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A little help with conditional logic

Octavian AugustusOctavian Augustus Alum Member
in Logical Reasoning 5 karma

Hey all, need some help on some conditional logic.

31.3.18. It is a match the pattern of reasoning argument.

The stimulus:

It is impossible to do science without measuring. It is impossible to measure without having first selected units of measurement. Hence science is arbitrary, since the selection of units is always arbitrary.

Now, the argument and correct answer is easy to spot. However, there is a subtle flaw (yes, I know, it is a match question-but just analyzing the flaw for practice):

The form of argument

1) If Science, must measure
2) If measure, must select units
3) selecting units is arbitrary

Therefore, Science is arbitrary

The flaw is that the author assumes a quality (arbitrary) is applied to all of science, because something necessary for science (selecting units) has that quality...

But sometimes it is not clear when a ‘quality’ like being arbitrary, is a necessary condition or not. The language “selecting units is always arbitrary” seems to imply a conditional relationship: If Selecting units, then arbitrary because of the word “always”.

How do we know that given language like always or everytime (usually a sufficient trigger) is not introducing a necessary condition? Or is it conditional, but for the fact that we say arbitrary is a necessary aspect of science we are going too far as to say that all of science is arbitrary? Or just that when we do science a part of that will be necessarily arbitrary.

It seems that sometimes a quality can be a conditional relationship:

If you’re tall then you’re good at basketball. Or tall people are always good at basketball.

**If it is conditional, then we have:

1) Science then measure
2) measure then select
3) select then arbitray

therefore,

science then arbitrary

And still have a flaw even though the conditional logic lines up? (Valid)

Is it a context issue? Is it an issue where I’m over applying the conditional language cues, but that there is not actually a conditional relationship?

Very much would appreciate any input.

Thanks!

Comments

  • taschasptaschasp Alum Member Sage ⭐
    edited March 2020 796 karma

    The real flaw here is that a whole is not simply the sum of its parts. Like you pointed out, just because something necessary for science is arbitrary doesn't mean that science itself is arbitrary.

    Here are a few similar arguments to demonstrate why this logic is flawed:

    Singing well requires practice. Practice has nothing to do with talent. Therefore singing well has nothing to do with talent.

    It is impossible to start a good company without good employees. Good employees always show up to work on time. Therefore, a good company always shows up to work on time.

    I put that last one there to show that this kind of reasoning actually becomes completely nonsensical when you really think about how its operating. It's not a valid form, and the conditional reasoning doesn't follow. So what was wrong with your conditional representation? Let's take a look again. You wrote:

    1) If Science, must measure
    2) If measure, must select units
    3) selecting units is arbitrary

    Let's represent the first two parts of the chain with S -> M -> SU. What is SU? Is it saying "if something is the act of measuring, than that thing is the idea of "selecting units"?" No, it's saying "if something must measure, that thing must select units." So maybe it's better to represent this as S -> MM -> MSU

    Now the last part? MSU -> iA? Wait a second. We just translated that to "If something must measure, it is arbitrary". That's not what the stimulus is saying. The stimulus says that if selecting units then arbitrary, not if something must select units then arbitrary. We are confusing the idea of selecting units itself for the idea of being something that selects units. Kind of like confusing hunger for someone who is hungry, or confusing the color red itself for something that is red.

    What's arbitrary is the units, not measurement or science. So we really need to represent this as S -> MM -> MSU; and, separately, SU -> iA. Since selecting units is arbitrary, we could say that something that Measures must do something that is arbitrary (which, to reiterate, is not the same as saying that something that measures is itself arbitrary).

    If we then also had an additional assumption, that IF some process requires doing something that is arbitrary, the process itself must be arbitrary; then we could finally deduce that S -> iA. But we don't have that. So the argument doesn't follow deductively.

    So at the end of the day, you have to be careful about the details of what your conditional relationship actually represents. The language does introduce a conditional trigger, it's just that the idea of "something that must select units" is different from the idea of "selecting units" itself.

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