Essay/Logic

Philosophy tool kit

Thinking like a philosopher need not be a strange and arcane art, if you get started with these tricks of the trade

Alan Hájek

What the...? Photo courtesy Let There Be Neon-NYC

Alan Hájek

is professor of philosophy at the Australian National University in Canberra. His research interests are in probability and decision theory, formal epistemology, and the philosophy of science and language. He publishes regularly on these topics. 

4,100 words

Edited by Sam Dresser

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Philosophers pride themselves on thinking clearly by seeing what follows from what, exposing sophisms, spotting fallacies, and generally policing our reasoning. Many have spent years honing their skills, often deploying them on arcane topics. But these skills are not the exclusive property of rarefied sages, accessed only with a secret handshake and insider training, as much as some philosophers wish this were so. Instead, some of these skills can be captured by generalisable, all-purpose techniques for the proper conduct of thought, whatever the topic. Many of these are easily taught and learned. As such, they can be utilised by non-philosophers too. At a time when we are bombarded more than ever with specious claims and spurious inferences, clear thinking provides a much-needed safeguard that we should all strive towards. 

Philosophers place a premium on certain tools for regimenting our thinking, especially logic and probability theory. However, there is a far richer toolbox at our disposal. Over the years, I have observed philosophers repeatedly using various argumentative moves or strategies, which can be encapsulated in rules of thumb that make their tasks easier. These are what might be called philosophical heuristics. This should come as no surprise: pretty much every complex activity has its heuristics, which experts teach and beginners learn – photography, calligraphy, diving, driving, football, foosball, judo, Cluedo, curling, hurling, climbing, rhyming, and so on. Such heuristics are especially well-documented for chess: ‘castle early and often’, ‘check every check’, and what have you.

There are also common heuristics for intellectual activities such as mathematics and creative writing. Here’s a good one for mathematics: if you are not making headway on a problem, modify it slightly to make it easier, and solve that one. A good heuristic for creative writing is to juxtapose familiar words and phrases in unfamiliar ways. One might use the ‘cut-up technique’, popularised by William S Burroughs and by David Bowie, in which written text is cut up and rearranged to create a new text.

Yet philosophy might be thought to be especially unsuitable for such heuristics. The word ‘philosopher’ comes from the Ancient Greek philosophos, meaning ‘lover of wisdom’. And wisdom, a skeptic might insist, cannot be so easily achieved. Philosophy strives for deep, profound insights, yet heuristics might by their nature be regarded as superficial. I don’t pretend that philosophical heuristics provide shortcuts to profundity – any more than chess heuristics provide shortcuts to becoming a grandmaster. That said, grandmasters do typically castle early and often, and check every check, consciously or not; a chess textbook that ignored these heuristics would be remiss. Likewise, good philosophers do use the heuristics I identify, consciously or not, often in the service of deep insights. Indeed, philosophy textbooks have been remiss in ignoring these heuristics.

If we think of logic and probability theory as all-purpose tools for checking for the consistency and coherence of our claims at a high level of abstraction, then the philosophical heuristics collectively form more of a Swiss army knife. Some of these heuristics have a broad application, like an LED light. Others have a narrower application, but are perfect for the occasions on which they apply, like a corkscrew. There is something of a trade-off between how frequently a particular heuristic might be used, and how specific its advice is. Too general, and the heuristic doesn’t provide an applicable strategy – for example: ‘Say something insightful!’ Too specific, and it can never be used in another context – for example, ‘the reply to Pascal’s wager (that you should believe in God because doing so is the best bet) is that it leaves open which God you should believe in’. The best heuristics find ‘sweet spots’ in this trade-off.

I work in the Western ‘analytic’ tradition of philosophy. Much of analytic philosophy involves arguing for positions. So some terminology will be needed here. For our purposes, an argument is a number of premises followed by a conclusion, where the premises are intended to lend support to the conclusion. A valid argument is one in which the support is as strong as can be: the truth of the premises guarantees the truth of the conclusion. A sound argument is one that is valid and whose premises are true (and so its conclusion is true, too). An unsound argument is one that is either invalid or that has at least one false premise.

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Let’s begin with a heuristic that is easy to use, but quite fertile. The word ‘the’ is the most common word in English. A locution of the form ‘… the X …’ – what philosophers call a definite description – typically comes with an assumption that there is exactly one X. We might be able to challenge that assumption, in two ways: perhaps there is more than one X; perhaps there are no Xs. So the heuristic here is to see the word ‘the’ in neon lights, as it were – by italicising it, underlining it, or otherwise mentally highlighting it – and to try each challenge.

Here’s an example that is not philosophical, and certainly not profound, but of considerable interest nonetheless. In his Inauguration speech, Donald Trump said: ‘January 20th 2017 will be remembered as the day the people became the rulers of this nation again.’ There are three occurrences of ‘the’ here; let’s focus on the first (the other two have plural nouns – ‘people’, ‘rulers’, but even they have a uniqueness presupposition – a unique set of people, and of rulers). ‘The day’ presupposes that there is exactly one such day. Some champions of the power of democracy will insist that there are many such days – namely, every day on which the people vote. Some skeptics of the power of democracy will deny that there is ever such a day, and that includes 20 January 2017. Either way, the definite description faces a challenge.

Turning to a more philosophical example, we often speak of ‘doing the right thing’. Sometimes, there is exactly one such action. However, there can be different senses of ‘right’– for example, what is rational, and what is moral. And even fixing on one of those senses, there might be more than one candidate for the right thing to do: multiple actions that are equally good. Or there might not be any such candidate. Think of moral dilemmas, such as the unspeakable one depicted in William Styron’s novel Sophie’s Choice (1979), or Jean-Paul Sartre’s one of a student who is torn between avenging the death of his brother in the Second World War, and looking after his mother.

Relatedly, and more generally, when evaluating some claim, mentally highlight each key term, and run through its contrast class, the set of relevant alternatives. It is helpful to stress the term and to intone the words ‘… as opposed to …’, to bring out that class. For example, one hears claims to the effect that ‘the human visual system is poor’. Well, let’s see: ‘the human visual system is poor’. Human, as opposed to what? An eagle’s visual system? Yes, the human visual system compares unfavourably. But what about a bear’s visual system? A bat’s? Now the human’s doesn’t seem so bad. Let’s continue: ‘the human visual system is poor’. Our visual system, as opposed to what? Our olfactory system? Surely not – we are better seers than we are smellers. Our auditory system? Even that doesn’t sound right.

A racial stereotype can all too easily be ‘confirmed’ if one attends exclusively to instances, not counter-instances, of it 

Philosophers use contrastive stress to reveal the logical form of various concepts. For example, causation seems to be a two-place relation: smoking a pack of cigarettes a day causes lung cancer – so far, so good. But consider: smoking a pack of cigarettes a day, as opposed to three or four, causes lung cancer? That doesn’t sound so good. If anything, relative to those alternatives, smoking (only) one pack a day seems to help prevent lung cancer. So it seems that causation is at least a three-place relation: C causes E relative to C’. Similar reasoning suggests that it is even four-place: C rather than C’ causes E rather than E’.

The contrastive-stress heuristic also helps one detect false dichotomies, a favourite strategy among philosophers. It is also a good corrective to certain cognitive biases to which we are prone: 

confirmation bias, the tendency to look for and to recall evidence that confirms, but not that disconfirms, one’s beliefs and hypotheses; and
congruence bias, the tendency to accept a belief or hypothesis without adequately testing alternative hypotheses.

Indeed, one of the most common fallacies is simply a failure to consider contrary cases. For example, a racial stereotype can all too easily be ‘confirmed’ in one’s mind if one attends exclusively to instances of it, as opposed to counter-instances.

Now let’s turn to a heuristic that is useful in various fields. Start with a potentially hard problem: someone makes a claim that is supposed to cover a wide range of cases, and you want to check whether it has any counterexamples. You might be facing a huge search space. Where should you look first? Here’s an easier sub-problem: check extreme cases to see whether any counterexamples lurk there – the first case, or the last, or the biggest, or the smallest, or the smelliest, or any similar superlative (always being aware of the definite descriptions!) Does the claim still hold there? This should drastically reduce your search space, as it now just involves the ‘corners’ or ‘edges’ of the original space.

For example, some philosophers are fond of making grandiose claims, such as: ‘Every event has a cause.’ Well, is that true? At first, you might be overwhelmed by its grandiosity – there are lots of events out there! But start by considering an extreme event – the first event, the Big Bang. There was no prior event to cause it, it did not cause itself, and it was not retro-caused by some later event, so we have our counterexample. To be sure, this assumes that there was exactly one Big Bang, but as far as I know, this is a respectable assumption. Or consider the extreme event that is the entire history of the Universe. There are many instances of causation within this entire history, but arguably it was not caused by anything. Any putative cause is just part of the entire history.

Well, perhaps it did have a cause – namely, God? Hold that thought; we will return to it soon.

Suppose a politician tells you: ‘You should not follow any advice given to you by a politician.’ What should you do with this advice? Follow it? That’s not following the advice, since it was the exact opposite. Not follow it? That’s exactly what the advice was, so you would thereby be following it. Self-referential paradoxes have kept philosophers employed since the ancient Greeks. Georg Cantor, Bertrand Russell and Kurt Gödel shook the foundations of mathematics by exploiting self-reference in various ways. We might set our sights rather lower, but still employ self-reference fruitfully.

For example, philosophers perennially debate realism about various subject matters – ethics, aesthetics, mathematical entities, the meanings of our words, the unobservable entities posited by science, and even ordinary macroscopic objects. A popular definition is that realism about Xs is the thesis that Xs exists independently of observers (for instance, realism about electrons is the thesis that electrons exist independently of observers). But wait – what about realism about observers? Observers do not exist independently of observers. How about: ‘Xs exist independently of minds’? That won’t do either – what about realism about minds? Minds do not exist independently of minds. So the self-referential heuristic here is to give a claim a taste of its own medicine.

Somewhat related is the time-honoured philosopher’s technique of showing that a view (or an argument) faces an infinite regress – its truth (or validity) depends on the truth of some proposition, whose truth in turn depends on the truth of some other proposition, whose truth depends on… The sequence of dependencies has no end.

Think again of the claim that every event has a cause. Focus on some event. According to the claim, it has a cause, which had a cause, which had a cause, which…, ad infinitum. This is at least puzzling, and perhaps worse. Another classic example is the regress of justification. In order to have justified belief in something, one must have justified belief in something else; but that requires having justified belief in something else; and this chain of justifications never terminates. (There are various replies – for example, that the chain does terminate in some foundational belief.)

An infinite regress is not necessarily absurd – some regresses are said to be ‘virtuous’ rather than ‘vicious’. But some positions lead to the ultimate absurdity: contradiction. These positions must be contradictory themselves, and therefore false. Here’s another good heuristic in mathematics: if you are not sure how to prove some claim, perhaps because it seems so obvious, try reductio ad absurdum reasoning. That is, suppose that the claim is false, and show that this leads to a contradiction. This provides a proof of the claim, one in which the claim is established conclusively by that reasoning.

Philosophers often employ reductio ad absurdum reasoning too. They also employ a related, but less conclusive, technique in order to show that an argument is unsound: ‘proves too much’. (‘Proves’ is tongue-in-cheek.) Start with some argument A that you think is unsound, but you cannot pinpoint exactly what is wrong with it – that’s a hard problem. Parody it with another argument, P, that has the same structure as A, but whose conclusion is obviously false; thus P is obviously unsound. Then argue that since A resembles P in important respects, it too must be unsound. This is not a proof, but rather an instance of analogical reasoning. The reasoning goes that, by parity of reasoning, A must have the same status as P; and by parody of reasoning – a turn of phrase, albeit used slightly differently, that I owe to Daniel Dennett’s Intuition Pumps and Other Tools for Thinking (2013) – that status is an unhappy one.

This strategy also resembles the mathematics heuristic that I mentioned earlier, of modifying a hard problem to make it easier. Here, we modify A to P and, in doing so, modify the hard problem of seeing that A is unsound to the easier problem of seeing that P is unsound, which it obviously is. However, unlike the mathematics heuristic, the ‘proves too much’ strategy typically does not involve going back to the original argument A, and diagnosing exactly what was wrong with it. It is tarred with P’s brush, and that’s supposed to be that. It’s rather like solving the easier mathematics problem, and resting content. To that extent, the strategy can be unsatisfying.

From Plato’s cave to Singer’s ‘drowning child’, analogical reasoning pervades philosophical thinking

Perhaps the most famous instance of the ‘proves too much’ technique is the 11th-century Benedictine monk Gaunilo’s parody of St Anselm’s ontological argument for the existence of God. According to the concept of God, a greater being cannot be conceived. Now, suppose that God does not exist. Then a greater being could be conceived – namely, one with God’s greatness and who does exist. But this is a contradiction: a greater being than God is both inconceivable and conceivable. So we must reject the supposition – that is, we must conclude that God exists. There’s an instance of reductio ad absurdum reasoning for you. Gaunilo then parodies it: consider the concept of the perfect island. A greater island cannot be conceived. Now, suppose that this island does not exist. Then a greater island could be conceived – namely, one with the island’s greatness and that exists. Contradiction. So the island exists. But this is absurd. So we should reject the ontological argument, which employs parallel reasoning – it ‘proves too much’.

‘Proves too much’ reasoning is a form of analogical reasoning. Now let’s generalise – itself an exercise in such reasoning. Roughly, such reasoning begins by citing similarities between some entity and another one; moreover, the latter entity has a further feature; one concludes that the former entity also has that feature. Schematically:

Entity X has properties F, G, H, …
Entity Y also has properties F, G, H, and also I.
Therefore, (plausibly) entity X also has property I.

The entities might be physical objects, such as planets, or even abstract objects, such as arguments. The properties can be similarly diverse: for example, having water and supporting life, or being unsound. The ‘therefore’ should be understood to flag an inductive inference, one in which the premises are thought to lend support to the conclusion, without guaranteeing it (hence the ‘plausibly’). In a nutshell: likeness in certain respects supports likeness in further respects.

Analogical reasoning has played an important role in the history of philosophy. Indeed, in Philosophical Essays Concerning Human Understanding (1748), David Hume said (perhaps overreaching): ‘All our reasonings concerning matters of fact are founded on a species of analogy.’ From Plato’s allegory of the cave in the Republic to Peter Singer’s ‘drowning child’ argument, analogical reasoning pervades philosophical thinking. But the most famous analogical argument of them all is a classic argument for the existence of God.

Philosophers speak of the argument from design but, attentive reader that you are, you are questioning the presupposition that there is exactly one. And indeed, there are many such arguments. I will present one, without claiming that it is the best version, but it does showcase the various heuristics that I have presented.

Look at a watch. You see that it is intricate, aesthetically pleasing, and behaves in a regular way. You also know that it had an intelligent designer. Now look at the world. You see that it is intricate, aesthetically pleasing, and behaves in a regular way. By analogical reasoning, you should conclude that (plausibly) it too had an intelligent designer – namely, God. Or so the argument goes. Its spirit is captured by the old hymn that begins:

All things bright and beautiful,
All creatures great and small,
All things wise and wonderful,
The Lord God made them all…

However, both the argument and the hymn are easily parodied. Look again at the watch. Despite its agreeable properties, it also has flaws – it keeps time imperfectly, its batteries occasionally need replacing, it is easily scratched. So you should conclude that it had a flawed designer. Now look again at the world. It too has its flaws. Monty Python began cataloguing them:

All things dull and ugly,
All creatures short and squat,
All things rude and nasty,
The Lord God made the lot …

You should conclude that the world too had a flawed designer, which is not how God is normally conceived. Hang on! The argument from design is in danger of ‘proving too much’.

In Dialogues Concerning Natural Religion (1779), Hume powerfully parodied a version of the argument from design. He also questioned the alleged similarity between human artefacts, of which we have experience, and the Universe; and we have no experience of other universes. Indeed, the Universe might be regarded as an extreme case of an entity, and as such quite unlike entities such as watches – we can question whether it could even enter into causal relations, like being created, at all. Finally, Hume contended that the argument of design involves an infinite regress: the intelligent designer, God, whose existence the argument purports to support, himself demands explanation, requiring a prior intelligent designer. And away we go.

One of the main arguments against the existence of God is the problem of evil. (Neon lights!) Consider this version of it:

1. If God existed, he would have created the best of all possible worlds.
2. Our world is not the best of all possible worlds.

Therefore,

 Conclusion: God does not exist.

Here, ‘worlds’ are entire universes, and ‘possible worlds’ are ways that a universe could be – we might think of them as instances of what is sometimes called the ‘multiverse’.

Premise 1 is meant to be plausible on many of the leading conceptions of God – in particular, ones that portray him as being omnibenevolent, omnipotent and omniscient. (All three qualities are necessary for the premise to be plausible – to see why, mentally highlight each of them, and run through the alternatives to which they are opposed.) The premise invites us to imagine various possible worlds, and to imagine God choosing which of these worlds to create. Premise 2 then compares our world to some of these alternatives. It seems we should grant it, since we can easily imagine our world being better – more happy people, less suffering. (One is reminded of the old joke: an optimist thinks that this is the best of all possible worlds; a pessimist fears that this is true.)

If God existed, he would have created something. Yet perhaps God exists, but didn’t create anything?

There are some problems with this argument that our heuristics help to tease out. With the first premise, I hope you saw ‘the’ in neon lights. Is there exactly one best of all possible worlds? It seems that there could be many. For example, start with a candidate for the best world, and imagine tweaking it in a way that makes no difference to its goodness – say, moving one insignificant particle by a nanometer, or mirror-reversing everything. Offhand, the result is equally a candidate for the best world. However, the argument in turn could be tweaked accordingly. Just make this premise ‘… he would have created a best possible world’ – one of the candidates. And the similarly tweaked premise 2 looks equally secure: this is not (even) a best possible world.

But there seems to be more of a problem on the other side: perhaps there is no best of all possible worlds. Rather, worlds can keep getting better and better without end – perhaps just keep adding another happy person, or another happy cow. Never mind the details of how God could create these better worlds. Any limitation on his ability to do so would seem to impugn his omnipotence.

The form of premise 1 is that if God existed, he would have created something. But a relevant alternative is that he might not have created anything. Perhaps God exists, but did not create anything?

Yet one might insist that he must have, perhaps regarding that as a part of the meaning of ‘God’. This brings us to the second premise. Again, note the contrast: our world, as opposed to other worlds. This prompts a different response: God did not create our world, but he created the best of all possible worlds (instead). This suggests that the argument is invalid: we can imagine premises 1 and 2 being true, without being committed to the conclusion. Or imagine that God did create the best of all possible worlds; and the second best; and the third best… Eventually, we get to our world, which is way down the list, but he created it nonetheless – perhaps because there is still a net balance of good over evil. Again, this suggests that the argument is invalid – only ‘suggests’, mind; perhaps it is impossible for one God to create multiple worlds, for reasons given by David Lewis in On the Plurality of Worlds (1986). It presupposes that God faces a world limit.

Where does this leave us? Well, we did not manage to prove the existence of God, nor prove his non-existence. (I hope you are not too disappointed!) But that’s par for the course in philosophy – it rarely proves anything conclusively. Instead, I hope I have given you some sense of what philosophical reasoning is like, and how that reasoning can be stimulated and enhanced by the use of various heuristics. Along the way, we saw some instances of what followed from what (or not), exposed some sophisms, spotted some fallacies, and policed some of our reasoning.

To be sure, the heuristics have their limits. There are many distinct abilities that go into making a good philosopher, and I do not pretend to give heuristics for all that philosophers do, or even a tenth of what they do. In particular, there are no short-cuts to profundity, and I should add that there will always be a role for good judgment and insight – just as there is in mathematics and chess. That said, heuristics can make difficult reasoning tasks easier, as much in philosophy as in mathematics and chess.

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