| | In Post 25, Claude wrote, Nothing -- no theory, whether scientific or philosophical -- is immune from change, alteration, and (GASP!!!!) improvement. In Post 30, I replied, "NO theory, whether scientific or philosophical?? What about the theory that 'no theory is immune from change, alteration and improvement'? Is that theory immune from change, alteration or improvement? If it is, then the theory is false, because it is self-referentially inconsistent. And if it ISN'T immune from change, alteration and improvement, then it is theoretically deficient and is therefore false as well."
In Post 31, Bob Kolker replied, The assertion that no physical theory is immune from potential falsification and open to change is not a physical theory or hypothesis. It is an observation ABOUT physical theories which has been borne out to some extent by experience. It's not a physical theory; it's a philosophical one. Remember, Claude's original statement wasn't confined to physical theories. He was referring to all theories, whether scientific or philosophical. And since his statement is philosophical, it is self-referentially inconsistent. So your reply, even if true, is not a defense of his statement.
Secondly, although not self-referentially inconsistent in the way that Claude's is, your statement that "no physical theory is immune from potential falsification" is still problematic, because it is too broad. For example, the physical theory that the sun revolves around the earth was falsified by observation and replaced with the theory that the earth revolves around the sun. But that doesn't mean that the latter theory is itself falsifiable. We know that the earth revolves around the sun. That is a fact, and facts cannot be falsified, which leads to my third point. You say, Most of 19th century physics has been empirically falsified. As we find out more facts it is reasonable to expect that some of our favorite theories will not cover some of these new facts. It is reasonable to expect this, if the theories are not held conclusively to be true. But it is not reasonable to think that a theory that one holds conclusively to be true could nevertheless be false. One falsifies a theory by discovering a truth. The geocentric theory was falsified by discovering the truth that the earth revolves around the sun. But a truth, by definition, cannot be falsified; otherwise, it wouldn't be a truth. One must distinguish between an X type assertion and an assertion ABOUT X type assertions. The latter is a meta-X assertion. In this way we do not get into self referential troubles. One can validly make this distinction only if the assertion about X is not itself an X. But the assertion that no assertion, whether scientific or philosophical, is immune from potential falsification is itself a philosophical assertion, a fact which is not altered by declaring it to be meta-philosophical. If I say, "All English sentences have a subject and a verb," my statement is an English sentence which refers to all English sentences including itself, a fact which is not altered by calling it a "meta-English sentence."
The "meta" approach to self-referential statements can be traced to Bertrand Russell, and his attempt to solve the paradox of "the set of all sets that are not members of themselves." The paradox arises when one asks if the set of all sets that are not members of themselves is a member of itself? If it is, then it isn't; and if it isn't, then it is. Hence, the paradox.
Perhaps a simpler example of this type of paradox is the statement, "The statement I am now making is false." Is this statement true or false? If it is true, then what it asserts is in fact the case. But what it asserts is that it itself is false. Therefore, if it is true, then it is false. (And if it is false, then what it asserts is incorrect, in which case, it is not false.)
In order to avoid this kind of self-referential paradox, Russell postulated that a statement can refer only to statements of a lower type. Therefore, since the above example -- "The statement I am now making is false" -- refers to a statement of the same type (because it refers to itself), it is, according to Russell, illegitimate. Hence, the distinction that Bob Kolker and others make between statements and "meta"-statements appears to have come from Russell. But Russell's theory does not solve the paradox. Statements can and do refer to themselves, and it does not serve the cause of logic simply to "legislate," or to declare arbitrarily, that they cannot.
Furthermore, as noted above, Russell's "solution" would imply that the sentence, "Every English sentence has a subject and a verb," is not an English sentence -- which is absurd. Besides, as Harry Binswanger notes, since Russell's theory states that all statements must conform to the theory, the theory is self-contradictory, because, in referring to all statements, it refers to itself, something that it claims no statement can do. Therefore, by Russell's own theory, his theory is false.
What, then, is the solution to this antinomy or self-referential paradox, if Russell's solution fails? Well, observe that, while a statement can refer to itself (contra Russell), it must, if meaningful, be either true or false. To make this point intuitively obvious, Binswanger asks us to consider the statement, "The statement I am now making is true." Is that statement true? No. Is it false? No again, for there is no actual (i.e., meaningful) statement here that can be considered true or false.
This is easy to see if one realizes that in order to verify the statement, "The statement I am now making is true," one must verify its referent -- the statement to which it refers -- which in turn necessitates that one verify the referent of its referent, and so on. We are thus lead to a vicious regress. Since there is no ultimate referent, no verification (or falsification) is possible. Exactly the same reasoning applies to "The statement I am now making is false". There is no self-referential inconsistency, because there is no ultimate referent -- no meaningful statement that qualifies as being either true or false.
The answer to the paradox that Russell and others have found so insoluble is to recognize that it is meaningless to talk about the set of all sets as being either a member of itself or not a member of itself. The answer is not to declare arbitrarily as a kind of logical "patch" that sets, classes or statements cannot refer to themselves, which is what Russell has done.
That doesn't mean, of course, that there are no statements about statements (or theories about theories) that are not self-referential. As I acknowledged above, the theory that all physical theories are falsifiable is a theory that does not refer to itself, because it is not a physical theory. The same is true for the sentence, "All Chinese sentences use pictographic characters," for even though the sentence refers to all sentences of a certain type, the sentences to which it refers are Chinese not English. But there is absolutely nothing wrong or incoherent about a theory's being self-referential. Many statements and theories refer to themselves, and if they do so inconsistently, then so much the worse for the statements or theories.
Claude Shannon replied to me as well. In response to my rejoinder, “What about the theory that ‘no theory is immune from change, alteration and improvement"? Is that theory immune from change, alteration or improvement?’,” he replied, To echo Prof. Kolker:
That's a simple declarative statement ABOUT theories; not a theory itself.
The fact that you couldn't distinguish the difference is very telling. It’s a simple declarative statement about philosophical theories that expresses a philosophical theory. And since, as we have seen, there is nothing which says that no theory or statement can refer to itself, theoretical statements can be self-referentially inconsistent, as the one you’ve expressed clearly is.
- Bill
(Edited by William Dwyer on 3/31, 9:00pm)
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