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(Presented at a Lawrence University Main Hall Forum, January 23, 2001. The text below contains MS Symbols Fonts.)
Aristotle is said to have written,
To say that that which is is not or that which is not is, is a falsehood; and to say that that which is is and that which is not is not, is true. (Aristotle, Metaphysics 1011b26)
On the basis of such statements, many philosophers are inclined to hold that Aristotle was committed to some form of correspondence theory of truth. Correspondence theories of truth entail that truth is a matter of correspondence to facts. I will present a version of such a theory.
First, I need to say something about the kinds of things whose truth, or falsehood, interests me. I am interested in the truth or falsehood of beliefs and the truth or falsehood of assertive utterances of declarative sentences. Hence, I would be interested in the the truth of such things as Paul’s belief that John loves Mary and Paul’s assertive utterance of the sentence,
1. John loves Mary.
So, what is it for, say, an assertive utterance of 1 to be true? A naïve version of the correspondence theory would have it that that such an utterance is true provided it corresponds to the facts.
This answer raises a number of related questions,
- What are facts?
- What is it for a sentence to correspond to a fact, or to the facts?
- What about false sentences; how does one account for falsehood?
What are facts?
A fact is the sort of thing that exists when n individual or particular things are related by an n-place relation. Hence, if a particular sheet of paper, p, is rectangular, then there is a fact consisting of that sheet of paper having the property of being rectangular. I would represent that fact as follows,
[R, p].
If the number 5 is greater than the number 2, then there is a fact consisting of the numerical greater-than relation, relating the number 5 to the number 2. I would represent that fact as,
[>, 5, 2].
In this notation, the order of the constituents is important. The expression,
[>, 2, 5]
would represent the fact that 2 is greater than 5,or the fact that the greater than relation relates the number 2 to the number 5, if there were such fact. If John loves Mary -- if there is such a fact as the fact that John loves Mary -- than that fact would be represented thusly,
f1 [loves, John, Mary]
but, if Mary does not reciprocate, then there is no such fact as the fact that Mary that John. In that case, the expression
f2 [loves, Mary, John],
would fail to denote a fact.
Facts such as these -- facts consisting of n-place relations relating n things -- are sometimes referred to as “atomic facts.” Atomic facts are, in fact, the only kinds of facts I think we need. Other kinds of facts that others, most notably Betrand Russell and Ludwig Wittgenstein, have seen fit to acknowledge include so-called “molecular facts,” “negative facts,” “general facts” -- both universal general facts, and existential general facts -- and “belief facts.” In my own work, I have argued that there are no good reasons to hold that there are such additional exotic facts. I think we can do without them and have attempted to develop my view solely in terms of atomic facts.
What is it for a sentence to correspond to a
fact, or to the facts?
What about the relation between facts and truth? Typically, the correspondence theory of truth is said to entail the sentence or a belief is true if, the belief, or sentence, corresponds to a fact, or to the facts. One then puzzles over the nature of the correspondence that must hold between the sentence, or belief, and the fact or facts if the belief is true. I find such puzzlement bewildering. Consider the sentence,
1. John loves Mary.
Is there really any puzzle about what fact would need to hold in order for sentence 1 to be true? I sometimes think that those who profess puzzlement here simply don't understand sentence 1. At other times, I suspect that those who profess puzzlement here have darker motives. Most of the time, however, I think that such puzzlement is the result of a misunderstanding of what it means to say that a sentence corresponds to a fact. Certainly, there is a way of understanding a sentence of the form of “S corresponds to the facts, or a fact,” so that it implies that some relation, that of correspondence, holds between sentence S and some fact, f. One then gets puzzled about the nature of this correspondence relation, why it should be such that if it relates S to f, the S is true, and how one determined of a particular S and f, when that relation relates S to f. I think this is a mistake. To say that a sentence corresponds to a fact is just to say that there is a fact of a certain sort. Sentence S corresponds to the facts just in case there is such a fact as the fact that S. It seems clear to me that sentence 1 will be true if and only if there is such fact as,
f1 [loves, John, Mary],
our old friend, fact that John loves Mary. A sentence like 1 is often called and atomic sentence. An atomic sentence is true if, and only if, it has a corresponding fact. A sentence corresponds to a fact, or to the facts, just in case there is a fact of the right sort.
What about false sentences; how does one account
for falsehood?
Bertrand Russell held that an atomic sentence is false if it corresponds falsely to a negative atomic fact. Let’s suppose that sentence
2. Mary loves John,
is false. On Russell’s view, sentence 2 is false because it corresponds falsely to the negative fact that Mary does not love John. Russell reports that when he suggested to a Harvard audience that there were negative facts—in addition to ordinary atomic facts—he nearly started a riot.
Let’s see what Russell meant by a negative fact. In our notation, one might want to represent it as follows
f3 [Ø [loves, Mary, John]
Now this won’t exactly do the trick; for if we take our notation seriously, and there is no sense having a notation if you aren’t going to take it seriously, you will see that the existence of a fact
f3 [Ø [loves, Mary, John]
implies the existence of the fact
f2 [loves, Mary, John],
and if there were such a fact as that, sentence 2, which we are using as an example of a false sentence, would turn out to be true; for it would then correspond to a fact. Hence, we cannot say that the negative fact that 2 is false in virtue of corresponding falsely to is represented in our notation by
f3 [Ø [loves, Mary, John]
Russell, who certainly saw this problem, proposed the following rendering of the fact that Mary does not love John,
- <-----
-
f4
[Loves, Mary, John].
Russell would have used
- ----->
- f5 [Loves, Mary, John]
to represent the fact that Mary loves John—if there were such a fact.
I don’t want to go into great detail about Russell’s notation. This is because, I don’t think there is any need to hold that there are negative facts. Russell maintained that true atomic sentences correspond truly to atomic facts and that false atomic sentences correspond falsely to negative atomic facts. I am have tried to avoid both the notion of corresponding falsely and the view that there are negative facts. I hold that a true atomic sentence corresponds to the facts and that a false atomic sentence fails to correspond to the facts. As for negations of atomic sentences, I hold that the denials, or negations, of atomic sentences are true when the sentences they deny are false and are false when the sentences they deny are true. I call this a “truth-functional” account of negation.
Consider, next, the sentence,
3. John loves Mary or Mary loves John.
Lets suppose that sentence 1 is true and sentence 2 is false. It thus follows that sentence 3 is true. Hence, apparently, sentence 3 corresponds to a fact. What fact? One option is to say that sentence 3 corresponds to the molecular fact that either John loves Mary or Mary loves John. In our notation such a fact would be represented by
f6 [V, [Loves, John, Mary], [loves, Mary, John]],
where V is an operator that yields a disjunctive molecular fact when it takes two atomic facts as arguments. In this manner, we would find ourselves committed to several different kinds of molecular facts: conjunctive and conditional, and perhaps others.
Russell, who accepted negative facts, rejected the claim that there were molecular facts. Why? Here is what I think. Consider the above molecular fact. It exists only if each of its components exist. Therefore, if sentence 3 is true, we are committed to the existence of the fact that Mary loves John—which we have said is false. We don’t want to analyze sentence 3 so that its truth entails that sentence 2 is true.
In this regard, I follow Russell’s lead and opt for a “truth-functional account” of the truth of molecular sentences. Sentence 3 is true if, and only if, either sentence 1 is true or sentence 2 is true. Since sentence 1 is true, the true of 3 is secured—even though sentence 2 is false. Similar truth functional analyses are in the offing for conditionals, and conjunctions.
So far, then, I am with Russell on molecular facts but not on negative facts. We turn next to the topic of general facts.
Consider sentences
4. All humans are mortal,
and
5. Some human is mortal.
Sentence 4 is a universal generalization and sentence 5 is an existential generalization. Presumably, both are true. This might seem to entail that each corresponds to a fact. This was Russell’s view: he held that general sentences are true in virtue of corresponding to general facts. Sentence 4 corresponds to a universal general fact and sentence 5 corresponds to an existential general fact.
In the notation I am using, the general fact corresponding to sentence 4 would be
f7 [("x), [®, [human, x], [mortal, x]]]
and the fact corresponding to sentence 5 would be
f8 [($x), [&, [human, x], [mortal, x]]].
These are rather exotic entities—though perhaps not quite so exotic as Russell’s negative facts. Fact 4 has two main components: a property and a complex function. The property is a property that such a function has if, for any given object there is a fact of the form of the factual function.
Consider this function,
ff1 [®, [human, x], [mortal, x]].
If every object is such that there is a fact of this form constituted by that object, then that function as the property expressed by ("x). If that function has that property, then there is such a fact as fact 4. If that function lacks that property, then there is no such fact. Such a fact is a universal general fact.
What about fact 5? It also involves both a property and an object. Once again, the property is a property of factual functions and the object is a factual function, in this case
ff2 [&, [human, x], [mortal, x]].
The property, which is represented by ($x), is a property that a factual function has provided there is at least one object such that there is a fact of the form of the factual function constituted by that object.
If some object is such there is a fact of this form constituted by that object, then that function has the property expressed by ($x). If that function has that property, then there is such a fact as fact 5. If that function lacks that property, then there is no such fact. Such a fact would be an existential general fact.
I think that there is no good reason to follow Russell and hold that there are general facts. Russell did, in fact, offer two arguments in support of the claim that there are general facts. I will not present them here. I will, however, discuss the basic idea behind them and explain why it might seem to suggest that there are general facts. In addition, I think that roughly the same idea is behind Russell’s claim that there are negative facts. Before I discuss this basic mistake, I will explain how I would account for the truth of both universal and existential generalizations.
If sentence 4 is true, then every object is such that if it enters into a fact of the form of
ff3 [human, x],
then it also enters into a fact of the form of
ff4 [mortal, x].
So, for example, if sentence 4 is true, if there is such a fact as
f9 [human, Rik],
then there is also such a fact as
f10 [mortal, Rik].
Presumably every object is such that if it enters into a fact of the form of
ff3 [human, x],
then it does enter into a fact of the form of
ff4 [mortal, x],
and, therefore, sentence 4 is true.
As for sentence 5, it is true if, and only if, at least one thing enters into both a fact of the form of
ff3 [human, x]
and of the form of
ff4 [mortal, x].
Let me then summarize. Here is the theory of truth I am proposing,
RFT P is true if, and only if,
Either P is a non-negative atomic sentence and there is a fact corresponding to P,
or
P = ØQand Q is not true,
P = Q and R, and Q is true and R are true,
P = Q or R, and either Q is true or R is true,
P = If Q, then R, and either Q is false or R is true,
P = "x (if Y(x), then F(x)) (i.e., every Y is a F), and for every object x such that there is a fact of the form of [Y, x], there is a fact of the form [F, x],
or
P = $x (Y (x) and F (x)) (i.e., some Y is a F), and there is an object x such that there is a fact of the form of [Y, x] and a fact of the form [F, x].
Russell’s Theory is somewhat different.
RT P is true if, and only if,
Either P is a non-negative atomic sentence and P corresponds truly to some atomic fact,
or
P = ØQand Q corresponds truly to some negative fact,
P = Q and R, and Q is true and R are true,
P = Q or R, and either Q is true or R is true,
P = If Q, then R, and either Q is false or R is true,
P = "x (if Y(x), then F(x)) (i.e., every Y is a F), and P corresponds to some universal general fact,
or
P = $x (Y (x) and F (x)) (i.e., some Y is a F), and P corresponds to some existential general fact.
The theory I am recommending differs from Russell’s in two main ways. First, unlike Russell’s theory, it does not entail that there are negative facts. Second, unlike Russell’s theory, it does not entail that there are general facts. If we take seriously Ockham’s Razor,
Ockham’s Razor: Don’t multiply entities beyond necessity,
then the theory I am proposing is more acceptable than the one Russell proposed.
Russell’s reasons for hold that there negative facts are, I think, closely related, and perhaps at bottom the same as his reasons for thinking that there are general facts. He seems to think that in order to decribed the world completely, one would need to list not only the atomic facts that there are but also the general fact that your list of atomic facts contains all the atomic facts that there are. He then maintains that you would then be committed to the truth of the sentence,
6. These are all of the atomic facts.
He then maintains that if sentence 6 is true, it must be true in virtue of corresponding to a fact. That fact would be something like
f11 [("x), [®, [atomicfact, x], [listed, x]]]
That fact would not be an atomic fact, and, therefore, is a general fact. Finally, he adds, if you have one general fact, there is no good reason to think that you don’t have all sorts of general facts.
I think this reasoning is flawed. Six is true because your list includes all atomic facts—there is no atomic fact that is not listed. Since that is the case, 6 is true whether or not there is also the general fact that all of the atomic facts are listed.
Russell’s reasoning, here, is a little more complex that I have let on. For he also includes the reason that if I were to determine that 6 is true, I would need to determine that there was such a general fact as the fact that all of the atomic facts have been listed. And no list of mere atomic facts will say that all of the atomic facts have been listed. Hence, in order to be sure that the list is complete—and that 6 is true—I need more facts than the facts the list contains. Hence, I need the additional general fact that the list is complete. Russell’s main concern, then, is that there is some missing fact.
This concern about missing facts is, I maintain, also Russell’s unstated reason for asserting that there are negative facts. Suppose that I want to know whether of not
2. Mary loves John,
is true. On my view, 2 is true if and only if there is such a fact as the fact that Mary loves John. Suppose that I go to my handy little list of atomic facts, look carefully through it, and determine that it contains no such fact as the fact that Mary loves John. This will do me little good, if I don’t already know that my list of facts is complete. Hence, unless I can be sure that there is no missing fact to the effect that Mary loves John, I cannot be sure that 2 is false. This, again, is a concern about missing facts. Here, then, we have Russell’s reason for holding that in addition to non-negative atomic facts we need negative atomic facts. The concern, again, in an epistemological concern about missing facts—facts that might exist but which might not have been listed on my list of atomic facts.
There is some irony here. If I am right about this, then Russell has made a mistake he warns others not to make. In an earlier work, The Problems of Philosophy, Russell wrote that questions of truth and questions of justification are distinct:
We are not asking how we can know whether a belief is true or false: we are asking what is meant by the question whether a belief is true or false. It is to be hoped that a clear answer to this question may help us to obtain an answer to the question what beliefs are true, but for the present we ask only ‘What is truth?’ and ‘What is falsehood?’ not ‘What beliefs are true?’ and ‘What beliefs are false?’ It is very important to keep these questions entirely separate, since any confusion between them is sure to produce an answer which is not really applicable to either. (PP 118-120)
Russell might have failed to heed his own good advice and this might well explain his commitment to the exotic facts of his logical atomism.
© 2001 Thomas C. Ryckman