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SAT Reading Practice Passage
SAT Reading Practice Test Comprehensive Passage
This passage is adapted from Bertrand Russell, “the philosophical importance of mathematical logic.” The following 10 multiple choice questions are based on the passage below.
| The mathematical theory of motion and other countries | |
| changes uses, besides the theories of infinite number and of | |
| the nature of continuum, two correlative notes, that of a | |
| functions and that of a variable. the importance of these ideas | |
| Line 5 | may be shown by an example. we still find in books of |
| philosophy a statement of the law of causality in the form : | |
| “when the same cause happens again, the same effect will | |
| also happen.” But it might be very justly remarked that the | |
| same cause never happens again. What actually takes place is | |
| Line 10 | that there is a constant relation between causes of a certain |
| kind and the effects which result from them. Wherever there | |
| is such a constant relation, the effect is a function of the | |
| cause. By means of the constant relation we sum up in a | |
| single formula an infinity of causes and effects, and we avoid | |
| Line 15 | the worn-out hypothesis of the repetition of the same cause. |
| It is the idea of functionality, that is to say the idea of | |
| constant relation, which gives the secret of the power of | |
| mathematics to deal simultaneously with an infinity of data. | |
| To understand the part played by the idea of a function in | |
| Line 20 | mathematics, we must first of all understand the method of |
| mathematical deduction. It will be admitted that | |
| mathematical demonstrations, even those which are | |
| performed by what is called mathematical induction, are | |
| always deductive. Now, in a deduction it almost always | |
| Line 25 | happens that the validity of the deduction does not depend on |
| the subject spoken about, but only on the form of what is said | |
| about it. Take for example the classical argument: All men | |
| are mortal, Socrates is a man, therefore Socrates is mortal. | |
| Here it is evident that what is said remains true if Plato or | |
| Line 30 | Aristotle or anybody else is substituted for Socrates. We can, |
| then, say: If all men are mortal, and if x is a man, then x is | |
| mortal. This is a first generalization of the proposition from | |
| which we set out. But it is easy to go farther. In the deduction | |
| which has been stated, nothing depends on the fact that it is | |
| Line 35 | men and mortals which occupy our attention. If all the |
| members of any class a are members of a class s, and if xis a | |
| member of the class a, then x is a member of the class s, In | |
| this statement, we have the pure logical form which underlies | |
| all the deductions of the same form as that which proves that | |
| Line 40 | Socrates is mortal. To obtain a proposition of pure |
| mathematics (or of mathematical logic, which is the same | |
| thing), we must submit a deduction of any kind to a process | |
| analogous to that which we have just performed, that is to say, | |
| when an argument remains valid if one of its terms is | |
| Line 45 | changed, this term must be replaced by a variable, i.e. by |
| an indeterminate object. In this way we finally reach a | |
| proposition of pure logic, that is to say a proposition which | |
| does not contain any other constant than logical constants. | |
| The definition of the logical constants is not easy, but this | |
| Line 50 | much may be said: A constant is logical if the propositions in |
| which it is found still contain it when we try to replace it by a | |
| variable. Mote exactly, we may perhaps characterize the | |
| logical constants in the following manner: If we take any | |
| deduction and replace its terms by variables, it will happen, | |
| Line 55 | after a certain number of stages, that the constants which still |
| remain in the deduction belong to a certain group, and, if we | |
| try to push generalization still farther, there will always | |
| remain constants which belong to this same group.’ This | |
| group is the group of logical constants. The logical constants | |
| Line 60 | are those which constitute pure form; a formal proposition is |
| a proposition which does not contain any other constants | |
| than logical constants. We have just reduced the deduction | |
| which proves that Socrates is mortal to the following form: | |
| “If x is an a, then, if all the members of a are members of b, it | |
| Line 65 | follows that x is a b.” The constants here are: is-a, all, and |
| if-then. These are logical constants and evidently they are | |
| purely formal concepts. | |
| Now, the validity of any valid deduction depends on its form, | |
| and its form is obtained by replacing the terms of the | |
| Line 70 | deduction by variables, until there do not remain any other |
| constants than those of logic. And conversely: every valid | |
| deduction can be obtained by starting from a deduction | |
| which operates on variables by means of logical constants, | |
| by attributing to variables definite values with which the | |
| Line 75 | hypothesis becomes true. |
SAT Reading Comprehension Practice Test Questions
SAT Reading Practice Test Question No 1
The main purpose of this article is to
Option A : explain a complicated theory through evidences.
Option B : elaborate on the function of mathematical deduction.
Option C : refute an obviously fallacious statement on logic.
Option D : propose an innovative approach of scientific induction.
SAT Practice Test Answer No 1
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Option B : elaborate on the function of mathematical deduction.
SAT Reading Practice Test Question No 2
What is the function of the first paragraph in the overview of the article?
Option A : It sets forth several tentative arguments to be discussed later in the passage.
Option B : It points out the fallacies embodied in the common beliefs.
Option C : It stresses the important role of functionality in mathematical logic.
Option D : It paves way for the later discussion by defining some key components of a concept.
SAT Practice Test Answer No 2
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Option D : It paves way for the later discussion by defining some key components of a concept.
SAT Reading Practice Test Question No 3
The statement in lines 8-9 “But…again” clearly serves as
Option A : a qualification to a previously made point.
Option B : a concession made to accommodate more opinions.
Option C : an assumption necessary to make a conclusion.
Option D : conditions neglectable in induction process.
SAT Practice Test Answer No 3
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Option A : a qualification to a previously made point.
SAT Reading Practice Test Question No 4
The word “worn-out” in line 15 has the closest meaning to
Option A : trite.
Option B : bored.
Option C : repeated.
Option D : tried.
SAT Practice Test Answer No 4
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Option C : repeated.
SAT Reading Practice Test Question No 5
The author suggests which choice about mathematical induction?
Option A : It is necessarily a part of the mathematical deduction.
Option B : It resembles mathematical deduction in functionality.
Option C : The process of making induction is inherently deductive.
Option D : The object of induction is always the same as deduction.
SAT Practice Test Answer No 5
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Option C : The process of making induction is inherently deductive.
SAT Reading Practice Test Question No 6
In the “classical argument” of line 27, the author treats
Option A : a factor.
Option B : an object.
Option C : a condition.
Option D : a variable.
SAT Practice Test Answer No 6
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Option D : a variable.
SAT Reading Practice Test Question No 7
By using the parenthetical words in lines 41-42, the author suggests that
Option A : mathematical logic embodies mathematics.
Option B : mathematical logic equals to mathematics.
Option C : mathematical logic is inherent in mathematics.
Option D : mathematical logic surpasses mathematics.
SAT Practice Test Answer No 7
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Option B : mathematical logic equals to mathematics.
SAT Reading Practice Test Question No 8
The author in the passage suggests that the best way to define the “logical constants “in line 53 is to
Option A : add values to such logical constants in the equations.
Option B : place them within groups or collectives of numbers.
Option C : assume the numbers of stages to be cleared
Option D : characterize them in terms of functionality of deduction.
SAT Practice Test Answer No 8
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Option D : characterize them in terms of functionality of deduction.
SAT Reading Practice Test Question No 9
The article refers to the Socrates example in lines 64-65 primarily to
Option A : emphasize that the logical constants shall have no bearing of any substance at all.
Option B : identify the definite set of variables in any sound logical deduction process.
Option C : reiterate the classic example in explaining the core of mathematical logic.
Option D : forma contrast of views now available in light of the discussion of logical constants.
SAT Practice Test Answer No 9
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Option C : reiterate the classic example in explaining the core of mathematical logic.
SAT Reading Practice Test Question No 10
In view of the article as a whole, how will the author most likely look at the statement “When the same cause happens again, the same effect will also happen.” in lines 7-8?
Option A : The form of cause or effect has no effect at all in shaping the validity of conclusion because they are both constant.
Option B : The effect can be predicted with more validity as the cause is easily changed or replaced with others.
Option C : The cause obviously is more important than the
Option D : The cause and effect can be replaced by variable of values to make the argument valid.
SAT Practice Test Answer No 10
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Option D : The cause and effect can be replaced by variable of values to make the argument valid.
SAT Reading Practice Test Question No 11
The author uses all of the following strategies in his discourse of logical constants EXCEPT
Option A : quotations.
Option B : hypothesis.
Option C : generalization.
Option D :assertion.
SAT Practice Test Answer No 11
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Option B : hypothesis.
SAT Reading Practice Test Question No 12
According to the passage, which of the following fails to fit into the form in lines 64-65?
Option A : All members of A are B, and B belong to C, so all of A belong to C.
Option B : Every member of A is B, and B leads to C, so every one of A leads to C.
Option C : A equals B, and all members of C belong to B, so A is equal to C.
Option D : A equals B, and all members of C belong to A, so all of C equal B.
SAT Practice Test Answer No 12
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Option C : A equals B, and all members of C belong to B, so A is equal to C.
SAT Reading Practice Test Question No 13
The word “conversely” in line 71 can be replaced by
Option A : adversely.
Option B : reversely.
Option C : inversely.
Option D : contrarily.
SAT Practice Test Answer No 13
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Option C : inversely.
