The theory of dependently sorted first order logic is developed. Two variants of the notion of a type setup, an abstract characterisation of language with dependent sorts proposed by Peter Aczel, are presented. It is argued that specialisations of these are appropriate for the characterisation of a notion of intuitionistic or classical dependently sorted first order theory and of semantic structure for the interpretation of those theories.

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This thesis draws a distinction between (i) reasoning about which scientific hypothesis to accept, (ii) reasoning concerned with generating new hypotheses and (iii) reasoning about which hypothesis to pursue. I argue that (ii) and (iii) should be evaluated according to the same normative standard, namely whether the hypotheses generated/selected are pursuit worthy. A consequentialist account of pursuit worthiness is defended, based on C. S. Peirce’s notion of ‘abduction’ and the ‘economy of research’, and developed as a family of formal, decision-theoretic models. This account is then deployed to discuss four more specific topics concerning scientific reasoning. First, I defend an account according to which explanatory reasoning (including the ‘inference to the best explanation’) mainly provides reasons for pursuing hypotheses, and criticise empirical arguments for the view that it also provides reasons for acceptance. Second, I discuss a number of pursuit worthiness accounts of analogical reasoning in science, arguing that, in some cases, analogies allow scientists to transfer an already well-understood modelling framework to a new domain. Third, I discuss the use of analogies within archaeological theorising, arguing that the distinction between using analogies for acceptance, generation and pursuit is implicit in methodological discussions in archaeology. A philosophical analysis of these uses is presented. Fourth, diagnostic reasoning in medicine is analysed from the perspective of Peircean abduction, where the conception of abduction as strategic reasoning is shown to be particularly important.

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This thesis defends inference to the best explanation (IBE) by giving an account of explanatory 'loveliness' in science. I begin by presenting IBE in generic form and showing how it out-performs rival accounts of induction. I then trace a path through the early literature which emphasises the role of background belief in determining loveliness. I then introduce crucial features of Lipton's account of IBE. I argue that Lipton's remarks on loveliness, through minimal, support the background-dependent view and that, appropriately construed, the view does not trivialise IBE.

The aim of this thesis is to present and motivate the relative modality view, whereby at least the non-logical alethic kinds of modality are mere relative forms of logical modality. The first chapter is devoted to presenting the relative modality view in general, providing a correct formulation, and considering some arguments for and against. The next chapter considers the particular challenges raised for the view by some essentialists. The third chapter turns to look at logical modality, the bedrock of the relative modality view, and presents an example of an account of logical necessity which suits it well. I argue that logical necessity is that necessity implicated in a deductively valid argument, and hence that its source is to be found in an account of the laws of logic. I argue that the laws of logic are constitutive-normative laws of thought. The fourth chapter takes a more historical turn. Here I argue that Kant can be understood as advocating a relative modality view, in particular for what he calls "real modality". In the fifth and final chapter I will draw on the conclusions of the preceding chapters to present a Kantian relative account of metaphysical necessity. Metaphysical necessity is that which follows, as a matter of logical necessity, from conditions on our having any experience of an objective world. I argue why this Kant-inspired kind of relative necessity is well-suited to play the role of metaphysical necessity, and consider how the view accommodates contemporary views about features of metaphysical necessity and its typical cases.

The subject of this thesis is a position in the philosophy of mathematics - defended by Bob Hale and Crispin Wright - known variously as neo-Fregeanism, neo-Logicism or abstractionism, and which claims that knowledge of mathematical objects can be based on principles - known as abstraction principles - which are in important respects like definitions of mathematical language. In the thesis, I make a distinction between two ways in which the abstraction programme might be carried out. These are the standardly defended static view, according to which abstraction principles can used to discover previously unrecognised objects lying within some fixed domain of quantification. The second is an expansionist view, according to which abstraction principles allow one to introduce new quantificational vocabulary, and thus expand ones domain of quantification to one which contains referents of mathematical terms. There are then two main aims. The first is to examine the static position, so as to identify the components of that view which make it committed to a standard domain, and to argue against the view. My main argument against the view concerns what has become known as the bad company problem. I argue that there is an epistemological component to the bad company problem which can not be avoided by the static abstractionist. The second aim of the thesis is to argue for and defend the expansionist view. In particular, I will claim that the expansionist view avoids the bad company problem, and that the expansionist view allows for an abstractionist foundation for set theory - an aim which (or so I will argue) has so far eluded the static view.

This thesis is about the metaphysics of logic. I argue against a view I refer to as 'logical realism’. This is the view that the logical constants represent a particular kind of metaphysical structure, which I dub ‘logico-metaphysical structure’. I argue instead for a more metaphysically lightweight view of logic which I dub ‘logical expressivism’. In the first part of this thesis (Chapters I and II) I argue against a number of arguments that Theodore Sider has given for logical realism. In Chapter I, I present an argument of his to the effect that logico-metaphysical structure provides the only good explanation of the semantic determinacy of the logical constants. I argue that other explanations are possible. In Chapter II, I present another argument of his to the effect that logico-metaphysical structure is something that comes along with ontological realism: the view that there is a non-language-relative fact of the matter about what exists. I argue that the connection between logical and ontological realism is not as close as Sider makes it out to be. In the second part of this thesis (Chapters III – V) I set out a positive view of the logical constants that can explain both why their meanings are semantically determinate, and why they form part of our vocabulary. On that view, the primary bearers of logical structure are propositional attitudes, and the logical constants are in our language as vehicles for the expression of logically complex propositional attitudes. In Chapter III, I set out an expressivist theory of propositional logic. In Chapter IV, I use this theory to explain how the logical connectives end up having determinate meanings. In Chapter V, I extend the expressivist theory to predicate logic.

This thesis orients around argumentative characterisations of logical non-monotonic reasoning, focusing on the arbitration between conflicting claims. These characterisations are studied in terms of ar- gumentation systems. In this context, groups of inference patterns, composed of arguments for and against a claim, are produced and evaluated for the purpose of testing the acceptability of that claim. The objective of this thesis is to investigate the generalisation of argumentation systems to communicative (dialogical) interactions, in which the reasoning process is distributed among opposing agents. Under this scope a variety of issues arise such as the form of these dialectics, the development of protocols concerned with different forms of argument evaluation, strategy development for decision making, and modelling of opponent knowledge used in strategy development. This thesis makes two main contributions to the study of dialogues. The first is the provision of a dialogue framework for structured argumentation. Through this framework it is shown that the structural form of arguments needs to be taken into account when strategising, since it may have considerable impact on the outcome of a game. It is also shown that not accounting for the structural form of arguments may compromise the soundness of argument evaluation results. The second is the provision of a modelling formalism which defines how information possibly known to an opponent can be built, updated and maintained in the form of an opponent model. Part of the proposed modelling methodology relies on statistical inference and can find practical application both within the broad area of artificial intelligence and multi-agent systems as well as in other areas.

We are often faced with normative claims about our logical systems and practice. 'classical systems are good', 'intuitionistic logics are deviant and therefore should not be used', etc. In this thesis I aim consider the nature of these norms. I ask: what is it to be a good or bad logic? What are the norms governing logical practice? The answer I offer traces back to the work of Cook (2000) and Shapiro (2012). I argue that Logic is best understood as a discipline concerned with the construction, development and application of a particular type of scientific model: logics. Logics are models in the same way that the Hodgkin-Huxley equations are a model of action potential. They are representational tools which have the capacity to be applied to target systems in order to satisfy a range of different functions. Thus, logics are to be evaluated in the same manner as any other model. Their value will stem from their satisfaction of a representational function. One way in which we might characterise this is to talk of the modes of assessment we usually attribute to scientific models {such as representational adequacy, simplicity, elegance and so forth). Logical practice is also therefore governed by the same norms applicable to scientific modelling generally. In essence, Logic is the search for the best model for a given target and function. Noteworthy about this approach to the normative issues are the following points: firstly, it recognises a greater variety of evaluations for logic than the simple binary of 'true' and 'false' or 'correct' and 'incorrect'. Second, what we might call 'non-correspondence virtues' (such as simplicity, unity etc.) become relevant to the assessment of logics. Finally, we find that Logic becomes open to functional and subject relativisms, along with methodological pluralisms, though the degree to which such pluralisms will actually exist will depend on the particular targets and functions to which our logics are applied