therefore, I is true (by s). If I is true, E is false (by c), thence there is no inference as to O. If O is true, A is false (by c), thence there is no inference as to I. |
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Conversion |
Is the interchange of the subject and the predicate, so that the original subject becomes the predicate and the original predicate becomes the subject. The original propositional is called the convertend.The derived proposition is called the converse. The convertend and the converse have the same quality. They may or may not differ in quantity depending on the mode of conversion. Rule of rules: No term undistributed in the convertend may be distributed in the converse. In inference, we must not take from the given more than is there to take. The rule does not state that terms must have the same quantity in convertend and converse; and there is nothing against a term distributed in the convertend and being undistributed in the converse. What we take out of the given may be less than is given but must not be more. There are two modes of conversion: 1. Simple: when the quantity of the the converse is the same as the convertend. Only E and I convert simply. No S is P No P is S No proteins are free from nitrogen. No things free from nitrogen are proteins. Some S is P. Some P is S. Some drag hunts are monotonous. Some monotonous occupations are drag hunts. 2. Per Accidens: when the convertend is universal and the converse particular. Only A propositions convert per accidens. All S is P Some P is S All sugars are soluble in water Some things soluble in water are sugars. Singular propositions cannot be converted where only the subject is singular. We can alter the order of the words but cannot transpose subject and predicate. Where both terms are singular, conversion is possible in theory. E.g Tully is Cicero Cicero is Tully. |
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Seventh general rule |
If either premiss is particular, the conclusion is particular. First case: both premisses are affirmative. These must be A and I, which between them have only one distributed term, and two would be required by the above corollary if the conclusion were universal. the conclusion therefore is particular.
All Nigerians are wise Some people are Nigerians .•. Some people are wise
Only one term is distributed 'All Nigerians'. Two would be required if the conclusion were universal.
Second case: one of the premisses is negative. The pairs must be either AO or EI. Each of these pairs contains only two distributed terms and since the conclusions are negative, three would be required by the corollary if the conclusions were universal. Therefore the conclusion is particular.
All philosophers are learned Some Nigerians are not philosophers .•. Some Nigerians are not learned.
Two distributed terms, 'all philosophers' and 'not philosophers'. Three would be required if the conclusion were universal.
No law students are liars Some people are law students .•. Some people are not liars.
The two terms in the first premiss are both distributed. Three would be required if the conclusion were universal. |
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Obversion |
Also known as Permutation, the quality of the proposition is changed, and for the predicate its contradictory term is substituted, the meaning of the proposition remains substantially unaltered. The given proposition is called the obvertend. The derived proposition is called the obverse. The obvertend and obverse should be equipollent.They have the same subject, and much the same thing is predicated of it in both propositions ; but the one affirms the predicate while the other denies its contradictory. To obvert: 1. Leave the subject and its quantity as they are. 2. Substitute for the predicate its contradictory. 3. Change the quality: a. In A and I propositions attach a not to the copula. b. In E and O propositions omit the not or its equivalent from the copula. The given proposition must be in full logical form with the copula expressed. Established contradictories, like untrue, irrational, etc, should be used in preference to compounds with not or non. All men are reasonable. No men are unreasonable.
No tigers are merciful. All tigers are merciless. No men are perfect. All men are imperfect. Some men are not trustworthy. Some men are untrustworthy. |
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Fifth rule |
If either premiss is negative, the conclusion is negative. In this case, the one premiss is affirmative, and the other negative; that is to say, the one extreme includes, or is included in the middle term, and the other extreme is excluded from the middle term. If anything follows, it must be the exclusion of the one extreme from the other, not the inclusion of the one extreme in the other; it must be the denial of relation between them, not the affirmation of relation between them. |
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Contrariety |
Of two contrary propositions, the one denies in its whole extent what the other affirms. They cannot both be true but they may both be false. They must be universal and of different quality, and therefore, in symbols, they are A and E. E.g All Cretans are liars. No Cretans are liars.
No actions are free. All actions are free.
The rule of inference: From the truth of one Contrary we can infer the falsity of the other. Since both contraries may be false, we cannot argue from falsity to truth, as we can in Contradiction. For instance, if it is false that all punishment is remedial or that no punishment is remedial, there is no valid inference as to the truth of their contraries.
T-T T-F F-nothing follows.
Rules of inference and non-Inference from contraries can be deduced from those of Subalternation and contradiction. If A is true, I is true(by s), therefore E is false (by c). If A is true, O is false (by c), therefore, E is false (by s). If E is true, O is true (by s), therefore, A is false (by c). If E is true, I is false (by c), therefore, O is false (by s).
If A is false, O is true (by c), thence there is no inference as to E. If E is false, I is true (by c), thence, there is no inference as to A. |
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Fourth general rule |
From two affirmative premisses a negative conclusion cannot follow: In other words, if the conclusion is negative, one of the premisses must be negative. For when both premisses are affirmative, the extremes are included in the middle term; but that can give no grounds that the one extreme excludes the other.
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Differences between contrariety and subcontrariety |
1. Denies in its whole extent. Denies particularly.
2. From the truth we may infer. From the falsity we may infer.
3. Both cannot be true but both may be false. Both may true but both cannot be false.
4. Cannot argue from falsity to truth. Cannot argue from truth to falsity. 5. A and E. I and O. |
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In setting out and testing arguments from sub alternation we must be careful to state whether the argument is from truth to truth or from falsity to falsity. Elaborate |
Subalternation is the relation existing between two propositions which differ in quantity but have the same quality and the same terms as subject and predicate respectively. The name subalternation is given also to the inference based on that relation. By a natural convention, the universal is regarded as above(super) and the particular as below(sub). Examples: All shepherds seek the good of their flocks. Some shepherds seek the good of their flocks.
No canals contain running water. Some canals do not contain running water.
Some patriots are disinterested. All patriots are disinterested.
Some arts are not crafts. No arts are crafts.
In symbols, the subaltern pairs are: A-I, E-O, I-A, O-E.
In two cases and in two cases only, there is material for valid inference: 1. From the truth of the universal, we may infer the truth of the particular. Because Whatever is in the universal is also in the particular. E.g All law students are philosophers. Some law students are philosophers.
2. From the falsity of the particular we may infer the falsity of the universal. Everyone knows the saying, 'you cannot argue from the particular to the universal', and it is a true saying with regard to arguments from truth to truth, but it is not true with regard to arguments from falsity to falsity. To argue from 'some children get mumps' to 'all children get mumps' is a downright fallacy- fallacy of composition. It is the argument from the truth of the particular to the truth of the universal. On the other hand, to argue from the falsity of 'some drones gather honey' to the falsity of 'all drones gather honey' is perfectly valid. Here we are told that it is false that some drones gather honey, which is the same as saying that drones do not gather honey; and so the statement in question is upset. It is false that all drones gather honey. The same argument applies whatever the subject or predicate; if it is false that some students like Logic, it must be false that all students like it. In general, if it is false that some S is P, it must be false that all S is P. Other examples: Some water run uphill. All water run uphill.
Some men are not mortal. All men are not mortal.
In setting out and testing arguments from sub alternation we must be careful to state whether the argument is from truth to truth or from falsity to falsity: if we are going from truth to truth, it has to be from the universal to particular because whatever is in the universal is also in the particular; if we are going from falsity to falsity, it has to be from the particular to the universal because if something is not true of a part, it cannot be true of the whole.
Note: From the truth of the particular there is no inference as to the universal because that is a downright fallacy, a fallacy of composition: the error of assuming that what is true of a member of a group is true for the group as a whole. |
