Indirect reasoning and syllogism | A Short History of Philosophy
Home Chapter History of Philosophy Introduction to Philosophy Ancient Philosophy Medieval philosophy Modern philosophy Contemporary philosophy philosophical discipline Hrestomatija Introduction to Philosophy - Ancient hrestomatija f. - Hrestomatija Medieval f. - Hrestomatija Modern f. - Hrestomatija Modern f. - Hrestomatija F. disciplines - hrestomatija Literature Philosophy Today Course philosophy Logic Basic forms opinions Miscellaneous
We have said already that the premise is based on the number and manner of reasoning, any conclusion can be divided into direct and indirect. Immediately halls of reflection conclusion we have covered halls of reflection in the previous lesson. Indirect reasoning is reasoning that starts from two or more premises and with whom some concepts that appear halls of reflection in the premises does not appear in the conclusion. These terms are called "intermediate concepts" and serve as a link through which we conclude.
The conclusion from only two premises called halls of reflection syllogism and a basic form of indirect reasoning in classical logic. Syllogisms halls of reflection that such premises and conclusions have a AEIOU testimony, therefore, the testimony of predikatskoj arranged form, detail is described by Aristotle. For example, following halls of reflection the conclusion of a syllogism:
The term "big cats" plays the role of the middle term (which is usually designated with the letter M). He appears in both premises, and there is no one in the conclusion. In addition to the role of the middle of the term there are two other roles in terms syllogism: P, or a great concept, a concept that is the predicate of the conclusion and landscaped syllogism appears in the first, large, premise, while the S, a small term, a term that is subject to conclusion and landscaped syllogism appears in the second, small, premise.
Our syllogism of lions is the correct one (valid in the wider and narrower sense), halls of reflection syllogism because the conclusion actually follows from the premises. If you accidentally ređali AEIOU attitudes that include large, small and medium term sometimes so are aligned positions (first two premises and a conclusion for them, for example: AA E) were correct, and sometimes it would not. To correct ways or forms of reasoning separated from defective (invalid in the strict sense of whom we spoke above), halls of reflection logicians have decided to try all possible combinations halls of reflection of premises and conclusions, and allocate the correct forms. The first is that Aristotle did, and we will now describe his method.
He singled out the first possible combination of terms in the position statement and this combination is called syllogism figures. Because the definitions of small, halls of reflection large and medium term, but largely determined by their position in the premises and the conclusion, the rest is just to vary the order of terms in the premises. Possible combinations was four, so we have four figures syllogism, called simply figure I, II, figures, etc. Here they are:
P - M
Our top syllogism of the lions was a syllogism and figures, and attitudes in him were all forms of universal-affirmative statements A and AA A. Of course, if we look at the combination AEIOU statements within one figure, it turns out that there are 64, making a total of 256, or a combination of modes of syllogisms. Fortunately, when they tested all of these modes it turned out that only 24 of them correctly, and that 5 of these 24 such that claims less than what can be deduced from the premises (For example, we were able to conclude the E statement halls of reflection that no S is not P, but instead only argue that some S is not P (A statement)). When subtracting these five, the rest is 19 correct mode. We will see that this number could be reduced by another 4, but first let's see how the logicians separated correct from incorrect mode.
To see that the correct modes, logicians have had to establish some rules valid syllogism, and are determined by them and valid modes. halls of reflection These rules are in turn divided into a group of axioms syllogism, that is, rules that do not prove theorems and syllogisms, halls of reflection which are rules that may prove as valid, if applicable axioms. For axioms correct syllogism halls of reflection is taken these five rules: The term (term) that is not broken down by individual premises, there can be no Torn apart in the conclusion. The middle term must be Torn apart at least one premise. Both premises can not be negative. If one premise is negative, the conclusion is negative. If both premises are affirmative, the conclusion must be affirmative.
Based on these axioms can prove the basic theorems that are valid for all figures syllogism: The conclusion must be at least one less the distributed terms, than it was in the premises. Both premises can not be particular. If one particular premise, and the conclusion is partikularan. Premise halls of reflection can not line up in IE combination.
Proofs of these theorems are not difficult. For example, the conclusion must be at least one less than the distributed term in the premises, because the premise is the middle term, which by axioms 2, must be distributed in at least one premise, and does not appear in the conclusion.
If you apply these rules to the 256 mode, stays those mentioned 24th As
Home Chapter History of Philosophy Introduction to Philosophy Ancient Philosophy Medieval philosophy Modern philosophy Contemporary philosophy philosophical discipline Hrestomatija Introduction to Philosophy - Ancient hrestomatija f. - Hrestomatija Medieval f. - Hrestomatija Modern f. - Hrestomatija Modern f. - Hrestomatija F. disciplines - hrestomatija Literature Philosophy Today Course philosophy Logic Basic forms opinions Miscellaneous
We have said already that the premise is based on the number and manner of reasoning, any conclusion can be divided into direct and indirect. Immediately halls of reflection conclusion we have covered halls of reflection in the previous lesson. Indirect reasoning is reasoning that starts from two or more premises and with whom some concepts that appear halls of reflection in the premises does not appear in the conclusion. These terms are called "intermediate concepts" and serve as a link through which we conclude.
The conclusion from only two premises called halls of reflection syllogism and a basic form of indirect reasoning in classical logic. Syllogisms halls of reflection that such premises and conclusions have a AEIOU testimony, therefore, the testimony of predikatskoj arranged form, detail is described by Aristotle. For example, following halls of reflection the conclusion of a syllogism:
The term "big cats" plays the role of the middle term (which is usually designated with the letter M). He appears in both premises, and there is no one in the conclusion. In addition to the role of the middle of the term there are two other roles in terms syllogism: P, or a great concept, a concept that is the predicate of the conclusion and landscaped syllogism appears in the first, large, premise, while the S, a small term, a term that is subject to conclusion and landscaped syllogism appears in the second, small, premise.
Our syllogism of lions is the correct one (valid in the wider and narrower sense), halls of reflection syllogism because the conclusion actually follows from the premises. If you accidentally ređali AEIOU attitudes that include large, small and medium term sometimes so are aligned positions (first two premises and a conclusion for them, for example: AA E) were correct, and sometimes it would not. To correct ways or forms of reasoning separated from defective (invalid in the strict sense of whom we spoke above), halls of reflection logicians have decided to try all possible combinations halls of reflection of premises and conclusions, and allocate the correct forms. The first is that Aristotle did, and we will now describe his method.
He singled out the first possible combination of terms in the position statement and this combination is called syllogism figures. Because the definitions of small, halls of reflection large and medium term, but largely determined by their position in the premises and the conclusion, the rest is just to vary the order of terms in the premises. Possible combinations was four, so we have four figures syllogism, called simply figure I, II, figures, etc. Here they are:
P - M
Our top syllogism of the lions was a syllogism and figures, and attitudes in him were all forms of universal-affirmative statements A and AA A. Of course, if we look at the combination AEIOU statements within one figure, it turns out that there are 64, making a total of 256, or a combination of modes of syllogisms. Fortunately, when they tested all of these modes it turned out that only 24 of them correctly, and that 5 of these 24 such that claims less than what can be deduced from the premises (For example, we were able to conclude the E statement halls of reflection that no S is not P, but instead only argue that some S is not P (A statement)). When subtracting these five, the rest is 19 correct mode. We will see that this number could be reduced by another 4, but first let's see how the logicians separated correct from incorrect mode.
To see that the correct modes, logicians have had to establish some rules valid syllogism, and are determined by them and valid modes. halls of reflection These rules are in turn divided into a group of axioms syllogism, that is, rules that do not prove theorems and syllogisms, halls of reflection which are rules that may prove as valid, if applicable axioms. For axioms correct syllogism halls of reflection is taken these five rules: The term (term) that is not broken down by individual premises, there can be no Torn apart in the conclusion. The middle term must be Torn apart at least one premise. Both premises can not be negative. If one premise is negative, the conclusion is negative. If both premises are affirmative, the conclusion must be affirmative.
Based on these axioms can prove the basic theorems that are valid for all figures syllogism: The conclusion must be at least one less the distributed terms, than it was in the premises. Both premises can not be particular. If one particular premise, and the conclusion is partikularan. Premise halls of reflection can not line up in IE combination.
Proofs of these theorems are not difficult. For example, the conclusion must be at least one less than the distributed term in the premises, because the premise is the middle term, which by axioms 2, must be distributed in at least one premise, and does not appear in the conclusion.
If you apply these rules to the 256 mode, stays those mentioned 24th As
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