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| public:t-713-mers:mers-24:reasoning-intro [2024/11/06 10:29] – [Syllogisms] thorisson | public:t-713-mers:mers-24:reasoning-intro [2024/11/06 10:32] (current) – [Well-Known Syllogisms] thorisson |
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| | \\ What is it? | A form of deductive argument/reasoning in which a conclusion is drawn from 2 given or assumed propositions (premises / statements). The premises and the conclusion are simple declarative statements constructed using only three simple terms between them, each term appearing twice (as a subject and as a predicate) \\ E.g. **all dogs are animals; \\ all animals have four legs; \\ therefore all dogs have four legs.** \\ The argument in such syllogisms is valid by virtue of the fact that it would not be possible to assert the premises and to deny the conclusion without contradicting oneself. \\ (Based on Oxford Dictionary and Encyclopedia Britannica) || | | \\ What is it? | A form of deductive argument/reasoning in which a conclusion is drawn from 2 given or assumed propositions (premises / statements). The premises and the conclusion are simple declarative statements constructed using only three simple terms between them, each term appearing twice (as a subject and as a predicate) \\ E.g. **all dogs are animals; \\ all animals have four legs; \\ therefore all dogs have four legs.** \\ The argument in such syllogisms is valid by virtue of the fact that it would not be possible to assert the premises and to deny the conclusion without contradicting oneself. \\ (Based on Oxford Dictionary and Encyclopedia Britannica) || |
| | 3 types: | Categorical, conditional and disjunctive. || | | 3 types: | Categorical, conditional and disjunctive. || |
| | \\ Categorical | The traditional type is the categorical syllogism in which both premises and the conclusion are simple declarative statements that are constructed using only three simple terms between them, each term appearing twice. \\ Assumes all premises are true. || | | \\ Categorical | The traditional type is the categorical syllogism in which both premises and the conclusion are simple declarative statements that are constructed using as few as three simple terms between them, each term appearing twice. \\ Assumes all premises are true. || |
| | | Example | **All men are mortal. \\ No gods are mortal. \\ Thus, no men are gods.** | | | | \\ Example | All men are mortal. \\ No gods are mortal. \\ Thus, no men are gods. | |
| | Conditional | Implies an (unspoken) "''if''" in its premises. || | | Conditional | Implies an (unspoken) "''if''" in its premises. || |
| | | Example | ** If you are injured. \\ I am qualified to assist with injuries. \\ Thus, I can heal you** (-- **given** that you accept my help). | | | | \\ Example | If you are injured. \\ I am qualified to assist with injuries. \\ Thus, I can heal you (-- //given// that you accept my help). | |
| | \\ Disjunctive | Uses an either/or premise. \\ If it is known that at least one of two statements is true, and that it is not the former that is true; we can infer that it has to be the latter that is true. || | | \\ Disjunctive | Uses an either/or premise. \\ If it is known that at least one of two statements is true, and that it is not the former that is true; we can infer that it has to be the latter that is true. || |
| | | Example | **A solid thing cannot be in two places at the same time. \\ X is a solid thing currently at position P1 now. \\ Thus, it CANNOT currently be at position P2.** | | | | \\ Example | A solid thing cannot be in two places at the same time. \\ X is a solid thing currently at position P1 now. \\ Thus, it CANNOT currently be at position P2. | |
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| =====Well-Known Syllogisms===== | =====Well-Known Syllogisms===== |
| | \\ Moduls Ponens | If a conditional statement \\ **if P then Q** \\ is accepted, and the antecedent P holds, then the consequent Q may be inferred. \\ E.g. **If it's raining then its cloudy. \\ It is raining. \\ Then it's cloudy. ** | | | \\ Moduls Ponens | If a conditional statement \\ **if P, then Q.** \\ is accepted, and its stated antecedent P holds, then the consequent Q must be rightly inferred. \\ E.g. **If it's raining then its cloudy. \\ It is raining. \\ Then it's cloudy. ** | |
| | \\ Moduls Tollens | A mixed syllogism that takes the form of \\ **If P, then Q. \\ Not Q. \\ Therefore, not P.** \\ Application of the general truth that if a statement is true, then so is its contrapositive ("if not-B then not-A" is the contrapositive of "if A then B"). | | | \\ Moduls Tollens | A mixed syllogism that takes the form of \\ **If P, then Q. \\ Not Q. \\ Therefore, not P.** \\ Application of the general truth that if a statement is true, then so is its contrapositive ("if not-B then not-A" is the contrapositive of "if A then B"). | |
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