This thesis has two goals. Firstly, we consider the problem of model selection for the purposes of prediction. In modern science predictive mathematical models are ubiquitous and can be found in such diverse fields as weather forecasting, economics, ecology, mathematical psychology, sociology, etc. It is often the case that for a given domain of inquiry there are several plausible models, and the issue then is how to discriminate between them – this is the problem of model selection. We consider approaches (...) to model selection that are used in classical [also known as frequentist] statistics, and fashionable in recent years methods of Akaike Information Criterion [AIC] and Bayes Information Criterion [BIC], the latter being a part of a broader Bayesian approach. We show the connection between AIC and BIC, and provide comparison of performance of these methods. Secondly, we consider some philosophical arguments that arise within the setting of the model selection approaches investigated in the first part. These arguments aim to provide counterexamples to the epistemic thesis of scientific realism, viz., that predictively successful scientific theories are approximately true, and to the idea that truth and predictive accuracy go together. We argue for the following claims: 1) that none of the criticisms brought forward in the philosophical literature against the AIC methodology are devastating, and AIC remains a viable method of model selection; 2) that the BIC methodology likewise survives the numerous criticisms; 3) that the counterexamples to scientific realism that ostensibly arise within the framework of model selection are flawed; 4) that in general the model selection methods discussed in this thesis are neutral with regards to the issue of scientific realism; 5) that a plurality of methodologies should be applied to the problem of model selection with full awareness of the foundational issues that each of these methodologies has. (shrink)