# How do correspondence theories handle statements like these?

I have a number of true statements. Each of these statements is a case where I have difficulty seeing how (assuming physicalism) the statement could correspond to a state of affairs. My question is: how do correspondence theories account for statements like these?

1. There are infinitely many prime numbers.

2. A unit circle has circumference 2π.

3. There is no Turing machine which solves the halting problem.

4. If 2+2=3, then there is a number larger than every prime number.

5. If a purple unicorn materialized in my room ten minutes from now, I would be surprised.

• This would be like saying the mountain is disobeying the map. Mathematics and logic are models, or maps. They do not always predict what is found. Sometimes the territory has not been fully mapped or modeled and are used old maps or maps of other territories. Sometimes they are approximations. Commented Apr 15, 2013 at 13:11
• @RicardoBevilaqua: I think at issue is whether or not these statements, which would conventionally be taken as true, can correspond to any 'facts' per se. (There is a notorious problem in exhibiting facts corresponding to universal negative statements, for example.) Commented Apr 15, 2013 at 13:32
• @NieldeBeaudrap There is no theory-independent way to reconstruct phrases like "really there", each theory has its own ontology. Convergence to the truth scientific progress seems to be impossible, if ontologies change with theories observations, and ontologies are relative to theories. Many past theories were not approximately true or truthlike. Ptolemy's geocentric theory was rejected in the Copernican revolution, not retained in the form “approximately Ptolemy”. Commented Apr 15, 2013 at 14:43
• @NieldeBeaudrap What is truth in Science? the progressive steps from Ptolemy to Copernicus or from Newton to Einstein are not only matters of improved precision but involve changes in theoretical postulates and laws. Science is progressive only on values other than the truth, such as simplicity, predictive accuracy, comprehensiveness, and requirements for consistency. Scientific theories are hypothetical and always corrigible in principle. They may happen to be true, but we cannot know this for certain in any particular case.What is "fact" in science? Commented Apr 15, 2013 at 14:46
• Statements 1-4 are mathematical propositions. Can you provide a source where physicalism is claimed to apply to mathematics? Otherwise, the question addresses a red herring.
– DBK
Commented Apr 15, 2013 at 21:12