Reading summaries

Hume, An Enquiry Concerning Human Understanding

Aug 27 · on the schedule

No argument can justify our reliance on past experience as a guide to the future.

Hume splits knowledge into relations of ideas, which are certain but empty of fact, and matters of fact, which depend on experience. Every claim about what we have not observed runs through cause and effect, and causal knowledge comes only from having seen one thing follow another. So the inference assumes that unobserved cases resemble observed ones. That assumption cannot be proved by reason, since a world that changes tomorrow involves no contradiction, and it cannot be proved by experience without already helping itself to the very assumption in question. What actually carries us across the gap is habit, not argument.

Salmon, “The Problem of Induction,” §1 and §2.1

Sep 1 · on the schedule

Trying to justify induction inductively fails, because the same move would equally justify its opposite.

Salmon frames Hume’s problem with two distinctions. Inferences are ampliative when the conclusion says more than the premises, and demonstrative when the premises guarantee the conclusion. Deduction is demonstrative but adds nothing; induction adds content but offers no guarantee. There is no inference that does both, which is why ampliative reasoning needs a justification it cannot get for free.

He then examines the self-supporting defence, on which induction is vindicated by its past record. The reply is that a counterinductive rule can be defended in exactly the same shape: applied to its own history of failure, it predicts its future success. A justification that works just as well for a rule and its opposite has not discriminated between them.

Goodman, Fact, Fiction, and Forecast

Sep 3 · on the schedule

Even granting induction, evidence alone cannot tell us which generalisation it confirms.

Goodman invents the predicate grue: applying to things examined before a future time and found green, and to other things only if blue. Every emerald seen so far is both green and grue, so the same evidence equally supports the prediction that the next emerald is green and the prediction that it is blue. No purely formal or syntactic rule of confirmation separates them, since the two hypotheses have identical logical form.

His diagnosis is that only some predicates are projectible, and his proposal is entrenchment: predicates earn projectibility through a history of successful use. For computer science the riddle is inductive bias — a learner that fits the training data still needs a reason to extrapolate one way rather than another.

Nozick, “Newcomb’s Problem and Two Principles of Choice”

Sep 8 · on the schedule

Two principles of rational choice that normally agree come apart, and neither can simply be dropped.

A reliable predictor has already filled an opaque box with a large sum if it predicted you would take that box alone, and left it empty if it predicted you would take both. The transparent box always holds a smaller sum. Maximising expected utility on the evidence favours taking one box, since one-boxers almost always end up rich. Dominance favours taking both, since whatever is already in the opaque box, adding the second box adds money, and your choice now cannot change what was sealed earlier.

Nozick argues the conflict arises when the actions are evidence for states they do not cause, and traces the same structure through related cases, including Prisoner’s Dilemma style situations. The dispute became the split between evidential and causal decision theory, which matters for how an artificial agent should be built to choose.

Searle, “Minds, Brains, and Programs”

Sep 10 · on the schedule

Running the right program is not sufficient for understanding, because syntax does not yield semantics.

Searle distinguishes weak AI, which treats the computer as a tool for studying the mind, from strong AI, which holds that a suitably programmed computer literally has a mind. Against strong AI he imagines himself locked in a room, matching Chinese symbols to other Chinese symbols by rulebook, well enough that his answers are indistinguishable from a native speaker’s. He understands no Chinese, yet he is doing everything the program does, so the program cannot be what constitutes understanding.

He then works through replies — that the whole system understands even if the person does not, that a robot with sensors would fix the problem, that simulating the neuron-by-neuron operation of a Chinese speaker’s brain would suffice — and answers each by internalising or extending the setup. His positive view is that intentionality depends on the causal powers of brains, which a formal program duplicates only in shape, never in content.

Block, “The Mind as the Software of the Brain,” §11.1–11.2

Sep 15 · on the schedule

Behavioural tests like Turing’s cannot define intelligence, because how the behaviour is produced matters.

Block sets out the computer model of the mind, on which mental processes are computations over representations and the mind stands to the brain roughly as software to hardware. He separates two questions that get run together: intelligence, a matter of how information is processed, and intentionality, a matter of how states come to be about anything.

Against the Turing test he offers a machine that holds a conversation by looking up every possible sensible exchange in a vast pre-written table. Its behaviour over any fixed stretch is indistinguishable from a person’s, yet all the intelligence sits in the programmers who wrote the table, not in the machine, which has no information processing worth the name. Behaviour is therefore evidence of intelligence rather than what intelligence consists in.

Churchland and Churchland, “Could a Machine Think?”

Sep 17 · on the schedule

Searle is right about symbol-shuffling programs but wrong to conclude that no machine could think.

The Churchlands accept that classical rule-and-symbol AI looks unpromising, but argue that Searle’s premise about syntax and semantics assumes what it should prove. Their comparison is a luminous room: someone waving a magnet in the dark produces no visible light, and it feels obvious that light therefore cannot be electromagnetic waves, yet Maxwell was right and the intuition merely tracked the low frequency of the waving. Intuitions about the Chinese Room may be misleading in the same way.

Their alternative is to look at what brains actually do: massively parallel networks of simple units with weighted connections, learning by adjusting those weights. If thinking depends on that kind of architecture, then an artificial system with the same organisation is a live candidate, and Searle’s argument leaves it untouched.

Pryor, “Guidelines on Writing a Philosophy Paper”

Sep 29 · on the schedule

A philosophy paper defends one thesis clearly enough that a sceptical reader could follow and resist it.

Pryor’s advice is procedural. Start from a narrow thesis rather than a topic, explain the view you are discussing in your own words, and reconstruct the argument you are attacking in its strongest form. Write for a reader who is intelligent but has not read the text, so every technical term gets defined and every step gets stated. Raise the best objection to your own position and answer it. Style should be flat and exact: short sentences, signposting, no build-up, no dictionary definitions, no padding. Expect the first draft to be a way of finding out what you think, and leave time to rewrite it.

Dekofsky, “The Infinite Hotel Paradox” (TED-Ed)

Sep 29 · on the schedule

An infinite set can be the same size as a proper part of itself — but not every infinity is that size.

Hilbert’s hotel has a room for every counting number and every room is occupied. One new guest still fits: move each guest up one room. Forty more fit the same way, and a countably infinite busload fits by moving each guest to twice their room number, freeing every odd room. Infinitely many such buses can be handled with a scheme that assigns each passenger a unique room, for instance using powers of primes.

The trick works because these collections are countable — they can be listed against the natural numbers. It fails for the real numbers, where a diagonal construction produces a guest who matches no room on any list. That distinction is what Part II needs: programs can be listed, and functions cannot.

Sets, Logic, Computation (Open Logic Project), §14.1–14.3

Oct 1 and Oct 6 · on the schedule

A precise, austere machine model is enough to capture the intuitive idea of following a procedure.

A Turing machine has an unbounded tape divided into squares, a head that reads and writes one square at a time, a finite set of internal states, and a finite table of instructions. Each instruction says: given this state and this symbol, write that symbol, move one square left or right, and enter that state. Nothing else is available — no memory beyond the tape, no operations beyond those steps.

The sections build up configurations and runs, work through small machines such as ones that recognise simple patterns or perform addition in unary, and define what it is for a machine to compute a function: started on a standard representation of the input, it halts with the output on the tape. Everything later in the unit is stated in terms of this definition.

Sets, Logic, Computation, §15.1–15.2

Oct 8 and Oct 13 · on the schedule

Machines can be counted and functions cannot, so almost everything is uncomputable.

Each Turing machine is a finite object — a finite table of instructions — so it can be coded as a finite string, and the strings can be listed in order. The machines therefore form a countable list, and each one can be referred to by its number. That same coding makes a universal machine possible: a single machine that takes the code of another machine plus an input and simulates it.

But the functions from natural numbers to natural numbers are uncountable, by a diagonal argument of the kind that defeats the infinite hotel. A countable list of machines cannot cover an uncountable range of functions, so most functions are computed by no machine at all. Uncomputability is the normal case; computability is the exception.

Copeland, “Computation”

Oct 15 · on the schedule

The Church–Turing thesis is about what a human clerk following a rote method can do, and is routinely overstated.

Copeland asks what makes a physical process a computation at all, and argues that a system computes only under an interpretation that maps its states onto the values of a function. He then states the thesis carefully: every function computable by an effective or mechanical method — a finite set of exact instructions, followed without insight, guaranteed to finish in finitely many steps — is computable by a Turing machine. It is a claim about that informal notion, and its support is the convergence of independent definitions on the same class of functions.

He separates this from stronger claims often attributed to Church and Turing: that the brain is a Turing machine, or that no physical process can outstrip one. Those are empirical theses about the world, not consequences of the original thesis, which leaves room for debate about hypercomputation.

Sets, Logic, Computation, §15.4–15.5

Oct 20 · on the schedule

No program can decide in general whether another program halts, and the same failure infects logic.

Suppose a machine that, given the code of any machine and an input, always answers correctly whether that machine halts. Using the coding from the previous sections, build a machine that consults the decider about its own code and then does the opposite: it halts exactly when the decider says it does not. The contradiction shows the decider cannot exist. Halting is a perfectly well-defined property with no algorithm that settles it.

The decision problem for first-order logic falls the same way. If there were an algorithm deciding which formulas are valid, halting behaviour could be encoded as formulas and settled by that algorithm. Since halting is undecidable, so is validity — a limit on mechanical reasoning itself, not only on programs.

Aaronson, “Why Philosophers Should Care About Computational Complexity,” §1–3

Oct 22 · on the schedule

The gap between possible-in-principle and feasible-in-practice changes philosophical arguments, not just engineering ones.

Aaronson’s complaint is that philosophy absorbed computability in the twentieth century but stopped there. Complexity theory asks how resources scale with input size, and the polynomial-versus-exponential divide is qualitative: an exponential procedure can be unrunnable on any conceivable machine long before the inputs get large. P versus NP asks whether problems whose solutions are easy to check are also easy to solve, which bears on whether finding proofs and creative work could ever be routine.

His illustration is Block’s lookup-table machine. Treated as a matter of principle, it seems to refute the Turing test; counted up, the table is vastly larger than the observable universe could hold. A resource bound thus rescues a philosophical position that the in-principle argument had defeated.

Steiner, “Libertarianism and Property”

Nov 3 · on the schedule

Rights over one’s own labour do not extend to the raw natural resources that labour is applied to.

Steiner starts from original rights: each person owns themselves and what they produce. Natural resources, however, are made by no one, so no one has a prior claim to them. The value of a holding therefore divides into a produced component, which belongs to the producer, and a natural component, which does not.

From this he derives redistribution that a libertarian can accept. Taxing away the value of appropriated natural resources and distributing it equally does not violate self-ownership; it corrects an unowned share that was taken. The result is a libertarianism that supports an equal claim on the earth rather than defending existing holdings.

Vallentyne, “Libertarianism and Self-Ownership”

Nov 3 · on the schedule

Full self-ownership is compatible with egalitarian ownership of the natural world.

Vallentyne presents libertarianism as a family united by full self-ownership — a complete set of control and transfer rights over one’s person — and divided over the appropriation of natural resources. Right-libertarians allow appropriation on easy terms, which lets initial acquisitions harden into large inequalities. Left-libertarians impose an egalitarian condition on appropriation: you may take natural resources only if you leave others an equally valuable share or pay them its worth.

The result is a position that keeps the libertarian ban on forced labour and interference with the person while reaching distributive conclusions closer to liberal egalitarianism. He presents it as the more defensible reading of the tradition’s own premises.

Shafer-Landau, “Consequentialism: Its Nature and Attractions”

Nov 5 · on the schedule

An act is right if and only if it produces at least as much overall good as any alternative.

Consequentialism holds that the whole moral job is to make the world go best. The classical version, act utilitarianism, counts well-being as the good and weighs everyone’s equally, with no discount for distance or relationship, and judges each act by its outcomes rather than by any intrinsic property.

The attractions Shafer-Landau draws out: it explains why the familiar moral rules matter, since following them usually helps, while allowing exceptions when following them would be disastrous; it supplies a single procedure for settling conflicts; it takes everyone into account impartially; and it makes morality answerable to how people’s lives actually go rather than to tradition. The same impartiality and flexibility are what the standard objections attack.

Rawls, “The Main Idea,” A Theory of Justice

Nov 10 · on the schedule

Just principles are those that would be chosen by people who do not know who they will be.

Rawls revives the social contract at a higher level of abstraction. The question is not what government we would consent to but what principles would be agreed on for the basic structure of society — its major institutions — by parties in an original position behind a veil of ignorance that hides their class, talents, and conception of the good. Ignorance makes the choice fair, because no one can tailor the rules to their own advantage.

He argues such parties would not gamble on utilitarianism, which permits losses to some for larger gains to others. They would instead secure equal basic liberties for all and allow inequalities only where these work to the benefit of the least advantaged. Justice as fairness treats the distribution of natural talent as arbitrary from a moral point of view.

Wolff, “Rawls’s Theory of Justice”

Nov 10 · on the schedule

The machinery of the original position is what does the work, and it is also where the objections land.

Wolff reconstructs the theory step by step: the original position and veil of ignorance, the two principles with liberty given priority over the difference principle, and the reasoning that is supposed to lead from one to the other, including maximin choice under conditions where probabilities are unavailable and the stakes are a whole life.

He then sets out the standard criticisms. Why is maximin rational rather than excessively risk-averse, when other rules would favour a utilitarian gamble? Does the veil describe people so stripped of identity that their choice tells us nothing? And is the difference principle compatible with the entitlement view, on which holdings acquired and transferred justly need no pattern imposed on them?

Waldron, “Property Rights and Welfare Redistribution”

Nov 12 · on the schedule

The best arguments for private property support welfare rights rather than blocking them.

Waldron separates two ways of grounding private property. A special-right argument appeals to something a particular person did — laboured, was given, contracted — and yields rights only for those who did it. A general-right argument appeals to something true of everyone, such as the importance of controlling resources for autonomy, and so claims property for all.

Special-right arguments are silent about people who never acquired anything, so they cannot justify a system in which many hold nothing. General-right arguments cover everyone, but then a regime leaving people propertyless fails by its own standard, and redistribution is what the argument demands rather than an intrusion on it. Property rights so understood are not a trump against welfare provision.

Johnson, “Property Rights in Computer Software,” Computer Ethics, ch. 5

Nov 12 · on the schedule

Software fits none of the existing categories of property well, so the question is what ownership should mean here.

Johnson lays out the legal instruments — copyright over expression, patent over process, trade secret over what is kept confidential — and shows how awkwardly each sits on software, which is simultaneously text to be read and a machine that does work. Copying costs nothing and deprives the owner of no copy, so the usual rationale for exclusive possession does not transfer.

She weighs the arguments: a Lockean case that programmers are entitled to what they made, a utilitarian case that protection is needed to fund development, against the cost of enclosing algorithms and ideas that others need to build on, and the fact that most software is written on top of work its authors did not own. The upshot is that the scope of software ownership is a policy choice to be justified, not a natural fact.

O’Neil, Weapons of Math Destruction, ch. 1, 5, 6

Nov 17 and Nov 19 · on the schedule

Models are opinions embedded in code, and the damaging ones share three features: scale, opacity, and self-confirming feedback.

Chapter 1 sets up the frame. Every model simplifies, and what it leaves out reflects what its builders valued. A baseball model is transparent and constantly corrected by results; a scoring model used on people is often secret, applied to millions, and never told whether it was right. Those are the models O’Neil calls weapons of math destruction.

Chapter 5 takes predictive policing. Because the software is fed recorded crime, and recorded crime depends on where officers were sent, directing patrols to the predicted areas generates the arrests that confirm the prediction — especially once minor nuisance offences are included. Chapter 6 turns to hiring and scheduling: personality screening that filters out applicants with no feedback on whether the filter worked, and shift-optimising software that stabilises labour costs by destabilising workers’ lives. In each case a proxy stands in for what is really wanted, and the people scored have no way to see or contest it.

Angwin, Larson, Mattu and Kirchner, “Machine Bias,” ProPublica

Dec 1 · on the schedule

A risk score can be equally accurate across races and still distribute its errors unequally.

The reporters obtained risk scores assigned to thousands of defendants in a Florida county and checked them against who actually reoffended over the following two years. Among those who did not go on to reoffend, black defendants were far more likely to have been labelled high risk; among those who did reoffend, white defendants were more likely to have been labelled low risk. Race is not an input, but correlated questions about arrests, family and neighbourhood carry the signal.

The company disputed the analysis, pointing out that a given score means roughly the same reoffending rate whichever group the defendant belongs to. Both sides were reading their own numbers correctly, and that is the setup for the impossibility results: when base rates differ, calibration and equal false-positive rates cannot both be satisfied, so fairness has to be chosen rather than computed.