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Philosophy, Logic, and Artificial Intelligence MASc
Logic is the area of inquiry which gets started by considering the idea of an argument whose reasoning is water-tight. Since philosophy consists in giving and assessing arguments, logic has always been a core area of philosophy, for philosophers to both draw upon and also to study.
To systematise the key ideas in logic, we need to shift into a more formal register, adopting the tools of mathematics and computer science. And those tools have also led to the creation of various techniques in artificial intelligence, providing us with a potential model of learning and non-water-tight reasoning.
Our MASc brings these ideas together. You will leave the degree with both a foundational understanding and practical skills in the concepts and mechanisms of reasoning. You will encounter various logical formalisms; address philosophical and logical foundations for reasoning; and explore modern realisations of artificial intelligence. To ensure this, our programme is built around a stable core of compulsory modules with a focus on philosophy, logic, AI, and their intersection.
Programme Structure
There are a few different paths through the degree. But whichever path you follow, you will take eight 15-credit modules in Terms 1 and 2, and then undertake a 60-credit dissertation.
The standard path through the degree
If you take the standard path through the degree, then these six 15-credit modules will be compulsory:
- Phil0078. Formal Epistemology
Our strength of belief influences our decision making. But how should we measure strength of belief, and what rational constraints are there on one's strength of belief? How should one's strengths of belief change in response to evidence? And how exactly ought one's strength of beliefs feed through into rational decision making?
These are the central questions that will be tackled in this module, where students will be introduced to the probabilistic representation of strength of belief, arguments for the rationality of probabilistic degrees of belief, arguments for various rational constraints on those beliefs - including constraints concerning belief updates in response to evidence - and to decision theory.
Formal epistemology is an increasingly important area of philosophy, and its influence on other areas of philosophy (traditional epistemology, philosophy of mind, philosophy of action, metaphysics, ethics, and political philosophy) has been profound. The field is also strongly interdisciplinary, with crossovers into economics, statistics, computer science, and political science.
- Phil0176. Meaning and Interpretation
The central questions we will examine concern the fact that language is meaningful; i.e., that words can be used to say something about things in the world. How does this happen? In what ways can language be meaningful? How do different elements of language get their meaning? The aims of this module are to examine these questions by looking at the most prominent philosophical theories of the meaning of names, the meanings of sentences, and the different ways that our words can be meaningful. Precise topics to be studied may change from year to year, but an indicative selection might include:
- Millianism, Fregeanism; descriptivism
- Semantic internalism and externalism
- Meaning-as-use and inferentialism
- Propositions and propositional attitudes
- Phil0196. Philosophy of Learning
This module will focus on philosophical and scientific theories of learning. Learning is the process by which animals, humans and some computers develop cognitive skills through interaction with their environment. Philosophers have variously denied the very possibility of learning (as in the rationalist tradition) and attempted to give substantive theories of the nature of learning. The module will examine major philosophical accounts of learning, historical and contemporary, and relate the issues raised in these accounts to recent research in developmental psychology and computer science.
- Phil0202. Dynamics of Social Change
This module provides an in-depth examination of philosophical questions in the epistemology and ontology of social change. Each week will combine the study of one or more key theoretical concepts, with relevant real-world case studies. Precise topics to be studied will change from year to year, but an indicative selection of topics that could be discussed in the module would be:
- Mechanistic explanations and social change
- Structural explanations and individual agency
- Wicked and super-wicked problems
- Social norms, and their role in explanations of social change
- Complex systems approaches to public policy
- Self-fulfilling prophecies and looping concepts
- Power, knowledge and social reality I: understanding power
- Power, knowledge and social reality II: epistemic injustice
- Agenda setting in democratic decision-making
- The role of the role of scientific expertise in democratic decision-making
- Evidence and public policy I: What should we measure, and how?
- Evidence and public policy II: Replication, scaling up and external validity
- PhilXXXX. Core Logic
This introduces students on the MASc to a core logic curriculum. We focus on ideas from proof theory, since these are often omitted from other intermediate logic courses (which tend to focus on model-theoretic semantics). Precise topics to be studied may vary from year to year, but an indicative selection of topics that could be discussed in the module would be:
- Review of model-theoretic consequence and basic proof theory
- Inferentialism
- Dummett-Prawitz proof-theoretic semantics
- Validity in a base (in the sense of Schroeder-Heister, Piecha, et al.)
- Base-extension semantics
- Introduction, elimination, and definitional reflection
- Hereditary Harrop formulae, uniform proof, and least fixed-point semantics
- Inferentialist resource semantics
- Comp0088. Introduction to Machine Learning
This module will give students an understanding of machine learning, at both the theoretical and practical level. Students will also learn how to solve real-world machine learning problems using the right tools. The module will typically cover topics in both unsupervised and supervised learning.
For supervised learning, typical topics would be
- Linear models for regression and classification: least squares, logistic regression
- Concepts of overfitting and regularisation, L1 and L2 regularisation.
- Boosting, Decision Trees, Random Forests
- Support Vector Machines
- Deep Learning: Neural Networks for regression and classification, Convolutional Neural Networks, Recurrent Neural Networks.
For unsupervised learning, typical topics would be:
- K-means, Principal Components Analysis, Embeddings & Representation Learning
- Expectation-Maximisation, Mixture of Gaussians, Hidden Markov Models
- Deep Autoencoders, Generative Adversarial Networks
You will then choose two 15-credit modules from an extensive list of optional modules (see below). Once you have completed your modules, you will undertake a 60-credit dissertation:
- MASc Dissertation
This is the capstone of the degree: an opportunity for you to engage in your own research, with direction from an expert, on any topic of your choosing, subject to two constraints on the topic: (1) it must be appropriate for a degree in Philosophy, Logic, & AI, and (2) there must be an available member of staff with appropriate expertise to supervise.
It will be between 9,000-12,000 words, recognising that more formal topics may reasonably have lower word counts than more discursive topics. Essays may include illustrative programming-based work.
Alternative paths through the degree
Students on the MASc degree may come from many different academic backgrounds. Some may have graduated with single-honours Philosophy; some with a joint-honours degree in Philosophy & Computer Science; some with a specialism in logic. Consequently, some of our students may have already studied some of the topics which are compulsory on the default path through the degree.
Rather than repeating what you may have previously studied, we offer some alternative routes through the degree, which will allow you to take optional modules instead of some compulsory 15-credit modules. Here are the alternative routes:
- Specialism 1. Suitable if you have already studied formal epistemology and meaning theory to a high level.
On this specialism, you take four 15-credit compulsory modules: Phil0196, Phil0202, PhilXXXX, and Comp0008. You then take four 15-credit optional modules. - Specialism 2. Suitable if you have already studied logic to a high level.
On this specialism, you take five 15-credit compulsory modules: Phil0078, Phil0176, Phil0196, Phil0202, and Comp0008. You will also take three 15-credit optional modules. - Specialism 3. Suitable if you have already studied machine learning.
On this specialism, you take five 15-credit compulsory modules: Phil0078, Phil0176, Phil0196, Phil0202, and PhilXXXX. You will also take three 15-credit optional modules. - Specialism 4. Suitable only for students who have completed UCL's Philosophy & Computer Science BA.
On this specialism, you take three 15-credit compulsory modules: Phil0196, Phil202, PhilXXXX. You will also take five 15-credit optional modules.
No matter what specialism you follow, you will always take eight 15-credit modules, and finish with the 60-credit dissertation.
If you wish to pursue one of these Specialisms, you should indicate this when you apply for the degree. Supporting evidence (such as the transcript from your previous degree) of your suitability for this Specialism will be assessed by the Programme Co-ordinator.
Optional modules
To allow you to tailor your degree to your own interests, we offer an extensive range of optional 15-credit modules. These optional modules can be roughly divided into three groups, depending on whether their focus is primarily Philosophy, Logic, or AI (but of course these boundaries are not sharp):
- Optional Philosophy modules may include: Philosophy of arithmetic & incompleteness; Philosophy of mind; Paradoxes; Early Wittgenstein; Realism and antirealism; Reasons & normativity.
- Optional Logic modules may include: Categories, proofs and processes; (Co)algebraic structures in computer-science; Proof-theoretic semantics.
- Optional Artificial Intelligence modules may include: Artificial intelligence and neural computing; Multi-agent artificial intelligence; Reinforcement learning; statistical natural language processing.
Please note that the list of modules given here is indicative. This information is published a long time in advance of enrolment and module content and availability are subject to change. Some of the optional modules may assume a high level of prior learning.