Logic

The prevailing view in North American philosophical writing seems to be that the phrase ‘just in case’ can be translated into the phrase ‘if and only if’. Consequently, this view holds that the phrase ‘just in case’ is best symbolized by the logical connective known as the biconditional (\leftrightarrow).

Now, this seems wrong to me for two reasons. One is the difference between ‘just in case’ in this sense and the sense it has in British English, as noted by Geoffrey K. Pullum:

  • British English: “We’ll bring an umbrella just in case it rains.”
  • American philosophers: “A formula is a tautology just in case it is true on all valuations.”

That’s a fine difference to note, but I also have a hard time grasping why ‘just in case’ should count as ‘if’ and ‘only if’ at all. That is, to me, ‘just in case’ sounds more like ‘only if’. It seems that it spells out a necessary condition but not necessarily a sufficient one. Consider:

  • Something is a tree just in case it is a plant.

Now, according to what seems to be the standard view, this is a false statement because something can be a plant and not a tree. That is, ‘if something is a plant then it is a tree’ is false, so this sentence, just like ‘something is a tree if and only if it is a plant’ is false.

But it seems to me that this sentence actually means ‘something is a tree only in the case that it is a plant’. That is, I’m more inclined to translate ‘just in case’ as ‘only if’. Under such a translation, the above sentence is true, because being a plant is a necessary condition for treehood.

The problem is that the lexical definition of ‘just’, as an adverb, spells out multiple meanings. One is ‘exactly’ or ‘precisely’, which supports the prevailing intuition that ‘if and only if’ best captures the meaning of ‘just in case’–that it means ‘exactly in the cases that’. But there is also the meaning ‘only’ or ‘simply’. This is the source of my intuition.

Meanwhile, it seems that a number of students in elementary logic classes agree with me, since I often see them translating ‘P just in case Q’ into something like ‘P\to Q‘. Officially their textbook and notes equate ‘just in case’ with ‘if and only if’, so I’m not meant to give them the marks for this, but I do empathize.