FOM: Goedel: truth and misinterpretations

Torkel Franzen torkel at
Thu Oct 26 14:24:57 EDT 2000

  V.Kanovei says:

  >Of course incursions of mathematical English are allowed as 
  >shortcuts, say, "any group contains an element a with aa=a" 
  >Zis a single ZFC formula, 
  >"modern philosophy likes to refer to chickens" is not.

  I don't see how this chicken sentence relates to the observation
that infinitely many true arithmetical sentences (of the indicated
form) are not provable in ZFC.

  >I did not make claims, I 
  >only asked that somebody explains what does it mean that 
  >"CH is true or false", and the only coherent explanation was 
  >that this is just the formula "CH or not-CH".

  To understand the metaphysical claim "CH is true or false" you
must understand what difference it makes to our thinking in or
about mathematics. Can you see any such difference? If you can't,
what are we arguing about?

  >I do not see why I must take on trust the prayer 
  >that either CH is true or CH is false,

  Take what on trust? What does it mean? What is problematic or
doubtful about "CH is true or false"? What difference does it make
whether or not we affirm "CH is true or false"?

  >3) but some parts of mathematics (finite combinatorics, geometry, 
  >probability, analysis, more) have successfully and undoubtfully 
  >survived harsh practical justification with most perfect mark.

  So it does make a difference what axioms we adopt? If I understand
you correctly, the difference it makes is that the finite
combinatorial consequences may or may not survive harsh practical
justification.  Very well, then: what reason do we have to think that
our current axioms are more likely to survive such justification than
any other axioms that we might invent?

Torkel Franzen, Lulea university

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