Exercise 1:  Inference-Indicators and the Logical Structure of an Argument

Due Date:   Wednsday, January 19

Proportion of Final Grade:  5%

        To offer an argument is to claim that certain things are the case, and that they provide a reason for believing that something else is the case.  The propositions that one puts forward as reasons for believing something else are the premises of the argument.  The proposition that they are intended to support is the conclusion of the argument.  The logical steps by which one moves from the premises to the conclusion are the inferences.

        To understand the logical structure of an argument is simply a matter of knowing what these three components are.  To determine what the logical structure of an argument is, then, one needs to answer the following questions:

(1)  What is the basic conclusion that this argument is attempting to establish?

(2)  What are the premises, or assumptions, that the person is putting forward in support of the conclusion?

(3)  What are the inferences that the person is making, and which are supposed to take one from the premises to the final conclusion?

        How does one go about answering these questions?  The answer is that a passage that contains an argument will generally contain a number of words or phrases that function as inference-indicators.  Consider, for example, the following sentence:
 

"I have just polished off two six packs; I am feeling very nauseous; I am unable to get up off the floor, and the rest of the world is spinning around me at something approaching the speed of light.  Therefore I am probably slightly drunk."

        Here the word "therefore" is an inference-indicator, and it functions to indicate that the fact that I have just polished off two six packs, am feeling very nauseous, am unable to get up off the floor, etc., is a reason for drawing the conclusion that I am probably slightly drunk.  So the pattern it points to is the following:

               [Reason, inference-indicator, conclusion].

        Other inference-indicators work in the opposite way.  They indicate that what follows provides a reason for what precedes.  Here is an example of that sort of inference-indicator:
 

"Mary is probably a better tennis player than I am, since she has beaten me 6-0 in each of the last ten sets we have played."

        Here the word "since" is an inference-indicator.  In particular, it indicates that what follows it - i.e., the fact Mary has beaten me 6-0 in the last ten sets that we've played - is a reason for believing what precedes it - i.e. that Mary is probably a better tennis player than I am.  So the pattern this sort of inference-indicator points to is as follows:

                    [Conclusion, inference-indicator, reason].

        Notice, however, that with words that are inference-indicators of this second type, it is sometimes possible for the word order to be inverted:
 

"Since Mary has beaten me 6-0 in each of the last ten sets we have played, she is probably a better tennis player than I am."

                [Inference-indicator, reason, conclusion].

But what is always true with this sort of inference-indicator is that the inference-indicator is always immediately followed by the reason.

I.  Some Common Inference-indicators of the Two Types

1.  Inference-indicators of Type 1:
                                    [Reason, Inference-indicator, Conclusion]

therefore                              hence                            consequently
so                                        thus                               accordingly
as a consequence                entails                            implies
from which it follows         means that                     proves that
establishes that                   shows that

2.  Inference-indicators of Type 2:
                        [Conclusion,  Inference-indicator, Reason]
                         [Inference-indicator, Reason, Conclusion]

since                             for                                   because
is implied by                 is entailed by                   is a consequence of
follows from                 is shown by                     is proven by the fact that

II.  Some Words that Are Not Inference-Indicators

(1) Contrastive Terms

For example:  but, yet, nonetheless, nevertheless, on the contrary

Such contrastive terms do not point to the presence of an argument, let alone to a specific inference.

(2) Enumerative Terms

For example:  first, second, third, next

These terms may indicate premises involved in an argument, but the do not point to a place where an inference is being made.

(3) Proof-Indicators or Argument-Indicators

For example:  can be proved that, can be demonstrated that, can be shown that

These proof-indicator or argument-indicator expressions point to a claim that someone is going to offer an argument for, but they are not inference-indicators, since they do not point to an inference - that is, a move from a premise to a conclusion.

(4) Conditional Statements and the Word “then”

        The word “then”, when it is not a temporal term, occurs within conditional statements – that is, statements of the form “if p then q” – and in such cases, it may be tempting view the word “then” as an inference-indicator.

        The source of this temptation is probably that some “if . . . then - - -“ statements are closely related to inferences.  Consider, for example, the statement “If Socrates is a man, and all men are mortal, then Socrates is mortal.”  Because this statement expresses a necessary truth, and does so in virtue of its logical form, there is a corresponding, valid argument, namely:

        (1) Socrates is a man.

        The basic idea, then, is that one can pick out passages that contain arguments, and begin to work out the logical structure of the argument, by looking for words and phrases such, as the above, that function as one or other of the two types of inference-indicators.  In doing this, however, there two points that it is important to be note.  First, there are other words and phrases, besides those listed above, that function as inference-indicators.  The above lists contain only some of the more common ones.

        Secondly, some words that sometimes function as inference-indicators do not always do so.  Thus, for example, the word "because" in the sentence, "Suzanne has been swimming very good times because she has been doing a good deal of weight training", does not function as an inference-indicator, since the fact that Suzanne has been doing a good deal of weight training is not being offered as a reason for believing that Suzanne has been swimming very good times.  It is being offered, rather, as a causal explanation of why she is swimming good times.  So it is important to distinguish, in the case of sentences containing the word "because", sentences that offer reasons for thinking that some claim is true and sentences that offer a causal explanation (or other type of explanation) of why something is the case.

        As another illustration of the need for care in identifying inference-indictors, consider the following three sentences containing the word "since":  (1) 1001 is not a prime number, since it is divisible by 11;  (2) Paul hasn't written to me since he went to Europe;  (3) Since Laura is living in Alaska, she no longer plays golf all year round.  In the first of these sentences, "since" does function as an inference-indicator, but in the second it indicates, instead, a temporal relation, while in the third it points to the presence of an explanation of a certain fact, rather than to a reason for thinking that something is true.
 
 
 

Instructions - Part 1

        Of the following eight passages, four contain arguments - which may be either good or bad arguments - whereas four do not.  Read the passages carefully, and decide which four passages it is most plausible to view as containing an argument - that is, as offering a reason for some conclusion.  Circle each of those passages.   (1 point for correctly identifying each of the four passages that are most plausibly viewed as offering an argument for a conclusion.)

 (1)  In the study that was carried out at the hospital on the effect of long exposure to Rubik's cube upon patients suffering from that syndrome, one patient went into a sort of trance after struggling with the cube for about four hours, and thus he remained, unwilling or unable to communicate with the outside world for a period of several days.  (Ronald Skinner, A Study of Stress)

 (2)  While so-called intellectuals would like to deny it, the simple fact is this:  if God did not exist, then everything would be morally permissible.  (David Horrorwitz, The Universities and the Subversive Left)

(3) You need a special pass to get into the pits where the cars are, and John does not have one.  So I guess that John will be unable to get into the pits..  (Billy Joe Patton, My Life in the Pits)

(4)  Why did Maggie become such an ardent Tory?  Was she moved by the force of Hayek's arguments against socialism?  No, the main reason seems to have been that her parents were strong supporters of the Tory party, and good friends of Winston Churchill.  (Jonathan Dewitt Guernsley, Britain and the Iron Maiden)

(5)  In fantasy, the self can be anyone, anywhere, do anything, have everything.  It is thus omnipotent and completely free - but only in fantasy.  (R. D. Laing, The Divided Self)

(6)  The things confession is concerned with belong to the very heart of personality, to its freedom and responsibility.  The danger of psycho-analysis is that it will deal with these same things from the point of view of natural occurrences and that it will constantly direct the attention of the patient to himself and his temporal existence.  Thus the soul's center of gravity may be transferred from the center - from the point of personal responsibility in the presence of the Unconditioned - to the impersonal, unconscious, purely natural sphere.  (Paul Tillich, The Religious Situation)

(7)  John used to spend most of time glued to the tube, watching soapies, and he was in really terrible physical condition.  But since he moved to Boulder, he has taken up jogging, and he has become quite sleek, and very fit.  (Streng Gustafson, On the Fitness Trail)

(8)  If God did not exist, life would be unbearable for me.  But life is not unbearable for me: on the contrary, I thoroughly enjoy living.  So God does exist.  (Theo Logicus, The Idiot’s Guide to Deep Thinking)  

Instructions - Part 2

        Each of the following eight passages contains an argument, and each argument contains exactly one inference-indicator.  For each  passage, (1) circle the inference-indicator, and (2) place brackets around the conclusion of the argument.  (1 point for each correctly identified inference-indicator, and 1 point for each correctly identified conclusion.)

(1)  If I am told a number and merely think about it, I am likely to forget it or transpose some of the digits.  If I repeat the numbers out loud or write them down, then I can remember them quite well.  This surely means that there is a part of our brain which remembers sounds and images, but not thoughts.  ( Carl Sagan, The Dragons of Eden)

(2)  From the moment of its birth surrealism was an international phenomenon - the spontaneous generation of an international and fraternal organism in total contrast to the artificial manufacture of a collective organization such as the League of Nations.  It would therefore be contrary to the nature of the movement to disengage, as some have suggested, a specifically English version of 'surréalisme'.  (Herbert Read, The Philosophy of Modern Art)

(3) The occupants of the vehicle were undoubtedly killed, since the vehicle, when it overturned and went off the road, plummeted 300 feet.  Why did the vehicle overturn?  Was it because of tire failure?  No, the reason was that the driver was speeding around the curve, and sport utility vehicles have a very high center of gravity.

(4)  . . . we know that there is no greatest prime number.  But of all the prime numbers that we shall have ever thought of, there certainly is a greatest.   Hence there are prime numbers  greater than any we shall have ever thought of.  (Bertrand Russell, "On the Nature of Acquaintance")

(5)  There is something basically wrong with out economy because a man working full time cannot support his family above the poverty level.  (George Meany, Past President, American Federation of Labor)

(6)  The existence of biological predispositions [toward crime] means that the circumstances that activate criminal behavior in one person will not do so in another, that social forces cannot deter criminal behavior in 100 percent of a population, and that the distribution of crime within and across societies may, to some extent, reflect underlying distributions of constitutional factors.  (James Q. Wilson and Richard Herrnstein, Crime and Human Nature)

(7)  An object offers as much resistance to the air as the air offers to the object.  You may see that the beating of its wings  against the air supports a heavy eagle in the highest and rarest atmosphere, close to the sphere of elemental fire.  Again you may see the air in motion over the sea, fill the swelling sails and drive heavily laden ships.  From these instances, and the reasons given, a man with wings large enough and duly connected might learn to overcome the resistance of air, and by conquering it, succeed in subjugating it and rising above it.  (Leonardo da Vinci, Notebooks)

 (8)  It is clear that those who hold that mathematical truths are not self-evident are not to be taken seriously, for they are quibblers who will argue with any assertion, whether reasonable or not.  (Newt Limburger, Intellectual Rubbish and the Academic Jungle)