Chad C. D. Clark Feb 26, 2001 Phil 307 The Logical Form Of Belief Russell says that there are an infinite number of logical forms that facts may take. He believes that the facts associated with beliefs have a different logical form than atomic facts. We can see that beliefs often have two or more verbs as in 'I believe the moon is not made of cheese.' Russell feels that this is an indication that the fact corresponding to this belief must also have a corresponding constituent for every verb found in the statement. For convenience he decides to refer to these constituents as verbs as well. Even though these facts have many constituents he says the facts are still irreducible. To make things even more confusing Russell points out that there are many different forms of beliefs such as 'I believe this is white.' and 'I believe there are just as many natural numbers as integers.' To accommodate this he says that the logical form of a belief fact varies from belief to belief. The strangest point he makes is that a belief has a fact but it must also be true or false. So there are facts which have a truth value. Russell decides that reality can be defined by everything that would have to be mentioned in a complete description of the world. He then reasons that false propositions shouldn't need to be mentioned but false beliefs would be needed in order to describe everything. So he concludes that because false propositions don't need to be present in the description of the world that they do not need to be a part of reality. If false propositions did need to be mentioned then we would be overcrowding our world and that doesn't seem like a good thing. He then says that of course we can't believe something that is not a part of reality so we can't believe false propositions. Thus Russell concludes that we can't believe propositions. The first weakness present here is visible when Russell says that he is relying on his well developed instinct and his belief that all that exists are facts. His instinct seems to be controlling his judgement. The mistake in this reasoning is simple and it is a wonder that Russell did not see it himself. He says that we can't believe a false proposition because it does not exist, yet he says that we can refer to the present king of France even though France has no king. How can we justify being able to refer to a nonexistent object and still be unable to refer to a nonexistent proposition? We could say that a proposition is not an object and that the two are just different. This is a claim that he used when discussing the Neutral Monism point of view of belief. If our natural language allows us to speak as if a nonexistent object were real and we solve the problem by breaking down the reference of the object to a description of that object then why can't we do something analogous with the problem of a belief statement that appears to refer to a nonexistent proposition? Without going into a long explanation of how this would work it appears to be a convenient solution. Take for example the case where Othello believes that Desdemona loves Casio and the love is really not present. It appears that we have a subject predicate relationship here where the subject is 'Desdemona loves Casio' and the predicate is 'Othello believes'. Russell points out that because the love is not present the proposition does not exists. This is why he refuses to admit the subject-predicate relation. We are passing our predicate function no input. When we grant that it is acceptable to appear to refer to nonexistent propositions we see that it is perfectly acceptable to pass them into our predicates. We are not as it may seem declaring the existence of propositions on the same level as facts we are merely introducing the idea of another symbol just like names are symbols. It is good to note here that in his first lecture he points out himself that a proposition is just a symbol and that when working with symbols we need to be careful not to apply properties of the symbol to the thing being symbolised. Also in the first lecture Russell claims that we can't split facts up into true facts and false facts. He further says that to make all facts true would be nonsense because something can only be said to be true if it could be false and facts cannot be true or false. This seems a bit circular for an argument but his point is a very strong belief that facts do not and cannot have a truth value. So in order to explain statements that can be and are true or false he decides to let the proposition be the thing which will have a truth value. So how then can Russell now tell us that propositions don't really exist and that their responsibility to represent things with a truth value really belongs to facts? Not all facts though, just a select special class of facts. The class of facts that correspond to beliefs. This raises another question. What about statements that can be true or false but are not belief statements? For example I have a bowl of bananas' and I say that they are green. In reality they are now yellow and I have just told you that is not the case but when I did so I did not believe that they were green I just said it. So here I have presented a proposition that does not involve a belief. Note we are not interested in what anyone believes about the banana's only with which statements can be true or false. The first statement made (that the banana's are green) does have a truth value. In this case it is false. When we allow propositions to have truth values we take away complexity from the rules of facts. When we allow a proposition to have a truth value we are not using that truth value as the subject to a belief predicate. Rather the components of the proposition are used with variables to describe a possibility and the belief predicate determines whether an occurrence of that possibility actually exists in someone's opinion. The logical form of the fact that makes a belief true when the belief is actually true or false when the belief is actually false consists of a set of quantified sentences and a reference to an individual. The set of quantified sentences describe the necessary environment to make the proposition being believed true. Then the fact says that the individual actually does believe it or rather the fact makes the belief statement true when the individual actually does believe that the described environment is the case. In such a case we have a positive fact. In the case when the individual does not believe the proposition we end up with a negative fact which makes the belief statement false. In either case the fact has no truth value whatsoever. Note that by changing propositions into descriptions we are not flooding the world with nonexistent propositions even though an unbounded possible number of these descriptions can exist. This is because a new description only appears when we construct it. We don't claim that a whole bunch of false names exist. Rather we realize that we can put letters or sounds together in as many ways as we like but only call a combination a name when we use it to name something. Being consistent with Russell we still allow many different forms of facts for beliefs. Each belief fact still has the basic components but the set of quantified sentences describing the environment changes to suit the form of the proposition being believed or not believed. It is apparent that the logical form of a belief related fact has components but none of these components is a fact in itself so this is also consistent with Russell in that this form of fact is irreducible. The question still remains as to what extent the verb of the proposition still remains after the proposition gets analysed away. So rather than explaining propositions Russell explains them away by adding complexity to the theory of facts with respect to belief but he seems to forget about other propositions that do not deal with belief. By allowing propositions to hold truth values we simplify the realm of facts and avoid contradictions with what Russell had said elsewhere. We can also shape the logical form of belief related facts to something closer to the predicate type relation that seems so comfortable to us with respect to our natural language. This has the appearance of exemplifying Occam's Razor which Russell is so fond of.