UC Irvine

When do two theorems mean the same thing? Obviously the answer depends on how one understands meaning. In this dissertation, we approach meaning as a topic analysable into more theoretically refined concepts which serve as targets for scientific models. This "model-based" approach, which emphasises the informative role of models in enabling surrogative reasoning, is put forth in Chapter 1 and informs our assessment of accounts in the subsequent two chapters. In Chapter 2, we propose the folkloric account of meaning in mathematics, whereby the content of a mathematical statement is the class of logical models that make it true, with respect to a background class of models chosen to capture a particular mathematical setting of interest. In Chapter 3, we critique Soames' structured proposition account arguing with the use of examples that it fails to identify the differences which are most salient in mathematics.