Note: I share this because this paper seems like a useful collection of somewhat general heuristics for making theoretical progress, especially in philosophy by ANU philosophy professor Alan Hajek . I expect this to be most useful for people who are very early on in their research careers, but perhaps it’s also a good reminder for more experienced researchers. To me, it felt like I knew many of the heuristics but still often fail to apply them. I encourage anyone to read the parts of the paper where Hajek discusses the application of these heuristics and gives examples of how to use them. (I would nevertheless skip large parts of the paper such as the first two sections). I also encourage everyone to share when and to what extent they find these heuristics useful and perhaps suggest additional ones that they have found helpful.
Some excerpts (in order of how interesting they seem to me, not how they appear in the paper; highlighting added by me)
’Future projects: dissertations and books waiting to be written
When you are looking for a big project to work on, take some big philosophical idea or program, and apply it to a new case. The scheme is to apply philosophical system X to specific problem Y, for suitable X and Y. This is the closest I can come to producing a heuristic for producing ground-breaking philosophy. Here the thought is that rather than merely responding to someone else’s agenda, you can do some agenda-setting of your own. And if ground-breaking philosophy when it succeeds doesn’t count as creative, I don’t know what does. However, even if the results are not quite so dramatic, still the heuristic encourages one to look beyond entrenched ways of thinking about an issue. System X is illuminated if a hitherto unrecognized application of it is revealed; progress may be made on recalcitrant problem Y if it is approached from a fresh perspective.
[...] Closest to my heart, Bayesian confirmation theory has illuminated the confirmation of scientific theories. (See Howson and Urbach 2006.) I believe it has yet to be applied to the confirmation of historical theories.′
’Begetting new arguments out of old
Arguments are often easily transformed from one domain to another. Arguments involving space can often be rewritten to create parallel arguments involving time; arguments involving time can often be rewritten to create parallel arguments involving modality; and we can reverse these directions. [...] 7.1.1 Parfit (1984) has an argument for the irrationality of discounting the future that turns on the absurdity of a similar spatial discounting.′
’Death by diagonalization: reflexivity/self-reference
You can’t bite your own teeth, unless something has gone badly wrong for you, dentally speaking. You can’t see your own eyes—not directly, anyway—unless something has gone very badly wrong for you, optically speaking. The next heuristic bids us to take a philosophical thesis, and to make it refer to itself, to plug into a function itself as its own argument, and more generally, to appeal to self-referential cases. This technique is another handy way of cutting down the search space when you are looking for counterexamples. Let us take our cue from Cantor’s ‘diagonalization’ proof of the uncountability of the reals, or Gödel’s proof of the incompleteness of arithmetic, or the halting problem, or Russell’s paradox, or the liar paradox. They remind us of the august history of the technique of selfreference; its application can yield profound results.
[...] According to the betting interpretation of subjective probability, your degree of belief in a proposition is the price (in cents) at which you are indifferent between buying and selling a bet that pays $1 if the proposition is true, and nothing otherwise. But I have degrees of belief about my own betting behavior—e.g. I am confident that I will not enter into any bets today. This degree of belief cannot be understood in terms of a betting price of mine.′
’Check extreme cases
Start with a hard problem: someone proposes a philosophical position or analysis and you are looking for trouble for it, because you suspect that there is something wrong with it. (The ‘someone’ might be you, in which case your job is to find trouble for your own position before someone else generously does it for you.) Try this simpler problem: look for trouble among extreme cases—the first, or the last, or the biggest, or the smallest, or the best, or the worst, or the smelliest, or … It is a snappy way to reduce the search space. Even if there are no counterexamples lurking at the extreme cases, still they may be informative or suggestive. They may give you insights that you would have missed by focusing on more run-of-the-mill, typical cases.
[...] Some philosophers regard ‘every event has a cause’ to be a necessary truth. At first, one may wonder how to argue against this claim—where should one start? The heuristic guides the search for a counterexample: start with extreme events. For instance, start with the start. The first event is an extreme event: the big bang. There was no prior event to cause it; it surely did not cause itself; and it surely was not retro-caused by some later event—so we have our counterexample.′
Heuristics for making theoretical progress (in philosophy) from Alan Hajek (ANU)
Link post
Note: I share this because this paper seems like a useful collection of somewhat general heuristics for making theoretical progress, especially in philosophy by ANU philosophy professor Alan Hajek . I expect this to be most useful for people who are very early on in their research careers, but perhaps it’s also a good reminder for more experienced researchers. To me, it felt like I knew many of the heuristics but still often fail to apply them. I encourage anyone to read the parts of the paper where Hajek discusses the application of these heuristics and gives examples of how to use them. (I would nevertheless skip large parts of the paper such as the first two sections). I also encourage everyone to share when and to what extent they find these heuristics useful and perhaps suggest additional ones that they have found helpful.
Some excerpts (in order of how interesting they seem to me, not how they appear in the paper; highlighting added by me)
’Future projects: dissertations and books waiting to be written
When you are looking for a big project to work on, take some big philosophical idea or program, and apply it to a new case. The scheme is to apply philosophical system X to specific problem Y, for suitable X and Y. This is the closest I can come to producing a heuristic for producing ground-breaking philosophy. Here the thought is that rather than merely responding to someone else’s agenda, you can do some agenda-setting of your own. And if ground-breaking philosophy when it succeeds doesn’t count as creative, I don’t know what does. However, even if the results are not quite so dramatic, still the heuristic encourages one to look beyond entrenched ways of thinking about an issue. System X is illuminated if a hitherto unrecognized application of it is revealed; progress may be made on recalcitrant problem Y if it is approached from a fresh perspective.
[...] Closest to my heart, Bayesian confirmation theory has illuminated the confirmation of scientific theories. (See Howson and Urbach 2006.) I believe it has yet to be applied to the confirmation of historical theories.′
’Begetting new arguments out of old
Arguments are often easily transformed from one domain to another. Arguments involving space can often be rewritten to create parallel arguments involving time; arguments involving time can often be rewritten to create parallel arguments involving modality; and we can reverse these directions. [...]
7.1.1 Parfit (1984) has an argument for the irrationality of discounting the future that turns on the absurdity of a similar spatial discounting.′
’Death by diagonalization: reflexivity/self-reference
You can’t bite your own teeth, unless something has gone badly wrong for you, dentally speaking. You can’t see your own eyes—not directly, anyway—unless something has gone very badly wrong for you, optically speaking. The next heuristic bids us to take a philosophical thesis, and to make it refer to itself, to plug into a function itself as its own argument, and more generally, to appeal to self-referential cases. This technique is another handy way of cutting down the search space when you are looking for counterexamples. Let us take our cue from Cantor’s ‘diagonalization’ proof of the uncountability of the reals, or Gödel’s proof of the incompleteness of arithmetic, or the halting problem, or Russell’s paradox, or the liar paradox. They remind us of the august history of the technique of selfreference; its application can yield profound results.
[...] According to the betting interpretation of subjective probability, your degree of belief in a proposition is the price (in cents) at which you are indifferent between buying and selling a bet that pays $1 if the proposition is true, and nothing otherwise. But I have degrees of belief about my own betting behavior—e.g. I am confident that I will not enter into any bets today. This degree of belief cannot be understood in terms of a betting price of mine.′
’Check extreme cases
Start with a hard problem: someone proposes a philosophical position or analysis and you are looking for trouble for it, because you suspect that there is something wrong with it. (The ‘someone’ might be you, in which case your job is to find trouble for your own position before someone else generously does it for you.) Try this simpler problem: look for trouble among extreme cases—the first, or the last, or the biggest, or the smallest, or the best, or the worst, or the smelliest, or … It is a snappy way to reduce the search space. Even if there are no counterexamples lurking at the extreme cases, still they may be informative or suggestive. They may give you insights that you would have missed by focusing on more run-of-the-mill, typical cases.
[...] Some philosophers regard ‘every event has a cause’ to be a necessary truth. At first, one may wonder how to argue against this claim—where should one start? The heuristic guides the search for a counterexample: start with extreme events. For instance, start with the start. The first event is an extreme event: the big bang. There was no prior event to cause it; it surely did not cause itself; and it surely was not retro-caused by some later event—so we have our counterexample.′