Chris Deleon has advanced the thesis that there is a difference between games and videogames. This difference consists in two points: first, that whereas games are artificial, videogames are not, and second, that whereas games have rules, videogames don’t. I want to discuss this idea.

He begins considering a simple game:

If I place tape on the ground, for example in the form of an intricate maze and declare that it’s a rule to not step over the tape, we are engaging in rule-based behavior. If I put something you want in a basket at one corner of the maze – perhaps a DVD – and move you to the other corner, then say you have 45 seconds to get the DVD without crossing over or moving the tape, we have constructed a game.

There’s a set of possibilities, the realization of which would ammount to stepping over the bounds imposed by the rules. Now, since the game is implemented in the real world, there is always a chance that those possibilities get realized. We could simply cross over the tape in order to get the DVD, or taking it after the 45 seconds have passed. The boundaries the rules impose don’t reach the material world; they are unlike physical laws, which can’t fail to hold. The term Deleon uses to describe this is “artificial”.

Let’s imagine those rules were implemented in a videogame. There is a layer over which lines are drawn, sketching a maze. The player can’t step over the lines; his camera movement simply stops when his position collides with the lines. Away from the player’s starting position, there is an object he must reach in order to obtain points, and there is a time limit for this. If the player doesn’t reach the object in time, he loses, and is asked if he wants to try again.

In this videogame, the player has no choice but to follow the rules of the game. He can’t step over the lines, and can’t do anything but decide to try again after the time limit passes. As a consecuence, the “rules” are much more like physical laws. Deleon doesn’t state it this same way, but we can say that that the player can’t step over the lines and that the player can’t keep playing after a certain time are the “natural” laws (as opposed to “artificial” rules) of this videogame world. To this point, I agree with him.

Deleon says:

A videogame is not a definition of rules, which are then enforced by the software-as-referee. A videogame is a definition of a simplified alternative reality, where what often get mislabeled as “rules” are not rules at all, but rather ways of referring to the constraints and possibilities of that artificial universe. The word “rule,” in such usage, is being used as a metaphor, and although it’s common to use the word in connection to videogames, I believe it’s a source of needless confusion to do so.

I think it is here that Deleon gets misguided. The videogame world is a model of the game played in the real world by following those rules; as Deleon says, a simplified alternative reality (in fact, his is a much better general description of a videogame world, since such a world doesn’t need to have a real-world analogue). The things Deleon has to say about the videogame worlds seem right to me, but I don’t think we can identify the videogame world with the game the videogame is (that is, I object him saying that “a videogame is a definition of a simplified alternative reality”). The player of the videogame isn’t the player in the game, however immersive the game is.

A videogame world is an artificial object. Its boundaries are designed by a person existing in a world which contains its implementation (so far, all designers have belonged to the real world, but one can imagine a simulated designer, and simulated games, in a virtual world). It seems to me that the implementation of the videogame world, which is in concrete played by someone, is the game proper. Most of such implementations exist over a certain platform; Super Mario Bros, for example, existed on the platform of the NES, and many others. The platform is what I will call a toy. A toy makes possible for the player to play in the real world in certain ways; for example, the NES controller makes it possible to jump precisely in the world of SMB. For a child, most objects can be treated as toys; I used to play with leaves (the entire world can be considered as a platform in an extended sense). The main thing to notice about this is that there are rules for playing a game with a toy, and this is always artificial, even in the sense Deleon proposes for the term. A game defines a further set of restrictions to the behaviour of the player through a set of rules, so from this standpoint, it is a set of rules.

A different example: you can have a ball, which allows you to play in many different ways; each way being a game, being a set of rules. Soccer is a game you can play with a ball, as is basketball. A NES allows you to play in many different ways; each being a game, being a set of rules.

When are two thought experiments the same? Is it necessary that they lead to the same result? Is it necessary that they embed the same hypothetical situation? In this paper, my aim is to discuss a series of issues about the question of the identity conditions of thought experiments. I will first consider an argument by Michael Bishop (1999), who has proposed that the identity conditions implied by the so called “argument view” are false, and thus that thought experiments are not arguments. He uses as example the case of the “clock-in-a-box”, and says in it there is one thought experiment but two arguments. I find this account of this case unsatisfactory. In order to show what I think is wrong with Bishop’s account, I’ll sketch a way how the identity conditions for thought experiments should be given, and a proposal of such conditions. Briefly, I’ll argue that we can say that two discourses express the same thought experiment if they serve the same epistemic role against a question (proposing the same sort of epistemic device).

Why Bishop thinks the argument-view is false

The argument-view for thought experiments, as defended by John Norton (1991), states that thought experiments are simply arguments which:

1. posit counterfactual or hypothetical states of affairs, and
2. invoke particulars irrelevant to the generality of the conclusion.

Bishop calls this sort of argument a t-argument.¹ The argument view itself has strong and weak versions. In the strong version, thought experiments simply are arguments, and can always be replaced by them. In the weak version, to perform a thought experiment involves the performance of an argument (i.e., to mentally follow the premises towards the conclusion). Bishop is against the strong version of the argument-view. He himself leans towards a mental-model theory account of thought-experiments (see Bishop 1998, p. 20.), such as Nersessian’s (1993), which allows for the truth of the weak version, since to perform an argument could be some sort of mental modeling; this is beyond the scope of this work, though.

According to Bishop, the argument-view has the consequence that:

3. Two tokens of a thought experiment are tokens of the same thought experiment type if they are tokens of the same t-argument type.

This means that, given that the same argument will lead to the same conclusion on every instance, no thought experiment can lead to different results in different instances. But this, Bishop argues, is shown to be false by actual cases where a single thought experiment can lead to different conclusions (by reflection on the hypothetical setup), such as the case of the “clock-in-a-box”, which he examines.

The case, as described by Bishop, is as follows. During the 1930 Solvay Conference, Einstein proposed a thought experiment aiming to be a counterexample of Heisenberg’s uncertainty principle. It consisted in the following scenario: there’s a box full of photons with a clock-controlled shutter in one of its walls. Its weight has been measured as w. Now, the shutter opens for a brief interval so a single photon escapes. The box is measured again, which gives us the photon weight, and thus its mass, which in turn allows for the determination of the photon’s energy using the E=mc₂ equation. In this scenario both energy and time can be measured with an arbitrary degree of accuracy, so Einstein concluded this showed that the uncertainty principle is false (since according to it, this shouldn’t be possible). In response, Niels Bohr proposed an argument that showed that in a scenario like that, there is actually a limit to the accuracy to which the time and energy variables can be measured. Bishop says that this argument convinced Einstein that the clock-in-a-box thought experiment failed to give support to his conclusion that the uncertainty principle is false. This couldn’t have happened, he thinks, unless the thought experiments proposed by Einstein and Bohr were the same: if Bohr’s were distinct to Einstein’s, the latter could have said that Bohr was changing the subject, and dismissed the objection. On the other hand, since the results of both instances are different, it can’t be said that they present the same t-argument without misrepresenting what happened. As a result of this, the clock-in-a-box case can be regarded as a counterexample to c): the tokens involved are instances of different t-arguments, but of the same thought experiment. Thus, Bishop says, thought experiments are not t-arguments.

On misidentifying something as a thought experiment

It might be the true that thought experiments are not arguments, but this is not my concern here. I don’t believe Bishop’s argument is sound. In this section, I want to examine the possibility that Bishop’s account of the clock-in-a-box case is wrong because of some sort of misidentification of the tokens involved in it. In the next section, I’ll propose that Bishop is wrong in assuming that Einstein shouldn’t have accepted his conclusion was mistaken unless Bohr’s thought experiment were the same as his, and will try to give a better account of the identity conditions for thought experiments.

When I talk of a problem of misidentification, I mean a case where a thing is identified as belonging to a class it doesn’t belong to (for example, to mistake a foe for a friend, or an absurdity for something coherent). In the clock-in-a-box case, a problem of this sort could arise in at least two ways: on the one hand, it is possible that Bishop identified (some of) the tokens of the clock-in-a-box case as thought experiments when they really weren’t, and on the other, it is possible that there were more tokens than those two identified. It could also happen for these sorts of misidentification to occur simultaneously, but it is unlikely that it is so in this case, due to the small number of the putative tokens involved.

If some of the tokens involved in a discussed case aren’t thought experiments, the problem of their identity as the same thought experiment is meaningless, of course. Is it meaningless in the case described by Bishop? It doesn’t seem to be. Excepting the difference in the degree of sophistication of the tokens, there doesn’t seem to exist much reason to say one of the tokens is of a different kind, even less not a thought experiment (both propose a hypothetical scenario and arrive at a conclusion, which can at least help identify the tokens as thought experiments). But maybe it is reason enough? It could be that no token should be regarded as a proper thought experiment in physics unless it applies a fully considered theory (if that were the case, Einstein’s token, if failed to account for the relativity effects involved in the scenario, as Bishop proposes, could be dismissed as a proper thought experiment).

On the other hand, if there were more than two tokens involved in the case, it would be possible that any identity relation between them (if existent) would work in manner different from the one Bishop presumes. Let’s assume the scenario presented by the tokens is the same, and that it is in itself a thought experiment (the condition of there being a conclusion for the thought experiment should be dropped). Then it could be said that the tokens we started with are type-identical (as thought experiments) to the scenario and by transitivity to each other, but not type-identical (as the specific thought experiments they are). Even though this possibility is distinct from Bishop’s account (since Bishop assumes for the sake of his argument that thought experiments should be considered as arguments, identity as the same argument should be presumably regarded as equivalent to identity as the same thought experiment; so when he says that Einstein’s and Bohr’s thought experiments are identical, he means identical both as arguments and as the thought experiments they are), it is not contrary to its conclusion.

Now, the identification of a token as a thought experiment depends on what thought experiments are supposed to be, but is in a sense a prior matter. No theory can be developed without there being at least a primitive way of identifying its objects, that is, its subject matter. Which are the means by which thought experiments are identified? Do these means track the essential features of thought experiments in a robust way? Thought experiments present several complications to these problems. First, the use of the term “thought experiment” has certainly varied over time (thought experimentation, as a sort of activity, can be supposed to have been stable over time, however); what Mach understood as Gedankenexperimenten seems to be quite different to the way things like Jackson’s Mary “thought experiment” is now understood. There doesn’t seem to exist a single historic line of development and use of the term. This results in a synchronic divergence in the use of the term. One way of making sense of this is to say that the term expresses a cluster concept covering several identification conditions from different disciplines (so a thought experiment in physics doesn’t need to be identified as such using the same means as a thought experiment in philosophy, for example). However, this is not enough since there is also divergence inside disciplines (in philosophy this is further complicated by the practice of interpreting historical texts as thought experiments), and also because there seem to be valid cross-disciplines identifying marks (like the appeal to the hypothetical).

The fact that the term “thought experiment” belongs to a certain technical jargon introduces another problem. The learning of its use can be supposed to be dependent upon the theoretical commitments of the speaker teaching it (the teacher is somehow involved with the development of the ideas about what thought experiments are, and this seems to me characteristic of all terms in a technical jargon); as a consequence of this, it can be supposed that the identification criteria learnt by the user are based on those commitments too.² Since the debate about what is the nature of thought experiments isn’t yet settled, it can be assumed that the term usage is homogeneous.

These difficulties make the problem of misidentification less pressing. Even though it remains a possibility, a critique oriented in this sense should be backed up by an account of thought experiments alternative to the one endorsed by its target. Since this is not my aim here, I will move to a different angle of the problem of the identity conditions.

To be the same thought experiment as…

When are two thought experiments the same? If this question is to be meaningful at all, there should arise situations where it isn’t trivial to give an answer to it. If two tokens are identified as thought experiments, and are alike in every respect, there is simply no doubt about them being the same thought experiment, and if they diverge too much, there is no doubt they are not. The question can only arise when the tokens diverge in some restricted ways. There are mainly two aspects thought experiments can diverge in: the hypothetical situation they propose and the results they arrive at. The question of when two tokens are the same thought experiment involves, then, to specify which of those aspects of a thought experiment must remain stable so a variation of it could still be considered the same thought experiment, and previously, to specify the conditions under which it can be said that a token is a variation of a certain thought experiment.

What, then, counts as a variation of a thought experiment? What must vary? A supporter of the argument view would say that a variation of a thought experiment must vary only regarding the particulars mentioned in it. It seems plausible, on the other hand, that someone who thinks that what is essential to a though experiment is the “feel” of it (its qualitative aspects) would try to preserve the references to individuals. I think that these sorts of distinctions are not so important regarding the stated questions. There must be a way of saying that a token is a variation of a thought experiment which is independent to whatever thought experiments ultimately or supposedly are. It is possible to see this clearly considering cases like the following: A variation of Jackson’s thought experiment where the character is a boy named John instead of a woman named Mary can’t be counted as a counterexample to a non-argumental account of thought experiments (or it being a variation of it as decisive evidence in favor of the argument view), but only to the restriction that the references to particulars should remain stable over variations on a thought experiment. Even so, the satisfaction of the condition under which a token can be counted as a variation of a thought experiment can serve as a desideratum for an account of thought experimentation: if because of such account it weren’t possible to say that a token which clearly seems to be a variation of a thought experiment is a variation of that thought experiment, then the account should be counted as incorrect.

The problem posed is best understood from the angle of the expressions used to present thought experiments, since it is very easy to see how they can vary. I think that most of the time, when we refer to a variation of a thought experiment we refer to a way of presenting a thought experiment.³ A thought experiment in this sense is a description of a situation mentioning a number of particulars and their properties and relations, given in a context where a theoretical framework is assumed and a conclusion can be drawn. The plausibility of the description depends on the framework, so a change in it will mean a variation in the meaning of the expression. Given a change in the framework, it is possible that a change in the conclusion occurs. We can describe a thought experiment as a 5-tuple of sets of the form 〈objects, properties, relations, framework, conclusion〉, where any of its member can vary somehow. However, as mentioned before, the variations can’t be as extensive as to turn the thought experiment in a different one if we are to say that we are in front of a variation of a thought experiment. A non-restrictive condition for a variation of a thought experiment can then be given as:

4. A thought experiment A:〈O_A,P_A,R_A,F_A,C_A〉 is a variation of a thought experiment B:〈O_B,P_B,R_B,F_B,C_B〉 if at least one member of any set in 〈O_A,P_A,R_A,-F_A,C_A〉 is the same as those in the corresponding members of B.

Since this can lead to saying that two quite different tokens are variations of each other, this must be restricted somehow. However, if d isn’t satisfied, I don’t think it is possible to say two tokens are variations of each other as thought experiments. My proposal regarding to this will be to add to d something like:

5. A and B can occur in the same discourse.

The point of this condition is that we must screen off cases where no one would plausibly relate the tokens. If two tokens of the form 〈O,P,R,F,C〉 appear in the same discourse (for “discourse” I mean any structured context of communication, like a paragraph in a paper or a dialogue), it is very likely that they are semantic and pragmatically related. In the same discourse we can find a thought experiment arriving to a conclusion C and a different conclusion implying ¬C, and also different thought experiments arriving at the same conclusion, even by different means. The condition is stated vaguely because it is very hard to give a precise definition of discourse if it is to encompass the kinds of communication media I’ve mentioned. We could however say that a discourse in the sense developed here has to have a unitary aim, like, for example, to answer a question or advance a thesis.

We can now give a set of conditions for the (type-)identity of two thought experiments. A thought experiment has a role within the context of a discourse; we could say that the aim of a discourse is only achieved if the parts of the discourse also satisfy their functions. Formally, the role of a thought experiment is satisfied if it is possible to understand that C on the basis of 〈O,P,R,F〉 (this doesn’t necessarily means, I hope, that C is some sort of logical consequence of 〈O,P,R,F〉, which would concede too much to the argument view); intuitively, a thought experiment succeeds if it arrives at a conclusion which helps with a problem (it can be itself the solution to a question, or be of help in order to understand a phenomenon).⁴ Within the context of a discourse, any substitution between variations of a thought experiment must keep C constant if the identity relation is to hold. From this it can be derived that

6. two thought experiments are identical if i) they are variations of each other, and ii) they can be substituted between each other in the context of a discourse without changing the satisfaction of the aim of the discourse.

This identity condition can easily accommodate cases where the thought experiment variation makes reference to different individuals with the same relevant properties (relevant because C wouldn’t be true if the particulars didn’t have them in the context of 〈O,P,R,F〉), and also cases where the relation between the objects in the thought experiment was distinct but structurally similar.

Returning to the clock-in-a-box case, it turns out that the identity condition proposed implies that Einstein and Bohr thought experiments are not the same thought experiment. Neither Einstein nor Bohr could have substituted the other’s thought experiment for his own if they intended to make the same point regarding the uncertainty principle (which was the aim of their respective discourses), even though they are variations of each other (Bohr’s thought experiment slightly varies the framework, the relations between the objects in the scenario, and arrives at a different conclusion; this latter point being the main reason the thought experiments can’t be regarded as the same).

Bishop, against this result, has proposed that these thought experiments can’t be different, because if they were, Einstein could have dismissed Bohr’s on the charges of changing the subject. The fault with this argument is that it fails to account for the various ways that variations on a thought experiment can be related to each other. Because they are semantic and pragmatically related (by definition), the chance that the proposal of a counter-thought experiment could count as changing the subject is slim; Einstein’s and Bohr’s aims are different, but logically related in that they are opposed.

Besides this, Bohr’s thought experiment gives reasons to think that the original thought experiment isn’t valid in a proper setup (that is, that under realistic conditions, its conclusion isn’t valid). This evidence is enough to abandon the original thought experiment with its conclusion. Whether it is or not the same thought experiment as Einstein’s (and I think I’ve shown it couldn’t be the same) is of no importance for its evaluation. What Bohr showed wasn’t that Einstein’s thought experiment didn’t have the result Einstein thought it had, as Bishop says, but that Einstein was mistaken to believe the scenario he proposed would support his conclusion: his thought experiment design was failed. Variations on a thought experiment don’t need to be identical for them to count as evidence in favour or against a thesis, and proposing the same sort of scenario is not sufficient for them to be the same thought experiment either.

Bibliography

• Bishop, Michael (1998), “An epistemological role for thought experiments”, in Idealization IX: idealization in contemporary physics (Shanks, N., ed.), pp. 19-33, Poznaǹ: Rodopi.
• Bishop, Michael (1999), “Why thought experiments are not arguments”, Philosophy of Science, 66, pp. 534-541.
• Bohr, Niels (1949), “Discussion with Einstein on Epistemological Problems in Atomic Physics”, in Albert Einstein: Philosopher-Scientist (Schilpp, P., ed.), pp. 199-242, Evanston, IL: The Library of Living Philosophers.
• Nersessian, Nancy (1993), “Thought experimenting as mental modelling”, in PSA 1992 (Hull & Forbes, eds.), vol. 2, East Lansing, MI: Philosophy of Science Association.
• Norton, John (1991), “Thought experiments in Einstein’s work”, in Thought Experiments in Science and Philosophy (Horowitz & Massey, eds.), pp. 129- 148, Maryland: Rowman and Littlefield.

1. Bishop says that (at least some of) the t-argument premises and its conclusion are supposed to be about the world. It seems to me that thought experiments can teach us how the world can be in a very wide sense, beyond the way the actual world is, so I’d like to read the clause in a sense compatible with this: it seems to me trivial to say that thought experiments are not t-arguments if it is essential for such an argument to have this essential relation to the actual world. It might be, though, that anything about a merely possible world is also about the actual world (though it will most likely be about something different from whatever it is about regarding the possible world). ↩

2. I hypothesise that the persons learning the use of the term can be quite open to regarding a token presented by the instructor as a thought experiment if the instructor says it is. This introduces a lot of complications. ↩

3. A brief observation on the question of what a thought experiment is: It is possible to distinguish between different contexts of thought experimentation, where the term thought experiment refers to different sorts of thing. First, there is the design context, where the thought experiment is devised as something to do and communicate; there, there is the communication context, where a thought experiment is a linguistic expression, and finally, there’s the performance context, where the thought experiment is mentally “carried on”. The question of what a thought experiment is, however, as usually attacked, seems not to acknowledge this distinction. If the distinction is made, it doesn’t make sense anymore to think of thought experiments as only mental processes (like Bishop seems to do). The distinction itself provides reason to think of thought experiments as abstract objects, since that seems to be the only reasonable way they could switch between the contexts (it should be said that they properly are the designed, comunicated and performed contents). ↩

4. The same thought experiment can have different roles in the context of different discourses (even if C is constant), so any identity condition should adapt to this possible variance. ↩

• Strawson, Peter (1950), “On referring”, Mind, New Series, 59, 235, pp. 320-344.

• Tarski, Alfred (1944), “The semantical concept of truth and the foundations of semantics”, Philosophy and Phenomenological Research, 4, pp. 341-375.

• Berger, Alan (2002) Terms and Truth: Reference Direct and Anaphoric, MIT Press.

• Hughes, Cristopher (2004) Kripke: Names, Necessity and Identity. Oxford: Clarendon Press.
• Kripke, Saul (1963) “Semantical Considerations on Modal Logic”, Acta Philosophica Fennica 16:83–94
• Kripke, Saul (1975) “Outline of a theory of truth”, Journal of Philosophy, 72, 19, pp. 690-716.
• Kripke, Saul (1980) Naming and Neccesity, Oxford: Basil Blackwell.