Addenda

Reduction

The possibility of reduction (or denial thereof) plays a very significant psychological role for many philosophers. The two extreme positions are:

1. Everything can be reduced to fundamental physics.
2. There is stuff that cannot be reduced to fundamental physics.

There is an immediate question: what does “reduced” mean in these sentences, and what is supposed to be reduced to what? When some analytic philosophers tried to clarify the notion of reducibility with syntactic tools, it was quickly pointed out that (1) is completely implausible. For most philosophers, however, the response was not to embrace (2), but to look for a more liberally defined relation that plays a similar psychological role. For example, many philosophers embraced the claim that everything “supervenes” on fundamental physics — and when this proved problematic, they moved to the claim that everything is “grounded” in fundamental physics.

• Cliff Hooker, “Toward a general theory of reduction”

Second order logic

Fact: Second order logic with Henkin semantics is “equivalent” to a first-order theory.

• Maria Manzano, Extensions of First Order Logic

Ramsey sentences

Historical background

• Introduced in Ramsey, Frank P. “Theories.” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Series 7, Vol. 7, No. 37 (1929): 697–707
• Taken up by Carnap in the 1950s
• Taken up again by David Lewis in (Lewis 1970) and (Lewis 1972)
• The Canberra plan
• (Melia and Saatsi 2006)
• (Dewar 2019)
• https://philpapers.org/browse/ramsey-sentences

Technical results

TO DO: Is there a connection between Ramsey definability and implicit definability?

References