## Over the years, I taught very many courses at LSE; here are materials for three of my favourites.

**Logic: PH101**

Deductive logic is the study of arguments or inferences. Its main task is to give an explicit characterisation of those arguments or inferences that are valid (and hence differentiate them from those that are invalid). Logic tells you exactly when some conclusion follows from some premises and when it does not.

Inferences play a fundamental role both in intellectual disciplines and in everyday life. For example, a scientist will test a particular theory by reasoning that if that theory were true then some other claim, one that can be checked experimentally, would have to be true as well. Mathematicians start with certain axioms and then infer other statements (theorems) from those axioms. Philosophy too is centrally concerned with arguments. More mundanely, we reason and draw inferences all the time – not always correctly – and our actions are guided by the conclusions we draw.

The course begins with a particularly simple system which nonetheless captures many important inferences. This is propositional, or truth-functional logic. Truth-functional logic turns out to be effective: that is, the question of whether an inference expressed in that logic is valid or invalid can be decided mechanically, by applying one of several (equivalent) algorithms.

Two other important notions turn out to be importantly related to that of validity of inference. These are (a) whether or not a given set of sentences taken collectively is consistent and (b) whether an individual sentence is or is not independent of a given set of sentences.

Truth-functional logic is powerful but not powerful enough: there are some clearly valid inferences which appear invalid when expressed in the language of truth-functional logic. We need a more expressive language and a more powerful logic and these are provided by Predicate Logic. Essentially any inference that is valid – even very challenging ones from science and mathematics – can be shown to be valid in predicate logic. But, unlike truth-functional logic, predicate logic is not effective: there is no algorithm that can be guaranteed to decide in a finite number of steps when an inference in predicate logic is valid. A system of rules of proof solves this problem: every valid inference can be shown to be valid using these rules of proof.

The final section of the course considers some foundational issues: what is the relationship between the formal reasoning involved in truth-functional and predicate logic and ordinary informal reasoning?: are the underlying notions of set and of truth as straightforward as they appear?

**Course Materials**

This is the link to a complete set of notes that I write for this course: **Worrall – Introduction to Logic**

**PH231/PH458 : Evidence and Policy**

Good policy decisions – whether concerning climate conservation, international development, poverty, education, medicine, or health – require rational deliberation over whether the proposed policy will (or is likely to) bring about the intended outcome. For instance, we might wonder if lowering CO2 emissions will reduce global warming? Or whether smaller class sizes enhance scholastic achievement? The obvious suggestion is that answers to such questions are the result of rational deliberation just in case they are based on good evidence and appropriate reasoning. But what counts as good evidence and appropriate reasoning? And what happens when different kinds of evidence pull in opposite directions? Are certain types of evidence more telling than others? And if so, why? In particular, is the claim (widely accepted in the clinical trials literature and elsewhere) that randomized controlled trials provide particularly telling, perhaps even definitive, evidence correct?

**Course Materials**

The following are guides to probability and to statistical testing that I wrote as essential background to the course:

Notes on Testing Statistical and Causal Theories

The following is a series of links to the slides from the course in one of the last years I taught it:

The following is a series of links to the seminar sheets from the course in that same year:

**PH213: Scientific Revolutions: Historical and Philosophical Issues**

Major changes in fundamental theories in science – so-called “scientific revolutions” – pose a number of important philosophical problems. In particular, what (if anything) makes those changes rational. Most of us start from the Modernist Enlightenment view that science allows mankind access to the truth about the Universe. But if so, then, when science changes its collective mind – switching, for example, from the geostationary theory developed by Ptolemy to Copernicus’ theory of a stationary sun – there had better be good reasons for that change, reasons presumably connected with the empirical evidence. (This is the problem of Scientific Rationality.) Moreover, if we are going to defend the Realist view that our current theories are at any rate approximately true descriptions of the underlying structure of the Universe, then we would seem to need to develop an account of continuity through “revolutionary” change. (This is the problem that changes in accepted theory pose for the thesis of Scientific Realism.)

This course consists of three main parts. First, a detailed examination of the Copernican Revolution and of the exact role played in it by evidence. Secondly, a detailed examination of the Darwinian Revolution and of the role played by evidence in it. Thirdly, a detailed look at an area of physics, namely theories of the constitution of light, in which more than one “revolution” has occurred. This will allow us to confront the issue of Scientific Realism in a very direct way.

The following is the introductory lecture:

The following is a lecture series on Copernicus’ Theory of the Universe:

The following is a series of lectures on Intelligent Design and Darwin:

The following is a lecture on ‘The Anthropic Principle’:

The following is a lecture on Newton:

The following is a lecture on Crucial Experiments and the 19th Century in optics:

The following is a lecture on Galileo and Observation:

The following is a lecture on the Wave Revolution in Physics and Scientific Realism: