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- St. Augustine of Hippo
1. All cats are mammals.The categorical syllogism has various forms and moods, which will not be detailed here, but the basic form simply entails two statements leading to a conclusion.
2. Fuzzy is a cat.
3. Therefore, Fuzzy is a mammal.
If P, then Q.Modus ponens means “way of affirmation” in Latin because it affirms the antecedent of the first proposition. One form of the cosmological argument takes the form of modus ponens:
P.
Therefore, Q.
If a contingent being exists, then a necessary being must exist as its cause.The other hypothetical syllogism is called Modus Tollens, which means “the way of denial.” This form of syllogism denies the consequent (the “then Q” part of the first statement). It is structured like this:
A contingent being exists.
Therefore, a necessary being must exist as its cause.2
If P, then Q.Disjunctive Syllogisms are either/or sentences. One statement is made with two alternatives, of which only one can be true.3 The disjunctive syllogism looks like this:
Not Q.
Therefore, Not P.
Either P or Q.The way the disjunctive syllogism works requires for one alternate to be denied for the other one to be true. It is a fallacy to affirm one alternate to eliminate the other, because it is possible for them both to be true. Geisler and Brooks offer an excellent example of this fallacy found in Bertrand Russell’s book Why I am not a Christian:
Not Q.
Therefore, P.
Life was caused either by evolution or by design.Geisler and Brooks explain: “This approach commits the formal fallacy of affirming one alternate. Even if the minor premise were true, the conclusion would not follow. For it is possible that both are true; that is, that evolution is designed.”4
Life was caused by evolution.
Therefore, it was not caused by design (so there is no reason to posit God).
Both P and Q are true.The conjunctive syllogism is fairly straightforward. Both terms in the first statement are separated and can be affirmed individually.
Therefore, P.
Therefore, Q.
(If P, then Q) and (If R, then S).The mathematician Pascal presented a dilemma with this syllogism:
P or R.
Therefore, Q or S.
If God exists, I have everything to gain by believing in him.The final syllogism presented here is the Sorites. This comes from a Greek word meaning “heap.” The premises are stacked together in a heap to come to a final conclusion. An example:
And if God does not exist, I have nothing to lose by believing in him.
Either God does exist or he does not exist.
Therefore, I have everything to gain or nothing to lose by believing in God.5
All A are B...............or...............If A then BThat is a basic look at basic logical syllogisms.
All B are C...............or...............If B then C
All C are D...............or...............If C then D
Therefore, all A are D......or.....Therefore, if A then D.
Many passages, both written and spoken, that appear to be arguments are in fact not arguments but explanations. The occurrence of certain premise- or conclusion-indicators such as “because,” “for,” and “therefore” cannot settle the matter, since those words may be used in both explanations and arguments. What we need to know the intention of the author of the passage.3So the careful thinker must discern the difference between explanations and arguments by looking closely at context and intention.
A deductive argument is one whose conclusion is claimed to follow from its premises with absolute necessity, this necessity not being a matter of degree and not depending in any way on whatever else may be the case. In sharp contrast, an inductive argument is one whose conclusion is claimed to follow from its premises only with probability, this probability being a matter of degree and dependent upon what else may be the case.4One way to look at this is as follows: in a deductive argument, no amount of additional information can change the conclusion of the argument. In an inductive argument, the conclusion may change when new information is discovered. Deductive arguments are certain, whereas inductive arguments are probable to some degree.
When an argument is unsuccessful, it has probably gone wrong in one of the following areas: 1) The evidence has not been thorough; contradictory evidence has been overlooked or ignored; 2) The evidence has not been accurate; false or unsubstantiated or misleading statements have been claimed as fact; 3) The conclusion has not clearly and uncontrovertibly come form the evidence; the relationship between evidence and conclusion has not been a firm one.1The most common categories of informal fallacies are those of irrelevance, confusion, and oversimplification. The author spends time focusing on each one of these categories, splitting them into smaller subcategories as he goes along. Within this book he lists some 170 fallacies (not an official list), with many falling into multiple categories.