Oct 27, 2011
Oct 23, 2011
Fisher, A. (2004). The logic of the real arguments. Cambridge: Cambridge University Press
Fisher’s The logic of the real arguments (first published in 1988) is an old-school, clear-cut, plain-spoken informal logic textbook. It shows us how to identify the conclusion, how to identify reasons, it tells us that an argument is a piece of reasoning, and that in order for us to accept it, it must contain a valid inference from true premises. You know – the whole deal.
But the book does contain a chapter which, the author claims, is not very often found in other “do-it-yourself” textbooks of logical analysis (with the exception of Thomas’s Practical Reasoning in Natural Language, we are duly informed). It is about ‘for the argument’s sake…” type of arguments. This, as you will have read between the lines, must have something to do with thought experiments. Fisher does not use the label, but analyses, voila!, Galileo’s experiment on falling objects. Which, by the way, is shown to be unwarranted so stick around.
First of all, let me spill out my prejudiced, not yet fully articulated, ideas about supposition. I am very much in line with Fisher account, and it would be cheating if I would use what he says to legitimize what I think. So, for “separational” purposes, here it is. Fisher acknowledges – out of intuition, I suppose, for nobody gets quoted – that a supposition is not an assertion, it is not presented as true. When I say “Suppose we can fly”, I’m (obviously, intuitively, etc.) not committed to the fact that we could fly.
[Just a short juicy digression: “Suppose we could fly” is a philosophically perverse move. If A says this in a conversation with B, then B is not asked to accept the possibility of a world where we do fly but the possibility of a world where we can fly. In other words, we might still not be able to fly in the “Suppose-we-could-fly” world. In the “Suppose-we-could-fly” world we don’t fly, we can fly. Which is dreadfully strange: why should one suppose a world where we can fly but we don’t?]
AAAanyway. Insofar as we both intuitively sense that supposition is not assertion, we agree. Fisher writes:
If someone begins an argument by saying “Suppose that oxygen does not burn” he is not asserting that oxygen does not burn – he is not presenting it as true.
A mathematician who… is not asserting (telling us) that … but asking us to consider the proposition with a view to drawing out its implications (113, my italicys)
The section in italics is what I want to pursue, and what Fisher leaves aside (and ultimately, in the analysis of Galileo, overlooks). Suppositions are not a different kind of assertion – they are not assertions in which the commitment of the speaker is weaker or absent. I say that from a speech act theoretical perspective and by this I mean: a supposition, insofar as it does not commit the speaker to the truth of the proposition, i.e. it cannot count as an undertaking of that commitment.
Lovely. But what are they? I believe they are directives. As described by Searle (1979, p. 13) directives have a different illocutionary point from that of assertive.
The illocutionary point of these consists in the fact that they are attempts (of varying degrees, and hence, more precisely, they are determinates of the determinable which includes attempting) by the speaker to get the hearer to do something.
And look at the syntax! “Suppose …”, “Let’s assume that…”, “Imagine that…” – are attempts of varying degrees to get the hearer to suppose, to consider etc., briefly, to commit to X “for the sake of the argument”. A command requests a specific act “mop the floor”. A supposition asks for a specific act too “take this as true”. A command has a preferred response “yes, sir”. A supposition has a preferred response “ok, I will”. The felicity conditions of a command can be under doubt, so attempts can be made to justify that they hold: “Because I want you to do it”, “Because I want you to do it and I’m your boss” etc. The felicity conditions of a supposition can be under doubt, so attempts can be made to justify that they hold: “For the sake of the argument”, “Because you have hold this view before”, “Because it derives from your theory”. The speech act which I believe is closest to supposition is proposal; hence, the fitting of the “let’s” idiom. Notice that preparatory conditions hold just the same: it cannot be obvious that B will undertake the commitment to A or that he already did. The following dialogue should seem odd:
B: I think that p!
A: Well, let’s assume p!
The reason it does not sound odd is because it jumps over a few steps which are implicitly taken. So,
B: I think the Sun rotates around the Earth
A: Well, suppose the Sun rotates around the Earth.
If a supposition is a request, the above dialogue should be pragmatically odd. I hope making it a bit more explicit will reveal the oddity:
B: I think the Sun rotates around the Earth
A: Well, (let’s) suppose the Sun does rotate around the Earth.
Who’s us in the let’s? Cannot be B. B is already supposing, i.e. B is already committed to p. But if there is no “let’s”, to whom is the request directed? Notice how well “well” fits in there. And well marks the drawing of conclusions (replace it at will with “well then”, “aha! if this is the case”, “then” etc.) I think the only way we can make sense of it, is if we make it into something like:
A: I don’t think p. (Don’t think non-p either, so far). But you do. Since this is the case, I am ready to accept it myself, and critically examine it. (Wait, why am I talking like Socrates?!). So let me – and therefore, since you are already in the reduction ship – let us undertake the commitment to p.
What I am doing, in saying suppose p – if I want to critically test it in a discussion, at least, but I cannot imagine a situation where a speaker supposes p for some other reason, can you? – I say, <AGREED! I COMMIT ALSO for the sake of the argument>. Remember the preferred response to a request? Acceptance, yes. Now fly away from this subject. Imagine two robbers standing behind a fence debating whether to rob a house or not. They squabble back and forth for a while and at the end the more audacious of them convinces the other one to do it. The last one will say:
B: Ok, let’s do it.
Consider one last example: academic writing is full of let’s and let us. (John Searle, accidentally, is an avid user). I’m not saying let in “let’s” should be interpreted literally – that, because of its idiomatic character. The imperative function arises quite independently of the meaning of “let’s”. Notice that, just as with other indirect acts, some are more built in language then others. Consider how oddly polite would “allow us” and “permit us” would be. Thus, aside from its teacher-in-the-class-sounding connotations, let’s cannot be explained unless this role-play (in which the author allows himself something as if he is a different person) is understood. “Thus, let us suppose” is a note-to-self. If A wants to tackle B’s claim and says “OK, let’s suppose p” it is A (not B) who need to commit to p. And it is worth mentioning that A thereafter commits to that because in the discussion he is in fact precisely on the other side, notice the nice fit of:
“I don’t agree, but OK, I will assume p just as you assert it”
Notice, then, the differences and the similarities between some of the ideas presented here and Fisher’s account. I too think that “Speaker does not undertake p” it is a good description of what happens but the way in which this is achieved in context is more roundabout than Fisher observes. I believe supposition cannot be explained outside a difference of opinion – since “I agree, but OK, I will assume p” is odd.
So now, the parties have agreed on the setting, and the antagonist goes:
A therefore B therefore … therefore X
The protagonist can, of course, object. Aristotle, as we shall see, might have objected to some of the intermediate claims extracted from his theory of motion. (Notice, parenthetically, that this time, although roles are played, the speaker is asserting A, otherwise he cannot make an argument. Fisher overlooks this, as I said earlier).
But if he, the protagonist, doesn’t object, then the antagonist has henceforth established – for the purposes of the discussion – the claim:
If A, then X
If what we’re playing here is theory choice, then A is a (or part of a) theory. It is a theoretical commitment.
After this, as the German would say, tout ira de soi.
If A, then X
But X is not the case.
Therefore A cannot be the case.
Old, overcooked modus tollens. Of course, at this point, we should like to say that the protagonist had better object. But, as it happens, the protagonist is seldom there to slap the antagonist (dialectically, I mean, of ocourse) in the face. So, once arrived at the conditional, it is hard to go back, since no sensible bloke would object to non-X. (Don’t be fooled by the easy-talk. You should not agree that this is what usually happens. It is just my feeling that this is how the strategy is commonly used. If the antagonist overlooked a thing that might make X true, he will make the frontpage of the FailWeek journal. Take Einstein’s epic one in clock-in-the-box.
If UNCERTAINTY PRINCIPLE, then you CANNOT MEASURE THE SYSTEM SO THAT BLABLABLA
But you CAN MEASURE THE SYSTEM SO THAT BLABLABLA
Therefore the UNCERTAINTY PRINCILPE cannot be the case.
As it happened, you could not.)
Oh, geez, where were we? A, right, Fisher’s account of Galileo…
To be continued.
De Mey, T. (2003). The dual nature view of thought experiments. Philosophica, 72, 61-68
What De Mey tries in this article is to show that the argument view and the experiment view on thought experiments are just that, namely, views. Neither of them is true – in the sense of capturing all there is to capture about thought experiments – but neither of them is false – in the sense of being logically rejected by the others. Thought experiments are both.
According to contemporary wisdom, one either holds that thought experiments are, basically, experiments or one subscribes to the rather deflationary view that they are, deep down, arguments 62
Now, De Mey’s plan is methodologically very shipshape: let’s first ask ourselves why we are wrestling with thought experiments in the first place, and then see what is the “nature” of thought experiments. Insofar as the theoretical (or meta-theoretical) purpose is in the blur, talk of whose definition is better is blank.
There are three problems, De Mey recognizes: (1) the problem of source of knowledge, (2) the problem of heuristic value, (3) the problem of evidential significance.
First: where do the goodies come from? “The very possibility of acquiring knowledge by means of thought experiments is generally taken to be a problem for empiricists” since it makes this knowledge difficult to trace back to experience. One way out of this is Norton’s empiricist account:
Thought experiments in physics provide or purport to provide us information about the physical world. Since they are thought experiments rather thanphysicaZ experiments, this information does not come from the reporting of new empirical data. Thus there is only one non-controversial source from which this information can come: it is elicited from information we already have by an identifiable argument, although that argument might not be laid out in detail in the statement of the thought experiment. The alternative to this view is to suppose that thought experiments provide some new and even mysterious route to knowledge of the physical world.
The “mysterious route” being surely Brown’s platonic account. Some thought experiments, Brown argues, do two things: they destroy a theory and build a new one. While the first part might be reconstructible as argumentation, the second part is not. Also, the second part does not involve new knowledge, nor does it derive its claim from previous data. (This should be taken with a grain of salt, since the fact that some conjunction of hypotheses cannot be the case can already be qualified as knowledge.)
Now, in connection to the second problem (the “heuristic value”), De Mey adds: “Whatever the merits of Norton's argument view are, it does not explain why thought experiments can be "psychologically helpful" (and thereby rhetorically effective)” (65). I agree with De Mey, but I think we hold this view for different reasons. He construes Norton’s account as theoretically incapable of shedding light on the rhetorical prowess of TE’s, while I construe Norton’s account as theoretically undeveloped, with the same result. In other words, is not like the account cannot say something explicatory about the heuristic value, it is that it does not. Just one step forward: although it does not, not only that it can, but it seems to me like it is the only one that can give a satisfactory answer. And half the road is already travelled: they are rhetorically effective because they are good arguments!
As for their epistemic significance, De Mey (2003, p. 66) speaks of the role TE's play in theory choice as their most "spectacular capacity" - whereas I think one should construe it as one of their defining ones. I think we would miss the property of terms if we would speak of a thought experiment every time someone supposes something. If any supposition triggers a thought experiment, then the label loses its classificatory values, i.e. it ceases to isolate a group of entities for the purposes it used to.
Norton's empiricist solution to the problem of the source of thought experimental knowledge can give us a first hint. Nobody doubts that arguments can play a role in theory choice. So, as far as thought experiments are arguments, their evidential significance seems fairly unproblematic (66)
There’s also Bishop (1998; 1999). He claims that the clock-in-the-box event works as an illustration as to why thought experiments are not arguments. The clock-in-the-box was a failed attempt by Einstein to confront Bohr with a counterexample to the uncertainty principle. It was considered a failure because, using the same set-up, Bohr pointed out that Einstein was missing something: in order to weigh the box, it must move in a gravitational field - since it does, the uncertainty principle (the measurements in question being mass and energy) holds.
Ok, now De Mey’s view. While beginning, he uses words in a certain way and, although he slides quickly to the more urgent problem, I believe he makes a good choice which needs underlining. Notice that for him, the thought experiment is not an experiment and an argument but a description of both:
thought experiments like that of the clock-in-the-box have a dual structure: they involve (1) the description of an imaginary situation and (2) the description of its settlement or winding up.
Their “evidential significance” is different according to what points (1) and/or (2) we choose to take into account. So much so that De Mey speaks of evidential significance1 and evidential significance2.
The last step for De Mey is to take a modern account of experimentation and cast thought experiments into it.
Sophisticated conceptions of experimentation, typically invoke more structural dimensions. Radder (1996), e. g., differentiates between three "phases" of experimentation: (1) preparation, (2) interaction and (3) detection. Firstly, during preparation the object and the apparatus are prepared in agreement with the plan of the experiment. Subsequently, interaction results in the transfer of information from the object to the apparatus. Finally, detection involves obtaining the information "by measuring or observing the relevant property of the apparatus (Radder 1996: 11).
Each phase (“make the device”, “use the device”, “read the device”) has a material realization and a theoretical interpretation. The first one is (or should be) theoretically-independent. The second one is theory-driven.
So there you have the solution:
So there are two ways to describe a thought-experimental process, i.e. in terms of its material realization and in terms of its interpretation. To do full justice to the evidential significance of a thought experiment then, of whatever kind it is, we need both. As far as the material realization of the thought-experimental process is what adherents of the experiment view on the nature of thought experiments stress (as I believe they do) and as far as the theoretical interpretation of the thought-experimental process is what adherents of the argument view have in mind (as I believe they do), we can safely conclude that it doesn't make sense to say that thought experiments are, basically, either experiments are arguments. They are, deep down, both experiments and arguments 76
Brown, J. R. (1991). The laboratory of mind: Thought experiments in natural sciences. London/New York: Routledge.
Illustrations from the laboratory of mind. This is the title of Brown’s (1991) first chapter. In the preface, and again in the introduction to this chapter, Brown acknowledges – in an explicit manner, which I fancy – the fact that he hasn’t got a definition to work with.
Thought experiments are performed in the laboratory of the mind. Beyond that bit of metaphor it’s hard to say just what they are. We recognize them when we see them: they are visualizable; they involve mental manipulations; they are not the mere consequence of a theory-based calculation; they are often (but not always) impossible to implement as real experiments either because we lack the relevant technology or because they are simply impossible in principle. If we are ever lucky enough to come up with a sharp definition of thought experiment, it is likely to be at the end of a long investigation.
But as he advances, he adds some spice. First he brackets out what are not thought experiments, that is, psychological experiments on thought or other inky stuff. Then he explains the “experiment” component as follows:
As well as being sensory [i.e. they are visualizable or experiencable], thought experiments are like real experiments in that something often gets manipulated: the balls are joined together, the links are extended and joined under the inclined plane, the observer runs to catch up to the front of the light beam. (Brown, 1991, p. 17)
The thought experimenter does two things: imagining and manipulating.
1. Galileo on falling bodies
Galileo first notes Aristotle’s view that heavier bodies fall faster than light ones. This was the prevailing view of motion and it had the advantage of being very close to one’s intuition: if a feather falls on your toes, you’re fine. But Galileo reasoned as follows. Suppose we tie two objects together: a cannon ball and a musket ball.
First, the light ball will slow up the heavy one (acting as a kind of drag), so the speed of the combined system would be slower than the speed of the heavy ball falling alone (H > H+L).
This might sound fishy to begin with, but imagine someone hopping in a fast-moving carriage. In order for the whole system to keep the speed, the poor horses need more strength, therefore, with the same strength put into action they will be slowed down.
On the other hand, the combined system is heavier than the heavy ball alone, so it should fall faster (H+L > H).
This does not sound fishy at all. It is heavier, and it should fall faster – so intuition tells us. But, of course, this is just half of the story, because Galileo does not only expose the paradox of Aristotelian mechanics, but resolves it. The right equation, he says, is that H = L = H+L. That is, all things fall at the same speed. (Namely, some will add, gravitational speed).
2. Stevin on inclined planes
So we have three self-evident situations: if a weight is on an horizontal plane, it will remain at rest; if a weight is on a vertical plane, it will fall; and if the weight is on an inclined plane, it will either fall or rest depending on the inclination. Great, but how could we get more precise about these things? If we could calculate the point of echilibrium, that would be great: every smaller inclination of the plane means rest every greater inclination means fall.
Stevin come up with this thing:
From the first figure, we wouldn’t know what to say: are the balls in an equilibrium? From the second, however, we are compelled to say: they must be, otherwise it would be perpetual motion (and perpetual motion is an absurdity, as far as we can know). Therefore,
when we have inclined planes of equal height then equal weights will act inversely proportional to the lengths of the planes
3. The flat planet with shrinking people
Now, Brown makes an interesting claim, which can only be understood under a very broad definition of the term “thought experiment”: “Consequently, [i.e. since Euclidean geometry is an a priori abstraction from everyday mechanics]we can see the results of Euclidean geometry (at least those produced before the rise of non-Euclidean geometry) as a vast collection of thought experiments” (p. 11). And further, “theorem of Euclidean geometry is then a kind of report of an actual construction carried out in the imagination.”
The thought experiment related to Euclidean geometry is one devised by H. Poincaré and H. Reichenbach. (The text is from Cohen, 2005, p. 45):
Imagine a planet made only of gases. At the centre the temperature is very high, and this is where all the gaseous people evolved and normally live. At the surface, however, the temperature is very, very low. In fact, M. Poincaré tells us, it is absolute zero. (The significance of this will become clear later.) As the gaseous people, let us call them ‘the Jeometers’, move around their planet, a small but subtle change takes place. Because of the change in temperature, the further they go from the centre, the smaller they become. And not just them, the smaller all the creatures and all the artefacts of the gaseous planet become. The most important thing is that everything changes at exactly the same rate, so nothing gets out of kilter.
One year, the Jeometers determine they must explore the upper reaches of their planet and construct a massive ladder which they stand upright with its top disappearing far into the clouds. One of the Jeometers’ geometers sets off up it, with the task of finding out how far the gaseous planet extends. There is great excitement, but it is dissipated somewhat when the geometer returns a few days later to say the ladder is nowhere near long enough.
For years and years sections of ladder are added, but it seems it is in vain. Each time the geometers return to say that the ladder is still not long enough.
Actually, as they ascend the ladder, both the Jeometers and the ladder itself are shrinking, shrinking so small that it is physically impossible for them to ever get to the outer surface. (At absolute zero, they will shrink to absolutely nothing.) Yet as they climb up, becoming colder and colder and at the same time smaller and smaller, the steps on the ladder, their measuring rods – everything – are also getting smaller and smaller, so they never realize the shrinking is happening. Eventually, the Jeometers decide their planet is infinitely large. Which it isn’t.
The substance of this thought experiment is to show that there is always a possibility to the effect that whatever geometry we invent, Euclidean or not, it may always fail to be the true one. In fact, “truth of geometry” is a strange expression since the statements of geometry are a matter of convention.
The geometrical axioms are therefore neither synthetic a priori intuitions nor experimental facts. They are conventions…. In other words, the axioms of geometry… are only definitions in disguise. What then are we to think of the question: Is Euclidean geometry true? It has no meaning. (Poincare, 1952)
4. Einstein vs. Maxwell
Classic electrodynamics told people this: light is a change (“oscillation”) in the electromagnetic field; and it works both ways. A change in the electric field gives rise to a magnetic field and a change in the magnetic field gives rise to an electric field. In response to this theory, (when, by the way, he was only sixteen supposedly…), Einstein thought of chasing a beam of light (oh, puberty…). The point of this chase – or “running along” – is to pinpoint impossibility: if change is essential for a light wave, then it should be so for any observer, be it a moving or at rest; but if you are moving with the exact speed c, then with respect to you, change is not coming about. Is like chasing a wave in the ocean. If your speeds are equal, then the hump of water does not change relative to you.
If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the basis of experience or according to Maxwell’s equations.
Brilliant! (Quite literally.)
5. Heisenberg γ-ray microscope
The uncertainty principle was very much debated in the mid-twentieth century. Many philosophers knock-knock-knocking on physics door were appalled and tried their best to disprove its (a) validity, (b) importance.
For us now, it is strangely important in our taxonomy. As it happens, the thought experiment connected to this principle is not designed to refute any theory and it is subsequent to the principle itself. Could it be that it is a case of illustrative thought experiment – in Popper’s terminology?
From the first principles of quantum theory, Mr. Werner Heisenberg formally derived the principle that the product of uncertainties in present knowledge of a system is always greater or equal to a certain constant (known as Planck’s constant). “This may be expressed in concise and general terms”, Heisenberg adds, “by saying that every experiment destroys some of the knowledge of the system which was obtained by previous experiments.”
And then comes the thought experiment. Notice the new flavour: the principle had already been formally arrived at! Heisenberg himself calls this thought experiment an “example”.
As a first example of the destruction of the knowledge of a particle’s momentum by an apparatus determining its position, we consider the use of a microscope. Let the particle be moving at such a distance from the microscope that the cone of rays scattered from it through the objective has an angular opening ε. […] But, for any measurement to be possible at least one photon must be scattered from the electron and pass through the microscope to the eye of the observer. From this photon the electron receives a Compton recoil of order of magnitude h/λ. The recoil cannot be exactly known, since the direction of the scattered photon is undetermined within the bundle of rays entering the microscope. Thus there is an uncertainty of the recoil in the x-direction of amount…
6. Schrodinger’s cat
Still indoors with quantum mechanics. The Copenhagen interpretation of the formalisms of quantum mechanics did not reject one (bizarre) possibility: namely that of a system being at two (superposed) states at the same time. Since we can only observe one – in other words, since for us a system is either one way or the other –this possibility remain only a theoretical one. On a philosophical level, sure, it said many things about our place in the universe: that we “create” reality, we restrict it to only one of its states, that we are doomed with only partial knowledge of the world, etc. But it remained a theoretical option nonetheless. This theoretical option however bugged many people, amongst whom Einstein of course, but als Mr. Schrödinger.
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The ψ-function of the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.
This thought experiment seems no different from the first, classic ones. It thinks up a possible state of affairs which supposedly (a) was overlooked by quantum physicists and (b) gives rise to absurdity. It’s difficult to say here whether the absurdity is a matter of logical contradiction or otherwise “empirical”-ish. (But it’s the same with Galileo’s balls. It is mainly because of our language that we think of an object falling “both slower and faster” than another one as being a contradiction. It is, just the same, mainly because of our language that we think of a living object being “both dead and alive” as being a contradiction).
The people considered in philosophical thought experiments can get very weird: we are asked to imagine people splitting like amoebas, fusing like clouds, and so on. Stevin’s frictionless plane, or Einstein chasing a light beam are homely by comparison.
Oct 15, 2011
The geometrical axioms are therefore neither synthetic a priori intuitions nor experimental facts. They are conventions…. In other words, the axioms of geometry… are only definitions in disguise. What then are we to think of the question: Is Euclidean geometry true? It has no meaning.
Poincaré, 1952, Science and hypothesis
Oct 11, 2011
As I was sitting in my chair
I knew the bottom wasn’t there,
Nor legs nor back, but I just sat,
Ignoring little things like that.
Garssen, B. (2009). Comparing the incomparable: Figurative analogies in a dialectical testing procedure. In F. H. van Eemeren & B. Garssen, Pondering on problems of argumentation: Twenty essays on theoretical issues (pp. 133-140). Amsterdam: Springer
A short paper on analogies. The question Garssen attempts to answer is this: Is analogy a type of comparison? The answer is: no. Let’s see.
Comparison argumentation stands in the pragma-dialectical theory as one of the three types of argument schemes alongside symptomatic and causal argumentation. In general, what makes pragma-dialecticians distinguish one scheme from another is the different type of “liaison” they provide from the premise to the standpoint. Regardless of their form in natural language, the reconstructed versions of these schemes are seen as different because they elicit separate critical behaviour. More precisely, you cannot use the critical questions that go with one scheme to test the other.
Comparison argumentation goes as follows. (Notice that X & Y below can be any referable object under discussion – these are not grammatical representations).
Y is true of X
because: Y is true of Z
and: Z is comparable to X.
One variant of this scheme is called by Garssen the “extrapolation of characteristics”. His example is this:
Camera surveillance in the centre of Amsterdam will prove to be very effective, because in London, camera surveillance proved to be highly effective before.
If we twist the language a bit, we get to:
The effectiveness of surveillance is true of Amsterdam
because The effectiveness of surveillance is true of London
and London is comparable to Amsterdam.
Notice, also, that this is not a logical reconstruction. This “scheme” does not have any merits on its own, but stands as a reasonable argumentation for the standpoint if the critical questions pertaining to it are satisfactorily answered. And this is a matter of degree.
Another type of comparison scheme could be identified with respect to prescriptive standpoints. (Notice that in the example above Garssen dealt with descriptive statements – i.e. which do not have modal aspect).
His example of this second variant is this:
The European committee should grand Belgium higher agricultural subsidies because it granted Italy higher subsidies as well.
This could be reconstructed in the same manner, but notice the extra sauce: the question of the adequacy of such argument hinges on whether the two (Belgium & Italy in our case) are indeed members of the same class. In legal contexts, this boils down to checking the legal provisions. However, in one way or another, the adequacy of the scheme depends on the acceptability of the answer to the critical question: Are they indeed members of the same class?
But now what about figurative analogies?
At first glance, they seem way off the track. (Conversationally too!)
Take this one. Answering to whether USA should intervene in Korea, president Truman is said to have asked:
The best time to meet the threat is in the beginning. It is easier to put out a fire in the beginning when it is small than after it has become a roaring blaze.
Here’s Garssen’s commentary:
Fire and war clearly belong to different classes of events. That makes it impossible to compare them in a direct way. In this case we have to look for similarities, not so much between the concrete features of fire and war, but between the abstract relations within what is said in the premise and what is said in the standpoint. It I predicted that the war in Korea will become unmanageable if we do not act immediately and that is exactly the reason why we should act now. Truman does not make a direct, literal, comparison between war and fire. That is why the standard critical questions that go with comparison argumentation (are there similarities? are there differences?) do not really apply.
The reason why this path was chosen: if we really set about to test this argument in the way normal comparison schemes would require, it wouldn’t stand a chance. Fire is unlike war in every direct (read: literal) sense. However, more intuitively, fire and war are alike on a more abstract level – they are alike in a sense, as the cautious philosopher would say. Therefore, one should reveal this in his or her reconstruction.
According to Garssen we could explain this intuition as follows: “figurative analogy is not argumentation based on a comparison relation but a way of presenting another type of argument scheme” (138). In other words, it is not that it is a looser, more far-fetched, type of comparison; it is a discursive device for introducing (and supporting) a sub-standpoint. Notice, again, the structure in the Truman example:
The best time to meet the threat is in the beginning. It is easier to put out a fire in the beginning when it is small than after it has become a roaring blaze.
We should go to war against Korea now/ We should not postpone our response to the war that is now developing in Korea. That is because the best time to meet the threat is in the beginning. It is like being confronted with a fire. It is easier to put it out in the beginning when it is small then after it has become a roaring blaze.
Garssen does not reconstruct this example. In fact, he doesn’t provide a full reconstruction of any of the examples. Let us try:
(1.) What happens in Korea (Y) is such that our response to it should not be delayed (X)
(1.1.) What happens in Korea (Y) is a threat (Z).
(1.1’) Threats (Z) are such that one’s response to them should not be delayed (X).
Notice that this is a case of symptomatic argumentation.
Where does our fire-analogy fit? Garssen’s answer seems to be: “Nowhere”. Because the fire-war figurative language is not part of the reconstructed argumentation. It is just a way of introducing an agreed upon starting point, namely (1.1’). So what the party really needs for his argumentation is this statement (1.1’), and the way he introduces it is by referring to a more well-known situation – or a more easily imaginable one – namely that when a fire threatens to become “a roaring blaze”. So what we have here is a case where the protagonist is urging the other party to recognize the principle (1.1’) as recognized in other, simpler, instances.
Oct 10, 2011
Popper, K. (1983). Two kinds of definitions. In D. W. Miller (Ed.) A pocket Popper (pp. 87-101). Glasgow: Fontana Press
There are, apparently, two kinds of approaches to the act of defining: the essentialist approach and the nominalist approach. The former is something of a fairytale today – at least when it is spelled out up to its ultimate consequences. Popper undertakes to refute the former and support the latter.
The Aristotelian view of knowledge is singular in its emphasis on the importance, let’s say, induction. However, although bringing sense-data in the game, its overall structure was mainly Platonic. So there is opinion and there is knowledge. Opinion is opinion. But where does knowledge come from? One should say: sound arguments. Aristotle would agree, for it is the truth of the premises and the validity of the demonstration (syllogism) that makes a conclusion true. Sweet. The only thing is, this leads to an infinite regress: how do we establish the truth of the premises? By means of a valid syllogism from other premises found one-step-backwards in our reasoning. How do we establish the tr… well, you get the idea.
Against this infinite regress, Aristotle – again, one should say Plato – distinguished a certain type of intuition by means of which we come to know the truth of our most basic premises. (The ones which we should posit as a basis for our sciences, for instance. No wonder Aristotle saw his legacy as a constant search for these basic premises which would ultimately form an encyclopaedia of starting points). The statements we thus acquire are there in our head because we can grasp the essence of certain slices of reality. Long story short: science = essences + logic.
Of course, this view of definition is obsolete. The role of definitions in science is very different from what Aristotle had in mind. As a matter of fact, the whole thing works the other way around: we don’t ask “What is gravity?” and try to respond, but we ask “What is the force which draws unsuspended objects to earth?” and decide to respond “It is gravity”. To put it speech act theoretically, a definition is a kind of declarative speech act, not an assertive one. It cannot be true or false. That is why, contrary to popular belief, definitions don’t play a big role in science, but, as it were, in spreading science and understanding. They are, when all’s said & done, labels. (NB: to report of a definition is, however, subject to alethic assessment as any other assertive is).
Does this mean that such intuition do not exist? Not necessarily. We might have them on some psychological level or another. Popper’s claim is methodological: it simply means that they do not play a role in establishing the epistemological values of a claim. They are private.
But here’s another thing. Suppose we do stick to the importance of definitions. The problem with this choice, as correct as it may be, is that it is untenable. It cannot hold in principle: one cannot define all the term one uses in a theory because that would lead to an infinite regress. You define one term by other terms which, if you define, you produce more terms. This demand resembles the one that all our statements must be proved.
How can nominalism be a solution to that? Well, Popper goes, let’s first bust a myth:
Aristotelianism and related philosophies have told us for such a long time how important it is to get a precise knowledge of the meaning of our terms that we are inclined to believe it. And we continue to cling to this creed in spite of the unquestionable fact that philosophy, which for twenty centuries has worried about the meaning of its terms, is not only full of verbalism but also appallingly vague and ambiguous, while a science like physics which worries hardly at all about its terms and their meaning, but about facts instead, has achieved great precision. This, surely, should be taken as indicating that, under Aristotelian influence, the importance of the meaning of terms has been grossly exaggerated. 97
This is, more or less directly, a criticism towards Wittgenstein I, for which philosophy is primarily to concern itself with making the meaning of terms clear.
Oct 3, 2011
Sorensen, R. (1992). Thought experiments. New York/Oxford: Oxford University Press
Never in my (admittedly, not particularly lengthy) life have I bumped into such a remarkable mixture of immodesty and disorder. In Thought experiments, nothing seems to escape prof. Sorensen’s wit. Read “not one single thing” for “nothing”. The book is a disparate plunge into microbiology, logic, psychology, epistemology, pathology, mathematics, biology, grammar and, par Socrate!, metaphysics. To be clear: the nature of the subject matter must have made delving into the above list almost a necessity. As anyone who gave it a bit of attention will concede, thought experiments appear everywhere. But there is a big difference between discussing a type of discourse throughout more than one field and discussing a type of field throughout more than one instances of a type of discourse.
I sense (from the book as well as from some of the reviews it received) that Thought experiments was intended as a monograph. Its explicit taxonomic objective is the first clue. If so, it is an unfortunate by-product of copyright laws that the curious student will have to trudge through 300 pages of the only book with such a telling title. Whoever edited this book is equally blameworthy for not spanking out tens and tens of pages the sole purpose of which is to squash doubts about the author’s literacy. Of course, “freedom of expression” etc. OK. But if not by prohibition, may students more trained in elementary law figure out ways of blocking capital works with capital titles being written after this fashion:
Rearranging the problem this way makes the problem easier, just as it is easier for a child to eat his steak after his mother has sliced it for him.
One of the advantages of watching a movie on a VCR rather than at a theatre is that you are free to fast-forward and rewind.
Predatory birds and snakes maneuver so that their prey can be swallowed headfirst. Consumers of information display similar preferences.
If you have more than one mouse, you have mice. But houses are not hice, nor blouses blice.
When stood up against Vaihinger, Kuhn appears pale and tame. Kuhn dips his big toe into the pool of incoherence. Vaihinger belly flops.
At first glance, covert presumption precluders are as innocent as new-laid eggs.
Thus, thought experiments developed from experiments in the way a spider's spinners evolved from legs.
To close this exhaust-pipe introductory passage, I leave you with the author appearing on page 124 in a photo of superlative irrelevance to the discussion.
OK, from this point on I shall take Sorensen’s book seriously.
Two purposes could be identified as red threads guiding the book: (1) to establish true and interesting generalizations about thought experiments, (2) to offer a resolution to the problem of thought experiment’s epistemic value (rapidly, are thought experiments of any epistemic value). The first one includes (1a) a taxonomy and (1b) a reconstruction of how they work. The second one includes (2a) an explanation of the role of thought experiment in science and philosophy, (2b) an answer to the “new data” problem – “But if you just ponder, then the information you have leaving the armchair is the same as the information you had when you sat down. So how can you be better off?” (p. 76).
You may have noticed that there is no “(x) a definition” point in the above list. Sorensen does provide one but it is at page 205 and it comes after the taxonomy, after a full-blown discussion of most relevant thought experiments and after the logical reconstruction. This being the case, I shall refrain from accepting the sentences below as constituting a definition:
“A thought experiment is an experiment (see p. 186) that purports to achieve its aim without the benefit of execution.” (p. 205)
“An experiment is a procedure for answering or raising a question about the relationship between variables by varying one (or more) of them and tracking any response by the other or others” (p. 186)
Anyway, taclking (1), Sorensen posits the profitability of what he names the cleansing model of thought experiments. He opposes it to other models which, in the past, purported to have found how these scientific and philosophical machineries work. Swiftly put, the cleansing model generalizes that all thought experiments are intended to refute by reduction ad absurdum.
“The cleansing model is inspired by incidents in which you recognize your own irrationality and then change your beliefs to remove the flaw. A friend of mine was a sensitive boy who became worried about the ants that he inadvertently crushed while walking about. His father assured him that he should not worry about killing ants because "there are millions of them." This satisfied my friend for a while. But his new equinamity was terminated by a thought about the growing human population. This illustrates the familiar situation where an inconsistency takes root, is detected, and is then weeded out.
This, I believe, is a good starting point: instead of debating what is the added value of creating a story to refute a claim, Sorensen begins with the simpler and more salient feature of thought experiment. Whatever may prove to be the added value of using them, one’s inquiry should start there: they are first and foremost tools for refuting a claim.
What type of claim? And how does the tool work? To the first question, Sorensen answers: either a universal claim or a particular claim. According to this division, the thought experiments that refute a universal claim are called necessity refuters. The type of thought experiments that refute particular claims are called possibility refuters. Of course, the claims need not be neatly designed as categorical statements, but their consequence always receives the abovementioned modality.
I should probably mention here that possibility statements are not refuted in the same way necessity statements are. Since possibility statements do not prohibit the truth of any one proposition, their logical falsifiability is zero. This has nothing to do with the field in which such statements occur. Also, regardless of the logical apparatus of a thought experiment “It is possible that x” cannot be used in an argument to arrive at “It is not possible that x”.
To the second question, Sorensen lays down these steps (p. 136):
i. S Modal source statement. Fertile sources of modal propositions include semantic theses (definitions, synonymy claims, entailment theses), testability theses (unverifiability, unfalsifiability, indetectability), feasibility claims, law statements, disposition and intention attributions, validity verdicts, and clusters of these—theories.
ii. S → □ I This proposition draws the relevant modal implication from the source statement
iii. (I & C) □→ W This proposition is read as a subjunctive conditional: if I and C were the case, then W would be the case. This proposition claims that the antecedent, which is the conjunction of the implication and the imagined situation, has a weird consequence.
iv. ¬ ◊W Absurdity. This proposition explains the weirdness as an impossibility
v. ◊C Content possibility. This asserts that the content of a that the content of the thought experiment is a possibility
Again, I grant Sorensen that this is a good place to start. After all, this is nothing less than (a more detailed version) of modus tollens. However, there is a minor point: the order of a sentences. Indeed, they are inconsistent in whatever order one arranges them, and thus Sorensen’s idea that thought experiments boil down to paradoxes is not affected by my rearranging. But if modus tollens goes as follows:
p → q
Then I see no reason for going:
p → r
r & s → q
To resume: the theory p predicts that r but since we know that s could be the case, and that the conjunction of r & s yields an absurdity, we conclude to non-p. I will argue later that the 3 extra steps from Sorensen’s model are not necessary – although I see how sometimes they can be an accurate reconstruction of this or that thought experiment. For now, let us observe that in order for such an apparatus to be academically potent, the other party must (be known to accept) s. If the possibility of a certain state of affairs is not granted, no thought experiment can be constructed. For instance, to take one of Galileo’s thought experiments, if the other party does not agree that two things can be attached to form one thing (balls, stones, whatever), the thought experiment has no power to persuade. In fact, the argumentative process goes the other way around: in the opening stage, both parties agree on s (& p, & r, & whatever else is needed), and on this agreement the antagonist builds his case.
The second point to observe is that the model does not fit the definition. Remember experiments being defined (quite adequately) as fiddling with one variable to observe changes in the other? Now what exactly is one varying in the model above? Where is the observed dependency? Let’s imagine the following theory: All ravens are born in the southern hemisphere. Let us now imagine that we know how no white things can be born in the southern hemisphere. If our universal statement implies “All white ravens are born in the southern hemisphere”, we have hereby unearthed an inconsistency. Have we made any changes?
The impression I get here is that the label of “experiment” still fits these uses of discourse because the possibility of s is provisionally accepted by both parties. They take it as their starting point – regardless of whether it is a real possibility entailed by any other theory they agree upon. At the end, in the concluding stage, the protagonist can always go back to the opening stage and revise his acceptance: indeed, many Aristotelians did just that to counter Galileo’s refutation.
The third point to observe – a point which is also stressed by Martin Bunzl in his review of Sorensen’s book – is that the thought experiment and the use of thought experiment are two different objects of study. For instance, our Galilean thought experiment was used to offer (some) support to the idea that velocity is universal and (total) corroboration with the thesis that weight does not matter. But the passage from the latter to the former is incidental and certainly not deductive. Going “Aha! You are wrong” and going “Aha! I am right” are two different steps. Sorensen discusses both, alternatively without making any explicit distinction.
Let us use this model to analyse Searle’s Chinese Room. In want of any definition, I will conclude that Searle’s Chinese Room is a thought experiment simply on the grounds that it is mentioned by many theorists interested in thought experiments. I leave in suspension the question of whether this is a satisfactorily accurate statement or not.
What is the S?
Well, at first glance, it must be something around the claim that:
(S1) Computers can think.
Notice that the chapter in which Searle presents his Chinese room (in Reith lectures) is entitled Can computers think? So it might be justified to start from S1. However, S1 is very ambiguous and it would be unfair to Searle to leave it at that. For instance, he mentions explicitly that what we are concerned with are digital computers, that is to say, machines which manipulate symbols and nothing more. By “nothing more” Searle means something like: however much they interact with the physical world, and however much they simulate human interaction with the physical world, the machinery does not produce intentional states of mind. It cannot “have a semantics”, as he puts it. So we might want to change S1 to
(S2) All sufficiently advanced symbol-operators can have any mental state
Whether this is indeed what Searle’s adversaries had put forward in the past is not relevant. I am, for now, interested in cramming the Chinese Room into Sorensen’s scheme.
The next thing is to draw “the relevant modal implication”. This implication could be:
(I1) A sufficiently advanced computer can understand Chinese
Yet again, we would like to make the implication more exact. Based on Searle’s text, we should like to say:
(I2) A sufficiently advanced symbol-operator, given proper conditions, can have the mental state of understanding Chinese
We need not nitpick: understanding here means “knowing the meaning of the sentences”. So let’s simplify, now that we know what we’re talking about:
(I3) All supercomputers in superconditions can understand Chinese.
(I4) If it is a supercomputer in superconditions, it can understand Chinese.
Now, the man locked in the Chinese room is not a very advanced computer. That is one of the points. But as the reductio goes, Searle asks us to imagine that that is the case, or that no significant difference occurs. He wants us to suppose that the cards are very sophisticated, and that the “program” they represent is the same as in the very advanced computer the theory is referring to. Indeed, computers are just that: “people” that manipulate “cards” really well and fast. Historically, anyway, this is in fact very precise.
But what would C be?
(C) Let us Searle is such supercomputer in superconditions.
Now, modus ponens:
(I & C) □→ W: All supercomputers in superconditions can understand Chinese & Searle is a supercomputer in superconditions, therefore Searle understands Chinese.
(¬ ◊W): Searle does not understand Chinese
This doesn’t make much sense. I mean, it does, but it is too stupid. Searle’s conclusion is that computers cannot think, this is what he explicitly claims to tackle, so the contradictory of (S), something like:
(¬S) No sufficiently advanced computer can have any mental state whatsoever.
Is Searle’s argument so blatantly invalid? Note that the reconstruction above is also the reconstruction made by Damper’s (2006) The logic of Searle’s Chinese argument. The step from (¬ ◊W) to ¬S is always invalid because I & C are less general then S. So, unless some sort of inductive step slips in the scene, all thought experiments (reconstructed by Sorensen’s scheme) which conclude to the opposite of S are invalid. Let me re-state it so that it is clear. By “supercomputer” I mean “very advanced digital symbol operator”. By “supercircumstances” I mean the Chinese Room scenario. (S) is what “strong Artificial Inteligence claimed. The rest has been discussed:
(S) All supercomputers in supercircumstances can have any mental state
(S → □I) If [All supercomputers in superconditions can have any mental state], then [All supercomputers in superconditions can understand Chinese].
(◊C) Let us suppose that Searle is a supercomputer in superconditions.
((I & C) → W) If all supercomputers in superconditions understand Chinese and Searle is a supercomputer in superconditions, then Searle does understand chinese.
¬◊W Searle cannot understand Chinese
(¬S) No supercomputers in supercircumstance can have any mental state
This is invalid. And simplified. And, I believe, wrong as a reconstruction.
Oct 1, 2011
A party of white men and Indians were amusing themselves after the day's work by attempting to throw stones across a deep canyon near which they had encamped. No man could throw a stone across the chasm. The stones thrown by the others fell into the depths. Only Char, the Indian chief, succeeded in striking the opposite wall very near its brink. In the discussion of this phenomenon, Char expressed the opinion that if the canyon were filled up, a stone could easily be thrown across it, but, as things were, the hollow or empty space pulled the stone forcefully down. The doubts of European Americans as to the correctness of this conception, he met by asking "Do not you yourselves feel how the abyss pulls you down so that you are compelled to lean back in order not to fall in? Do not you feel as you climb a tall tree that it becomes harder the higher you climb and the more void there is below?"
“Many passions and phobias center on genuine goods and evils; they only acquire the status of disorder by virtue of what they interfere with. Some critics of analytic philosophy will say that the problem is more than interference. One criticism is that the obsession with clarity tempts the analytic into aping science. Thus, we find the accoutrements of notation, jargon, and specialization, as well as the cultivation of cordial relations with physics, biology, and psychology and parvenu indifference toward neighbor humanities. Another grievance is that the pursuit of clarity squeezes the life out of other values: neglect of other goals leads to their extinction. The imbalance creates a delusional fear that one's thinking is flabby and excessive along with a grim determination to slim down. The resulting academic anorexia is highlighted by parodies of analytic philosophy. The analytic is pictured as an eccentric who is so obsessed with sharpening his tools that he gives no further thought to what he is sharpening them for. Or he is
compared to the drunk who loses his keys at his door but chooses to search for them under the street lamp because the lighting is better. Clarity is not enough!”
Roy Sorensen, Thought experiments