i came across this SMBC comic today. In quick what it does is make the efforts to use the law that contraposition come the well known adage:

“If you"re not part of the solution, girlfriend are part of the problem.”

Reversing it choose so:

¬S → ns = ¬P → SMaking it a reasonable conclusion that:

“If you room not component of the problem, you are part of the solution.”

Is that dispute valid follow to the rules of timeless logic? I believe there is miscellaneous fallacious, possibly in the means the first statement is notated, but I cannot number out what.

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inquiry Mar 3 "13 at 23:47

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As Joseph Weissman declared in the comments, in ~ the source of that is a false dichotomy. I"ll look in ~ this formally, however if friend think around the sort of polarised soul that is typically to be discovered behind declaration such as "If you"re not part of the solution, you"re part of the problem", girlfriend can begin to watch yourself.

An indistinguishable formulation to ¬S(u)⇒P(u) in timeless logic (being a material implication) is S(u)vP(u): that is, either you room a part of the solution, or you are a component of the difficulty — leaving no room for anything i beg your pardon is neither (but, incidentally, leaving room for points which room both, which because that societal problems can have examples in well-meaning yet uncritical zealots). A dichotomy is specifically such a proposition i m sorry holds of all variables: in this case, ∀x:S(x)vP(x), i m sorry in the old observed is instantiated v the worth x = u =you. If the global statement is unsound, however, that is a false dichotomy.

In not blocked usage, a "false dichotomy" is still essentially the very same as what I"ve claimed above, because the expression "false dichotomy" is only usual currency among those who study logic, or rhetoric (e.g.in the form of law). How many problems space there, which space so clean-cut and simple that anyone is always either making the problem clearly far better or worse, and never acting in such a means that either has no impact, or more perhaps having an influence whose worth is rather ambiguous? no to point out the frequently unrecognised intricacy of assessing what the actual influence of someone"s plot is.

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Of course, declaration such together "if you"re not component of the solution, you"re component of the problem" room not really intended to it is in formally sound. They"re attractive phrases which are meant come stick in her head in bespeak to make you much more conscious of your behaviour— and the contents of the idea precisely is that if you"re not mindful of her behaviour, you"re most likely to it is in perpetuating part problematic system. So oversimplified declaration such together this maybe serve a positive role: they are part of the solution.

But the worth of together stock paragraph come indigenous not assessing the expression itself an extremely critically, as soon as uncritical reasoning is precisely what that is expected to combat. (The after-effects of assuming that it must have actually formal, critical value is the basis because that Wienersmith"s joke.) If one assumes that such share phrases represent an important thinking, one can become preoccupied v interpreting them as received texts, fairly than doing original and cost-free thinking about whatever subject might be at hand. Phrases as "if you"re not component of the solution, you"re component of the problem" have the right to itself be component of the problem, if one is came to with an essential evaluation the one"s behaviour. However if one already accepts the the influence of behaviour deserve to be facility and an overwhelming to assess, the acknowledgment that making use of a share phrase has ambiguous energy shouldn"t be too shocking.