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36 Cards in this Set
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Immediate Inference |
It is the bringing in of a proposition from one or more propositions. From Latin, 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.
The derived proposition is the affirmation or denial of the given proposition.
Inferences are good and bad, valid and invalid. Purists confine the term to good and valid inferences and there is much in their argument that a bad inference is no inference. The validity of the inference depends on the form of argument.
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 by 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.
The principal modes of immediate inference are: by Sub alternation, by opposition, by obversion, by conversion, and by contraposition. In sub alternation, where there is a super(above), there must be a sub(below), and a shorter term has for centuries been recognized as covering both aspects of the relation. |
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Subalternation |
Sub alternation:It 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 sub alternation 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. You must always state whether you are going from the universal to the particular or from the particular to the universal. If a mark of quantity is not expressed in the proposition, express it before treating the proposition. Must, proverbial expressions, every(distributive), all(collective) are marks of universals. 'May' is a mark of particular. In symbols, the subaltern pairs are: A-I, E-O, I-A, O-E. If we consider any pair of subalterns we see that both propositions may be true, or both may be false, and that the universal may be false and its particular true.
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. E.g All law students are philosophers. Some law students are philosophers. •Whatever is in the universal is also in the particular.
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.
Note: From the truth of the particular there is no inference as to the universal.
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.
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Contradiction |
Our presentation is on ContradictionAs you may have noticed, ever since we started Logic, we have been building. So, before we lay yet another block today, I would like to recapitulate what we've been learning since last week.We started inference and we agreed that Inference is the mental activity that involves having to move from the affirmation or denial of one proposition to the affirmation or denial of another proposition. Or we can simply say that it is the bringing in of a proposition from one or more propositions. We have the given proposition and the derived. The derived proposition is the affirmation or denial of the given proposition.The technical terms valid and invalid are used in place correct and wrong inferences respectively. There two aspects of inference: it is both in the mind and in the facts. The 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 inferring mind. There are two methods by which inference proceeds: induction and deduction.There are two forms of inference: mediate and immediate.And we are dealing with immediate inference in the mean time which we agreed that it is that in which two propositions complete the argument and that it is more concerned with truth and falsity.The principal modes of immediate inference are by sub alternation, by opposition, by obversion, by conversion and by contraposition.We learned one of the modes of inference on Monday which is Sub alternation. We learned that sub alternation is the relation that existing between two propositions which differ in quantity but have the same quality and the same terms as subject and predicate, respectively. For example, following the rule, we can derive the proposition: Some shepherds seek the good of their flocks from the given proposition: All shepherds seek the good of their flocks. In symbol, the subaltern pairs are: A-I, E-O, I-A, O-E. Where A is universal affirmative, I is particular affirmative, E is universal negative and O is particular negative. A little tip, where the quantity is not expressed, there is a need you express it. And for that I refer you to page 53 and 54 of A A Luce's Logic where you find the marks of quantity.The rules of inference in sub alternation: it is in two cases only that there is material for valid.1) from the truth of the universal we may infer the truth of the particular. And that is because whatever is in the universal is also in the particular. De umnia et de nullo. 2) from falsity of the particular we may infer the falsity of the universal. And that is because if the particular is false, the universal is also false and cannot be true.The rule of non inference under sub alternation states that from the truth of the particular, there is no inference as to the universal. Because by doing that, you will commit the fallacy of composition.You cannot go from some law students are philosophers to all law students are philosophers. We also learned that sub alternation does not state in opposition. Today, we are going to start discussing the modes of inference that state by opposition. What is opposition?Opposition is the relation between two propositions which have the same terms as subject and predicate, respectively, but which differ in quality. There are three modes of opposition: contradiction, contrariety and sub contrariety.We shall be looking into Contradiction which is the topic for our presentation. 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 from A A Luce, page 68. Paragraph 3.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-O, E-I, I-E, O-A. See page 72, at the bottom of the page. Contradictories are in the middle. 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.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 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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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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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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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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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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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.
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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 WD 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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Rule 1 |
INTRODUCTION: A. A. Luce, in our study material, Teach Yourself Logic to Think More Clearly, describes Syllogism in two aspects; the simpler and easier description: A Syllogism is a triad of connected propositions so related that one of them called the Conclusion, necessarily follows from the other two which are called the Premises; And a more penetrating and more instructive description: A syllogism 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. Syllogism therefore, is an argument composed of two connected premises which relate two terms to the same third term and a conclusion that follows (as a consequence of the two premises) which relates the two terms to one another. The two Premises and the Conclusion are connected propositions. They must comply with the following structural conditions: i. Their terms, numerically six, must be in fact three terms, each occurring twice, ii. The subject of the conclusion must occur in one of the premises, iii. The predicate of the conclusion must occur in the other premise, iv. The third term known as the Middle term must occur in both premises but not in the conclusion. The Middle term joins the two premises together and the two other terms join the premises to the conclusion. Syllogism is a connected whole. 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. Syllogistic Inference is known as Mediate because it hinges on the third term known as the Middle term, the Medius Terminus. The Middle term is the hinge of the syllogism; without it, the premises would fall apart and no mediate inference would be possible. (A. A. Luce, 1958). Logic is more concerned with the form of reasoning of an argument rather than the content. It concentrates more on validity than the veracity of the fact of an argument. For a syllogism to be valid, it has to comply with the formal rules. One of these rules, is our topic of presentation. 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. 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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Marks of quantity |
The sense of the proposition should be the first consideration. Proverbs are usually universal. He who, they who, whoever, must(knaves must be fools, all knaves are fools), every, never, never a, none, no, indicate universals. May(the learned may be wise, some learned are wise), can be, could be, a few, most, many, often, generally, sometimes, all....not, indicate particulars. All....not are O propositions. |
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Middle term |
It is the hinge of the Syllogism, without it the premisses would fall apart, and no mediate inference would be possible. The name goes back to Aristotle who named it so because he wrote in the middle. He normally wrote his Syllogism in the form, P is predicated of M. M is predicated of S. P is predicated of S. Probably, too, he thought of it as coming midway in meaning as well as in position.
Syllogistic inference is known as Mediate, because it hinges on the third term known as the middle term, Medius Terminus. |
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Contrary terms |
Two terms are contrary when they are the most opposed of those coming under the one head or class. E.g white, black. Wise, foolish. Late, early. |
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Propositions |
They are sentences to which the principles of Logic apply. |
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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. |
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Order of Terms |
The order of the terms in a proposition is for logic, neither here nor there. The important thing to look at is not the order of the terms but the meaning of the proposition . The first question to ask is: about what or whom are we speaking? The second question is: what are we saying about the subject? |
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Thought and speech |
Discourse is thought. Discourse is speech. Thought and speech are coordinate, concomitant functions of man's dual nature; because he is a rational spirit he thinks; because he is a rational spirit in a living body he utters his thoughts. |
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The Copula |
The copula is the hinge of the proposition; on it turns the relation between subject and predicate. The copula is the connecting link between the subject and predicate of a proposition. Silence is silence, and golden is golden; but if you wish to express the golden character of silence, you must connect the two words by the copula. •No copula expressed or implied, no proposition. •The copula, if expressed, is the present tense of the verb to be__is, is not, are, are not, etc. •If the copula is expressed, the predicate is often an adjective or an adjectival attribute. E.g Larch trees are deciduous. Fir trees are not deciduous. The elephant is long-lived. The mouse is not long-lived. Cycling is the cheapest form of transport. Books are a solace to the weary. •The copula, if implied, is shown usually by the inflection of the verb. E.g Birds fly. Ostriches cannot fly. Sunshine ripens the corn. The moon does not affect the weather. History repeats itself. •In poetry the copula can be left entirely to the imagination. E.g Happy the man who all his time and toil Hath spent through life upon his native soil. •The copula is a mark of predication. It shows that something is asserted or denied of a subject. It is not a mark of existence. When we say the elephant is long-lived, we do not say or mean that the elephant exists long-lived. Existence may be implied, but what we affirm is simply that the attribute long-lived applies to the species elephant. •The copula does not indicate present time. In Socrates is mortal, nothing is said about the present existence of Socrates. •• |
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Syllogism |
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. 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.
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.
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.
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.g All lawyers are good Guy is a lawyer And one to join them to one another e.g .•. Guy is good.
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Categorical proposition |
A categorical proposition is one stated without qualification or condition.-simple categorical proposition or simply, propositions. S is P, S is not P. |
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Distribution |
A term is said to be distributed if the whole of it is covered by the predication, and if only part of it is covered by the predication, it is said to be undistributed. |
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Common terms |
Common terms are so called because they are common to several persons or things, e.g shoes, ships, kings. They are also called general terms because they are shared by members of a genus or group, e.g soldier, A common term when uniquely described becomes singular, e.g the gloomy Dean, the first gentleman of Europe. |
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Singular terms |
Singular terms are individuals, either persons like Socrates, Jack, Jill, the present chess champion, the reigning toast, or individual things like the Book of Kells, the first space-satellite, the last rose of summer, the largest fish in the lake. Singular terms are as a rule subject of their propositions, they can be predicated only of another singular term e.g the principality is Wales. |
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Infinite terms |
A concrete general term negated, e.g not-man. |
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Form and formalism |
Formal Logic need not become formalist, and it loses its touch if it does. We are not studying dead words, but living discourse. For instance the word and is no mere connective form. 3 and 2 make 5 is the same mathematically as 2 and 3 make 5 but he learned logic and died is not the same as he died and learned logic. For in discourse and involves sequence. Form in Logic must be kept in touch with content. We cannot separate the form of discourse from its content. |
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Logic |
Logic comes from the Greek word, logos which means discourse. Discourse is connected thought expressed in words. It moves this way and that like a shuttle in the loom weaving the fabric of reasoned argument. Wherever men debate, discourse and argue, Logic is a court of appeal in the background; whenever a man debates a matter in his own mind, a silent Logic arbitrates. |
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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 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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Form and content |
Logic is Formal Logic. It stufies the form of discourse. The opposite of form is content or subject matter. Form is the order of terms the proposition is presented. It is a course or track or framework. Content is what the proposition is speaking of. Man is mortal. The whale is a mammal. The grass is green.
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Truth and Validity |
Logic promotes truth, yet we can go far in Logic without knowing or caring much whether a particular statement is true or false, in the ordinary acceptation of those words. By true in ordinary speech, mean true to fact, and by false we mean the opposite. A statement true to fact may in its context infringe a rule of Logic. And a statement false in fact may in its context conform to the rules of Logic. The logician is not directly concerned with fact but is much concerned with the observance of the rules of Logic, and therefore he uses the pair of technical terms, valid and invalid to express respectively what conforms to the rules of Logic and what doesn't. Valid in Latin is Validus which mean strong.
Logic concentrates on the form of the reasoning, for the most part, and is not directly concerned with the truth of the content of Syllogism. If the Syllogism complies with the formal rules, it is valid; if not, not. If the conclusion follows from the premisses, the conclusion is valid, and the Syllogism as such is valid even though premiss and conclusion may not be true to fact. E.g All fish are cold-blooded Whales are fish .•. Whales are coldblooded The first premiss is true, the second is false, the conclusion is false but the conclusion is correctly drawn from the premisses and is therefore valid in its Syllogism even though it is not true to fact. |
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Terms |
The word term, comes from the Latin terminus, a limit or boundary, for the terms of a proposition limit the movement of the thought. A term in its verbal aspect is defined as a word or combination of words which can stand by itself as the subject or predicate of a proposition. E.g the real wolf bites, big bad wolf, man, the human race. A term in its real aspect is defined as whatever we can think of and speak of as the subject or predicate of a proposition. E.g when we style Socrates, a concrete term, we do not mean the eight letterer name but the real Socrates. The subject of a proposition is that about which the statement is made. The predicate is that which is affirmed or denied about the subject. |
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Contradictory term |
Two terms are contradictory when the one is the negative of the other. E.g white, not-white. Wise, not-wise. Late, not-late. |
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Benefits of Logic |
1. Precision is the first fruit of the study of Logic. Precision will sharpen your statements and add point and force to your arguments. 2. Consistency is another fruit of Logic. Consistency in thought and speech, in feeling, character, and action, is a mark of rationality and a fruit of Logic. 3. Logic helps you to acquire and retain knowledge and to detect a bad argument. 4. Your thinking, speaking and writing gain clarity, precision and firmness. 5. Logical analysis drills the mind into exactitude. 6. Logic helps you in weighing pros and cons, and in sifting evidence. 7. Logic will leave you with a mature, critical faculty and a standpoint of your own. Other disciplines can do this for you too but Logic where it acts, acts quickly. 8. Logic points beyond itself, it will introduce you to deep questions about mind and body and to the problems of thought and thing. Logic at its lower level blends with grammar, at its height merges with philosophy. 9. Logic trains the mind to draw the right conclusion and avoid the wrong, to make true inference and not the false. |
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Second 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 there is to give. 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 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 CONCLUSION 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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Structural conditions |
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. |
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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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Third 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 not 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: No wise people are liars James is not an unwise person .•. James is not a liar
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