Specter of Reason

In my last post, in response to Timothy Williamson's hesitations regarding naturalism, I rambled a bit about possible difficulties in sorting out a naturalistic understanding of mathematical truth.  I was reflecting on the problem of universality:  Logical and mathematical truths are not truths about the actual world, but extend to all possible worlds.  That would seem to be very hard to explain, if logical and mathematical truths are limited by local factors--factors which ground them in facts about our world.  Today I have worked out a possible solution. The first step is to distinguish between two types of possibility:  logical possibility and physical possibility.  Another way of putting it is that possibility can be relative to a logical framework or a physical one.  When we say that something is physically possible, we mean it cannot be ruled out by the laws of physics (or, if you don't want to favor physics above other sciences, we can just sa...

Over at Blog & ~Blog , Ben says that the sentence "this sentence is false" (which I will refer to as P), and similar sentences, are meaningless. Ben says that the Liar Paradox (which occurs whenever we try to decide whether P is true or false) disappears once we accept that P is meaningless. I'm not convinced, which is not to say I think the Liar Paradox poses a real problem. I just prefer a different approach. Ben's view is that the predicate "is true" does not add any content to a sentence, and therefore, a sentence which only has "is true" as its predicate cannot be meaningful. While it may be true that "'Snow is white' is true" means the same as "Snow is white," this analysis (called disquotationalism) does not clearly apply to all cases where "is true" is the predicate of a sentence. I think it only applies to cases where "is true" is predicated of a sentence. Thus, we may find semantic eq...

I recently posted about the Miners Paradox, which Janice Dowell has been discussing over at PEA Soup . My initial reaction was to reject two of the premises in the argument, thereby undermining the paradoxical conclusion. However, as Janice pointed out to me, this is insufficient, because common sense tells us that the premises are true. That forced me to elaborate upon--though not reject--my initial response. The issue has to do with ordinary language and philosophical logic. Specifically, how do we know when and how to apply the rules of logic to ordinary speech? While modus ponens may be one of the simplest rules in logic, its application to ordinary language is not always obvious. The Miners Paradox may be instructive in this regard. I'll repost the paradox, as presented by Janice: MINERS: 10 miners are trapped in a flooding mine; they are either all in shaft A or all in shaft B. Given our information, each location is equally likely. We have just enough sandbags to ...

I want to better explain why I reject the idea that logic refers to something, such as abstractions or Platonic forms. Words and sentences, of themselves, do not refer to anything. Rather, people can use words and sentences to refer to things. (This should be clear when we remember that the same words and sentences can refer to different things, depending on the context of utterance.) Furthermore, the meaning of a sentence is not always its referent; for we can understand sentences even when a referent is unspecified, and also in cases where the referent is non-existant. (E.g., "The King of France is bald.") From these points it follows, first, that the referent of a sentence depends on how it is used in a particular context; and, second, that sentences can be meaningful even if they have no known referent. When we look at the meaning of a syllogism, we may easily find referents. For example, All men are mortal. Socrates is a man. Therefore, Socrates is mortal. Taken by...

This post won't do its title justice. I'm not going to delve too deeply into the nature or history of logic. But I want to paint a general picture of how I understand the topic, because it came up in a discussion I've been involved with on another blog. The question was raised, If there are no minds to recognize the laws of logic, do the laws of logic still exist? If there are no systems which instantiate the rules of inference, then the rules of inference do not exist. When something exists that does instantiate the rules of logic, then the rules of logic exist. I wouldn't assume that human brains are the only systems capable of instantiating the rules of logic, of course. Now, consider how mundane my point here actually is. What I am saying about logic can be said about anything at all. Like apples, for example. If there are no entities which structurally correspond to what we call "apples," then there are no apples. It is conceivable that we could live in...