[FOM] Wittgenstein?

[praatika@mappi.helsinki.fi]

Harvey Friedman <friedman at math.ohio-state.edu>:

> *DID LW WRITE ANYTHING THAT CAN AT LEAST BE REASONABLY INTERPRETED AS 
> BEING SIGNIFICANT FOR THE FOUNDATIONS OF MATHEMATICS? IF SO, EXACTLY 
> WHAT?*

In general, I am inclined to think that W's work has been more directly 
relevant for the philosophy of language (esp. his later philosophy) and the 
philosophy of logic (esp. his earlier philosophy) than to FOM (as Harvey 
understands it), and in particular that his views on the philosophy of 
mathematics (mostly) have only historical interest. 

Nevertheless, I think that one should not ignore W's contributions. After 
all, he introduced the familar truth tables for propositional logic.
This was, in part, based on his criticism of Frege and Russell on the 
interpretation of logic. They had conceived both propositions and logical 
connectives as names (of truth-values or facts, and logical objects). 
Against this, W pointed out that (i) propositions can't be names, for it 
makes no sense to negate a name, as we negate a proposition; and (ii) that 
connectives cannot be names, for otherwise e.g. --p would say something 
very different from p. 

Also, both Frege and Russell thought that logical truths are the most 
general truths about reality (reality understood as containing also the 
above mentioned logical objects) - all this was quite confused. W., on the 
other hand, argued that logical truths say nothing about the reality, but 
are "tautologous". In this way, he pioneered the modern understanding of 
logical truths as true under every possible interpretation.  

Today, we may take all this to be so obvious that we forget that at the 
time these issues were so badly misunderstood even by the greatest. I think 
that W made here important contributions that helped logic to get to the 
right track. 

(All this was in W's early publication Tractatus (1921))

But this is all history. If Harvey rather ment by his question to ask 
whether there still is in W's (later) work something little known but deep 
and highly relevant for FOM, I can only give my own opinion: I don't think 
so. (True believers will certainly disagree with me here.)

Best

Panu


Panu Raatikainen

PhD., Docent in Theoretical Philosophy
Fellow, Helsinki Collegium for Advanced Studies
University of Helsinki
 
Address: 
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E-mail: panu.raatikainen at helsinki.fi
 
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