## Fuzzy logic

Briefly, I just thought I would post about Fuzzy logic. Fuzzy logic is the idea that we should not approach propositions thinking them to be either true or false, but rather true to some degree. In other words, one could say of the proposition “the tea is strong” that this is 0.3 true, whereas one could say of the proposition that “2+2=4” is 1.0 true. In this way we might consider all propositions not merely true ‘in one sense or another’ but rather true in one single sense to a degree.

This logic has been developed and has been helpful for computer programming and other endeavors. Probably the principle reason it was employed was because of any example of a Sorites paradox. For instance, suppose you have a heap of grains – is ‘a heap of grains’ a real thing? Well, at first it seems obvious that it is a real thing, until one asks for a definition of a heap. If I begin taking away grain after grain from the heap, at what point does it cease to be a heap? When there are 100 left? When there are 10 left? When there are 3 left? Somewhere in-between? What precisely determines that something is a ‘heap’? If nothing, then it is clear that we are confused when we call it a ‘heap’, or else that ‘heap’ is an idea in our mind which has to do with a matter of degree. Something can be ‘more truly a heap’ than something else. We can substitute any example in its place, such as whether it is raining outside, whether some man is bald, whether somebody is smart, and a host of others. These examples have been taken to be challenges to bivalent logic. The proposition “that man is bald” should be, it is suggested, understood not to be ‘true or false’ but ‘true to some degree’. This logic has been impressively developed and has, as I indicated, proved useful in many respects.

I am also very critical of it when it tries to apply itself to metaphysics. A proposition can only be true or false in the strict sense, I take it, if it is intelligible. Our colloquial language may admit of statements which are not strictly either ‘true or false’, but our logic must retain the conviction that propositions are either true or false.

We can demonstrate this with a simple example. Let us suppose somebody says that it is 0.7 true that it is raining outside. Obviously whether it is raining outside is one of those things which it is hard to define – what moisture-level, or what ‘droplet’ finally crosses the strict threshold from raining to ‘not raining’? However, it has been responded by philosophers defending bivalent logic “Well, is it 1.0 true that it is 0.7 raining?”

In other words, is it actually true that it is raining to some degree?- or rather that “it is raining” to some degree? Well, it seems that statement itself is either true or false, in a bivalent sense. Imagine if it were not. One might respond “Well, it is 0.9 true that it is 0.7 true that it is raining” and of course that person would be obtuse if they did not anticipate the question: “well, is it 1.0 true that ‘it is 0.9 true that it is 0.7 true that it is raining’?” and so on. Either nothing is strictly true at all, which is clearly offensive to reason, or else bivalent logic is ultimately inevitable.

Therefore, even when we use fuzzy logic, we must ultimately hold the conviction of bivalent logic.

Does this discredit fuzzy logic? No, I don’t think it does. It only makes us aware that fuzzy logic is developed to deal with certain kinds of general ‘propositions’. It may be helpful in other ways as well, but ultimately fuzzy logic cannot be thought to be informative fundamentally for metaphysics. One way of seeing this is to recognize that all such ‘general propositions’ can be reduced to more basic propositions along with a general phenomenal description.