Sunday, February 11, 2007

Better Reasoning VI: Enthymemes

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In the previous couple of posts in this series, various valid argument forms have been introduced. There is one further complexity that arises with real arguments, that has yet to be mentioned.

One thing that people may have noticed with the valid argument forms is that they seem to involve rather a lot of repeating the same phase over and over again. For instance, in a Modus Ponens inference, the phrase symbolised by P in the argument form appears in both the antecedent of the first premise and in the second premise. In practice, people seldom talk, write, or reason this way. Instead, it is common for people to take little logical 'short cuts'. Consider the following two arguments,

(a) "If it is cloudy, then the solar cell will not work well, so it won't work well today."

(b) "If it is cloudy, then the solar cell will not work well. It is cloudy today. So, the solar cell will not work well today."

Essentially, (a) and (b) make the same argument. Notice though that passage (a) sounds much more natural, while the version in passage (b) sounds kind of leaden and overly pedantic. The reason for this is pretty obvious. Passage (a) uses contractions, and does not explicitly state the second premise. Passage (b) sticks much more closely to the valid argument form. On the face of it, it would seem that if the version in passage (b) is a valid instance of a Modus Ponens inference, then that would seem to guarantee the the version in passage (a) was valid also. Yet, there is a bit missing. What is going on here?

The version of the argument that appears in passage (a) contains an Enthymeme. This term has a Greek origin and means roughly 'in the mind'. It turns out that in many cases in natural speech and writing, we do not have to explicitly state all the parts of the argument, because we are able to easily and almost automatically, fill in the missing parts, with our minds. However, this adds a further complication to identifying valid arguments in real world reasoning.

The very automatic nature of the way we fill in missing parts of arguments can actually make it a little bit difficult to spot enthymemes at first. However, knowing the valid argument forms makes finding enthymemes just a little bit easier. Enthymemes need to be treated with care, however. This is because letting a reader, or hearer fill in missing parts of an argument can serve to hide from explicit scrutiny fairly dubious premises and conclusions. Consider the following argument,

"Gun control legislation is a restriction on freedom, so it shouldn't be passed into law."

As stated, this argument lacks any of the special logical words mentioned in the previous posts. Thus, it does not appear to match any of the valid argument forms and would consequently appear to be invalid. It turns out that this is not the problem with the argument, though.

One of the principles that is useful when dealing with enthymemes is the so-called 'Principle of Charitable Interpretation'. The idea here is that it is easy to make an argument look bad. However, if an enthymeme can be added that would make an argument a valid one, then it is reasonable to add that enthymeme. If the premise 'If something is a restriction on freedom, then it should not be passed into law' were added to the above argument, it would appear to be a valid case of a Modus Ponens inference. After doing this, we can write the argument out more formally as follows,

(1) If something is a restriction on freedom, then it should not be passed into law.
(2) Gun control legislation is a restriction on freedom.
Thus,
(3) Gun control legislation should not be passed into law.

By convention, Enthymemes have their number underlined, to make them stand out. With the argument written out like this, we can now see that the argument is a valid instance of a Modus Ponens inference. However, we can also see that there is something very wrong with the first premise. After all, all legislation has the effect of restricting freedom in some way! My 'freedom' to drive at any speed I feel like is restricted by speed limit laws. My 'freedom' to steal your stuff is restricted by laws about theft. Thus, the premise is patently false. However, when the argument is made without this premise being explicitly stated, people may not realise how silly it is and may be fooled into accepting the conclusion of the argument. This nicely illustrates the way that enthymemes need to be identified and handled with care.

Let us consider another example. This one comes from the real world. Some years ago some group stated putting up notices around our campus that simply said "Jesus or Hell." It is not unreasonable to think that the people putting up these notices wanted to persuade people of something. Thus, these notices were probably supposed to provide arguments. The question is, what was the intended argument?

Noticing that the single premise has the word 'or' in it offers a clue. It is at least plausible that the posters of these notices intended their readers to perform a Disjunctive Syllogism inference. If this is correct, then there are two enthymemes, the second premise and the conclusion. So, the intended argument probably looked like this when presented more formally,

(1) Jesus, or Hell.
(2) Not Hell.
Thus,
(3) Jesus.

Of course, it could have been the case that the notices were posted by a local group of Satanists and the intended conclusion was "Hell"! In both cases, this would be a valid Disjunctive Syllogism inference (recall that there are two forms of this kind of inference). This is one of the incipient dangers of relying upon enthymemes. Readers and hearers may not draw the intended inferences.

In conclusion, let us look at another, yet more complex real world example. This one comes from an opinion piece written by Michael W. Brandl, that appeared on the InsideHigherEd web site on the 2nd of Feb. this year (the full text is available here). Brandl is writing about the issue of the use of second hand textbooks by students. In the process of arguing his point, he made the following argument,

"To begin with, if every student were to buy only used textbooks then no new textbooks would be sold. Thus, no new textbooks would be produced, rapidly diminishing the quality of education."

The first thing to notice is that the conclusion (indicated by the term 'thus') concerns the production of textbooks and the quality of education. However, the consequent of the If...then,... premise concerns the sale of new textbooks. Thus, there needs to be something to connect these topics. One natural way to do this, would be to add another If...,then... premise. This can be done validly, by the inference called Hypothetical Syllogism. Notice also that Brandl also seems to think that it is reasonable to believe that 'every student were to buy only used textbooks'. (This case has some similarities to passage (a), above). Having noticed these points, we can write out the argument more formally as follows,

(1) If every student were to buy only used textbooks, then no new textbooks would be sold.
(2) If no new textbooks would be sold, then no new textbooks would be produced, rapidly diminishing the quality of education.
Thus, [By Hypothetical Syllogism, from (1) and (2)]
(3) If every student were to buy only used textbooks, then no new textbooks would be produced, rapidly diminishing the quality of education.
(4) Every student were to buy only used textbooks.
Thus, [By Modus Ponens, from (3) and (4)]
(5) No new textbooks would be produced, rapidly diminishing the quality of education.

This example is quite complicated, but notice how we have ensured that the argument at least has the virtue of being valid. However, it is questionable whether the argument sound. For instance, it seems rather unlikely that a circumstance would arise under which every student would buy only used textbooks. Thus, by carefully rooting out the ethymemes in this argument, we are in a much better position to figure out whether or not we should be persuaded by it.

In this posting, the notion of an enthymeme has been introduced and illustrated with a number of examples. This shows some of the more sophisticated features of real world arguments, which are not immediately obvious. Understanding these things also assists us in improving our own reasoning and gives us more powerful tools to analyse the arguments of others.

The CP

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3 Comments:

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5:35 AM  
Anonymous pharmacy said...

Enthymemes: the root of evil lawyers, what a shame!

3:53 PM  
Anonymous Cheap Viagra Online said...

It was What I liked the most, this quotation "Gun control legislation is a restriction on freedom, so it shouldn't be passed into law." I think this is a sarcasm to make us see and understand how those procedures are, sometimes laws are blind and something should be changed.

7:49 AM  

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