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Source : http://www.csun.edu/~tab2595/PRAC_EXAM_1.pdf

Is the following argument valid or invalid?

(1) No email messages are written carefully,

(2) but every love letter is very carefully written. ( the instructor's empasize)

(3) Thus, no email messages are love letters.

Surely, without the adverb " very" the argument iis valid.

Does " very" change anything here? What is the standard answer?

Should we treat " very carefully written " as a whole predicate by itself?

Or should we introduce a quantification over " degrees of carefull writing"?

Is there a formalisation that makes the reasoning valid?

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  • 1
    No standard answer; if you make use of the ambiguities of natural languages, no valid arguments at all. If you formalize it... then it depends on the way you formalize it. Dec 6 '20 at 10:05
  • 4
    If it were me, I would go with valid. If a letter is very carefully written then it is carefully written, just very much so. It would be different if you were talking about some specifically defined technical term, such as high frequency vs. very high frequency radio waves. If the examiner were to mark the answer 'valid' as wrong I would say the examiner is indulging in foolish pedantry.
    – Bumble
    Dec 6 '20 at 10:27
  • @FloridusFloridi If the argument is couched in everyday language, then you assume the most routine interpretation for the vocabulary used. Thus, "very carefully" implies "carefully" and the argument is valid. It should be said that we can distinguish between formal and informal validity. However, if the question is whether the argument is valid, and not whether it is either informally valid or formally valid, then you have to assume that an argument which is informally valid is valid. Dec 6 '20 at 17:25
  • Even if "very" does change the meaning it is in the right direction, "very carefully" implies "carefully". So the most this argument can be accused of is missing an (obvious) step.
    – Conifold
    Dec 6 '20 at 20:26
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I think the other comments have it right; we can spell this out in more detail. Let "E" denote the class of email messages, "C" the class of carefully written things, "L" the class of love letters. Assume that if something is very carefully written, then it's carefully written, much like if something is very poorly written, it's poorly written. We can formalize the argument then as:

(1) No Es are Cs

(2) All Ls are Cs

(3) Hence, no Es are Ls

Which is valid. You could, of course, treat 'very carefully written' as denoting its own class, call it "V". This doesn't undermine validity, given our assumption above, though we need to add a premise:

(1) No Es are Cs

(2*) All Ls are Vs

(3*) All Vs are Cs

(4) Hence, no Es are Ls

This is valid as well since combining (2*) and (3*) in this argument amounts to (2) in the preceding valid argument.

Having looked through the other questions on the exam, I doubt your instructor is looking for anything more detailed in this question than the syllogistic reasoning outlined here and in other comments.

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  • Would you also agree the order of the premises 2 and 3 make a difference? The figure of the syllogism is determined by the order. The figure you use is the fourth figure. If the premises 2 and three are transposed you would have a first figure AAA which would yield ALL Ls are Cs in the prior syllogism above that was given. Also weren't two premises used to derive All ls are Cs instead of adding just one extra premise?
    – Logikal
    Dec 7 '20 at 23:47
  • I'm using "syllogistic reasoning" loosely here; I wasn't attempting to interpret the argument in any of the traditional figures. Fortunately, the order of the premises doesn't affect the validity of the argument, even if it would affect which syllogism figure is presented. Dec 8 '20 at 14:26

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