School of Social and Political Sciences - Theses
Permanent URI for this collection
Search Results
1 - 1 of 1
-
ItemModels and consequence( 2008)The conclusion of an argument is a consequence of the premises if the truth of the premises guarantees the truth of the conclusion. This guarantee is often formulated as that the conclusion is true in every model where all the premises are true. Models are used to give precise, mathematical theories of consequence. The use of models has been central in a lot of the recent progress in logic. This thesis is a philosophical investigation into the connection between consequence and models. In this thesis I show that there are two central concerns that any model based theory of consequence must address: (1) What type of theory is it? What are the models intended to be? (2) What form does the theory take? How does the theory use the models in characterising consequence? Two particular types of theory are focussed on in the thesis. Interpretational theories take their models to be interpretations of the language under consideration. Representational theories take their models to represent the world as being a particular way. This distinction draws on the work of Etchemendy in [40]. I show that choices of this nature have significant effects on theories of consequence. On example of this is that nonclassical logics of these different types have different commitments regarding truth gaps and gluts. I also show that there are different subtypes of both interpretational and representational theories which depend how much of a model is considered significant for the interpretation or representation respectively. There are different forms or shapes that a theory can take. Theories which reduce consequence to truth preservation in all models - with no side constraints - suffer from a tendency to produce incorrect results. In [40] Etchemendy shows that this is the case for interpretational theories. I will show that this is the case for any theory with an unconditional form and that it is not primarily due to the theory's type. The most obvious alternative form of theory relies on the condition that the theory only provides an account of consequence if there are sufficiently many models. Conditional theories of consequence do not produce incorrect results in the way that unconditional theories do, but they are not guaranteed to provide any account of consequence.