by Matt Qvortrup
https://philosophynow.org/issues/156/Philosophers_on_Baths
Philosophers on Baths
Re: Philosophers on Baths
Archimedes famously said Eureka! We all know that, and we might also remember that his exclamation came when he was stepping into a bath and realised that the volume of water displaced must be equal to the volume of the part of his body he had submerged.
Here is an example of cause and effect that is not based on a constant conjunction.
How do you "realise that the volume of water displaced must be equal to the volume of the part of his body he had submerged" ?
You couldn't really try and measure it before you realised it should be the case. Before you realised it should be the case why should you think that sort of measurement was useful?
It probably isn't exactly true, because the parts of body submerged will also be compressed. This is apart from cases where a submerged object dissolve, or acts like a sponge, or a purely logical possibility happens such as the part immersed becomes a different object, or disappears. Then the bent stick phenomena might make it seem, from visual experience, that the volume of a submerged object should increase; even if the water level doesn't correspondingly increase.
Hume "There is no object, considered in itself that can afford us a reason for drawing a conclusion beyond it". But it seems to me that we don't want to have to go beyond objects in our understanding of causal situations. We don't want things to appear from nothing, ( "nothing comes from nothing") or disappear into nothing, We want to be able to trace factors around in causal situations, so that all alterations are a rearrangement of the same old continuing stuff. This is because if we don't have to go beyond the same old continuing stuff as the situation develops, just because of that fact. the continuation of the same old stuff must appear sufficient to bring about that development of the situation. And, being naive realists, we naturally want and expect the contents of situations, themselves, to bring about what happens in the situation.
Hume's statement was aimed at any attempt to make a logical deduction from the idea of any state, to the idea of any other, and in turn, I suppose, was aimed at any vaguely Aristotelian notion that what happens in a situation results by a logical deduction from the essence of the substance involved. But this notion would seem to require a logical deduction from one object, substance, or essence, to what happens to another such thing, who's idea would be logically outside the idea of the first. Billiard balls seem to provide a good illustration of this point. But on the contrary, we are not trying to make a logical deductions from the idea of any state, but are making comparisons to see if we apparently need something new, or the continuing same stuff can bring about the result.
Here is an example of cause and effect that is not based on a constant conjunction.
How do you "realise that the volume of water displaced must be equal to the volume of the part of his body he had submerged" ?
You couldn't really try and measure it before you realised it should be the case. Before you realised it should be the case why should you think that sort of measurement was useful?
It probably isn't exactly true, because the parts of body submerged will also be compressed. This is apart from cases where a submerged object dissolve, or acts like a sponge, or a purely logical possibility happens such as the part immersed becomes a different object, or disappears. Then the bent stick phenomena might make it seem, from visual experience, that the volume of a submerged object should increase; even if the water level doesn't correspondingly increase.
Hume "There is no object, considered in itself that can afford us a reason for drawing a conclusion beyond it". But it seems to me that we don't want to have to go beyond objects in our understanding of causal situations. We don't want things to appear from nothing, ( "nothing comes from nothing") or disappear into nothing, We want to be able to trace factors around in causal situations, so that all alterations are a rearrangement of the same old continuing stuff. This is because if we don't have to go beyond the same old continuing stuff as the situation develops, just because of that fact. the continuation of the same old stuff must appear sufficient to bring about that development of the situation. And, being naive realists, we naturally want and expect the contents of situations, themselves, to bring about what happens in the situation.
Hume's statement was aimed at any attempt to make a logical deduction from the idea of any state, to the idea of any other, and in turn, I suppose, was aimed at any vaguely Aristotelian notion that what happens in a situation results by a logical deduction from the essence of the substance involved. But this notion would seem to require a logical deduction from one object, substance, or essence, to what happens to another such thing, who's idea would be logically outside the idea of the first. Billiard balls seem to provide a good illustration of this point. But on the contrary, we are not trying to make a logical deductions from the idea of any state, but are making comparisons to see if we apparently need something new, or the continuing same stuff can bring about the result.
Re: Philosophers on Baths
Archimedes had also to realise that a heavier substance will have less volume for the same weight as a lighter substance. Consequently he could tell if the crown was made from a heavy substance, gold, or something else if he knew how much it weighed and what its volume was. So he needed a way of measuring its weight and its volume. And the way of measuring is volume was to immerse it in a fluid, and note how much the volume of the fluid increased.
In the context of measuring weight, Archimedes himself is also famous for his demonstration of the law of the lever, which uses a way weights can be compared, but we could also describe it as producing a principle for comparing weights. But all this only works if weights and volumes continue. According to the axiomatic method we are supposed to list all our assumptions at the start of our demonstrations, but Archimedes does not mention this assumption. So it seems he must have overlooked it as something that is too obvious to mention--this is surprising.
But further, in passing, raising the water level, or the level of a fluid, IS raising a weight; the weight of the fluid raised. And the distance a weight is moved is work. We can also raise a larger weight a smaller distance, by arranging for a smaller weight to move a larger distance in the opposite direction, as in the law of the lever, or as in hydraulics. And this seems a principle made use of in pulleys (pulleys don't necessarily move a large distance in the opposite direction to the direction of the load, and also the screw) and the Archimedes screw. (Also, it seems Aristotle held the law of the lever was linked to the perfection of circular motion, but if raising a fluid weight by submerging a weight is a balance, like a lever is a balance, this does not involve circular motion.)
But all this is much too quick for philosophy, and for rigorous mathematical demonstration. Archimedes and his bath involve comparisons and continuation of volumes. It also involves the comparison and continuation of properties. It will be no good if the weights of objects continually change for no reason, and it will be most helpful if they continue unchanged. The volumes wont continue if their objects dissolve, compress, evaporate, or are porous. Because we are only considering volumes that don't change for no reason, or for any of other reasons listed. This can seem as if we are making it definitional what sort of objects and properties we are considering. But this is a confusion, because definitions don't make things happen. On the present view we are restricting ourselves to a particular sort of object by our 'definition', but it is the existence of these sorts of object together in a situation that makes the result come about, not a definition.
As an example of issues involved in deciding what shape something has, and so what volume it has, let us ask why we think a round coin is round? After all a round coin will look lozenge shape from nearly all angles. I think this is because we don't want to draw conclusions beyond objects, as situations unfold, or develop, we want the same unaltered object to continue through the various variations we may notice regarding it. To this end, if we supposed the coin was lozenge shape, then although we could manipulate a lozenge so it looked round, unless we used lenses, the round size would appear smaller than the lozenge, just as a lozenge is smaller than its round coin, because the perspective and angle cut the apparent size down. But on the other hand if the coin is round we can easily account for its various lozenge appearances by perspective and the changed angles from which we look at it. And this sort of thing can be checked using geometry, others testimony, and comparison with other objects that are supposed to remain the same. This sort of principle will also be involved in judging if a lever, for instance, is symmetrical, although the view supposed is normally one where it is obviously symmetrical. (wrong again!).
Although it doesn't really apply to the normal experience of a coin, geometry can show why objects appear to change relative position at different distances from the observer, if they remain the same object. For example, the moon seems to follow you along if it is near the horizon and you move, say in a car. This is because the further away an object is the smaller the angle it changes for any distance moved, as you can see by a taller or shorter triangle with the same base. The taller it is, the smaller the angle at its top. So the moon, being at the top of a very tall triangle, does not seem to move relative to yourself although you move a large distance, and although the roadside scenery, being a lot nearer speeds past, showing large changes in apparent relative position.
Hume would try to explain this by coherence, and the way the mind runs along the different possible perceptions of such a coin, these principles of convenience making us regard the differently perceived states as one object for pragmatic reasons. But, on the contrary, if we don't have to go beyond the same state as that varies in its appearance to us, this claim does not have anything to do with the imaginations principles of connection.
I can further illustrate how we don't like things coming in and out of existence, because we don't understand it, with the childhood trick two little dickie birds sitting on a wall, where bits of paper stuck on fingers are made to disappear and re-appear, by swapping protruding fingers. Also the magicians trick of pulling a rabbit from an empty hat seems to work on the principle that obviously an empty hat is insufficient to produce a rabbit, and the case of the miracle of the feeding of the five thousand is similar. But it is not just that we don't like this sort of thing. In these cases we can't just suppose what is already there produces the difference, so the developing situation, apparently, can't be self sufficient. But if on the contrary we can see what happens as the result of factors already present, continuing, such situations will appear self sufficient. If situations do appear self sufficient then they can't appear to need to depend on anything else, so they will appear to be independent of ourselves and 'our understanding'. Nevertheless mighty oaks grow from small acorns and so the natural world can seem full of cases where the situation is miraculous from this perspective. It seems possible that some attempts at understanding are attempts to meet this apparent challenge of the discrepancy between situations apparently not appearing themselves sufficient, and our incorrigible naive realists objective to see how they are. In this way we can have an objective that is not based on any guarantee, or probability as to what will happen, although success towards this objective will give a reason as to what further should happen and why.
Another example illustrating this aim of seeing how a situation is self sufficient is provided by evolution through natural selection, which, especially originally, wasn't very good at providing any predictions. But because it showed how the natural world was itself sufficient to produce life forms and their relationships as currently observable it made the need for any grand designer god to account for these things, redundant. And explained the phenomena just by this 'showing how the environment was itself sufficient'.
Lets start again by noticing how to compare weights, and how we can know if any object has a weight. It seems that a weight can only be known by its effects . Such effects would be by squashing or stretching other objects, or by balancing other objects (or weights), or by feelings of heaviness when we try to push, pull, or lift an object. This last set of cases seem different from the others in that they involve qualitative feeling, perhaps with some movement, while the others involve quantities of movement only. Feelings and motions seem, on the face of it, completely different things; we could for instance see something move without any feeling being involved, and we can probably imagine, or dream, a feeling of weight, or heaviness, without seeing anything move (or close our eyes). Nevertheless, it may be that feelings of weight are a natural sign for the sort of interactions an object will have, just as words can be artificial signs for things completely different from the words. If the feelings of weight were such a naturally occurring sign or indication for how an object will behave, this might be very useful, and also very convincing as to how the object will behave. But for all that the connection would seem intellectually unsatisfactory because the feeling will just be found conjoined with something completely different--a motion--and how could we know that on other occasions it will also be found like that? Or why should it be the case if things are found like that?
These effects that I have mentioned are sorts of happening to other objects that are found to occur in the presence or application of an object. This is the sort of conjunction that Hume requires for his 'constant conjunction' theory of causation, except that we don't need the 'constant' element in that theory to supply the motivation or cause for our supposing the conjunction will happen again on a new occasion. And we don't need the constant element to supply the motivation for a universal idea, or law, from which we can deduce what will happen in a new instance. --I don't know whether this may seem a disastrous move from an empirical point of view, which is why no-one makes it.-- But this is because we are TRYING to see how that very object that was involved in such a conjunction, could produce, by continuing to act in that way, the occurrence in this new situation. This is so we can make progress towards our (incorrigible naive) objective of seeing how the contents of the situation could themselves be sufficient to bring about what happens. It is true though that we often can suppose how objects act will be as similar objects have acted. In this sort of case the objects will not have continued into the new situation being considered. But a different reason we might suppose a similar object should be found conjoined with a similar effect is, again, derived from thinking that the contents of a situation should be themselves sufficient to produce what happens. Because, if we do tend to think in this way we may also feel that (even if we don't know how they do it) if the contents of a situation THEMSELVES produce what occurs, and if we suppose we we have another situation with identical contents, then it should produce the same results, or there should be some difference between the two situations after all--which will give us a motivation to re-investigate both situations. Or else we'd have to admit we can't see how both identical situations could themselves produce different results (of course, it would not be logically impossible for identical situations to be found giving different results.) A related basis for inductions of this sort are arguments from symmetry. For instance, in the law of the lever, it is supposed that if both sides of a lever are symmetrically identical to each other, they should balance, as there could be no reason why one side would fall or rise more than the other. Philosophers don't normally seem to mention this sort of thing as a way of reasoning inductively, which apparently gives a reason why what happens on one occasion should happen on another and so does not just assume that the past will resemble the future. To repeat the reason is derived from causal realism; that the contents of a situation should themselves be sufficient to bring about what happens, and we can't see how this could be the case if identical states issue in different results (as with symmetry), even though that is perfectly imaginable from the point of view of what is logically possible.
There may be several reasons why philosophers never mention such a basis for induction, although it at least seems different from supposing the future will resemble the past. Firstly, perhaps they think if symmetrical arrangements produce identical effects this is a prime case of something that must be learnt from experience. I agree that experience can show similar states don't produce similar effects. We could also find it easily the case that similar states--or symmetrical states-- are obviously producing similar effects. But none of this shows we can't suppose symmetrical arrangements should produce similar effects because they should each be self sufficient, but how can we produce a different result when there is nothing different to produce it? Secondly, they don't think we can make sense of anything itself bringing about anything-- but the basis works even if we don't know how anything could actually itself produce anything. It relies on having any chance to to progress towards the objective of seeing how the contents of a situation could themselves be sufficient to produce what occurs. Thirdly they are looking for some increase in probability as to what will happen, or at least some probability for the alternative basis for induction. And fourthly it must seem a bit a-priori, and a-priori principles that have any meaningful content seem un believable and to raise questions about themselves that are just as awkward as what they are supposed to resolve. But symmetry, or causal realism, doesn't come with any guarantee, or probability as to being true. It does not come with a knowledge that it is true. But, if it were true that would give a self sufficient reason why e.g. symmetry, should be true, and should be a useful basis for making inductions. (This sentence may seem circular but if there were a self sufficient basis for something to happen, that could explain why it happens. That is not circular. Symmetry might be one of the things explained in this way. That is not circular. Symmetry might be used to judge a degree of self sufficiency, as what is symmetrical should in one case produce what is produced in the other. This is about the degree of self sufficiency apparent. Perhaps exact similarity, or perfect symmetry in constitutive reductions, might be as far as we can get towards apparent self sufficiency.)
But it may be that philosophers don't recognise symmetry as a different basis for inductions. Perhaps they think 'One side acts in a particular way, then we suppose we have another side that looks symmetrical to the first, so on the basis that a new instance will resemble a previous instance in a respect, when it resembles it in another (i.e. that the future resembles the past), then the second side should act the same as the first. So 'symmetry' is just another case of supposing the future will resemble the past.' However if we suppose there is a self sufficient reason for something to happen then it is not just the similarity between events that makes them act, or result in the same thing. A self sufficient reason for something to happen is different from a similarity of occurrences, although, if present, it should produce similar occurrences on similar occasions.
Hölder, Mach, and the Law of the Lever: A Case of Well-founded Non-controversy (openedition.org)
The above links to a discussion worth considering involving the nature of proof in mechanics, focusing on the proof of the law of the lever of Archimedes. But the discussion centres round the adequacy of the proof (or reasoning)' whether or not it assumes what is proved, or the assumptions contain what is proved; and the origins of the premises/assumptions, i.e. are they known a-priori, or derived from experience. However my question is "does the reasoning show how objects continuing to act as supposed WOULD act in the way "deduced", or described?" --I'm not concerned whether our 'knowledge' or thought that the objects have weight and continue 'with' it--continue to exhibit it, is known a-priori or by experience, but whether, if they do continue to act like that together in a situation, what the result would be. It is difficult to separate out this question. They are looking at origins and logical certainty, I am looking towards the result of the origins continuing to act as originally, in various situations, in which case those new situations can be seen as self sufficient in terms of that continued original behaviour.
Mach does not seem worried about allowing that things being symmetrical should produce the same results (balance). What he finds raises the question of 'how we could know that?' is when the proof moves from the symmetrical arrangements of weights along a suspended or balanced beam, to an A-symmetrical arrangement at reciprocally differing distances from the original balancing point. But, if weights symmetrically arranged around a point balance at that point then we can take any sub group of the originally arranged weights, find the point around which they are symmetrical and they will balance at that point. Since they balance at that point, that is the point at which their combined weights in effect act, just as the distributed weights on the original symmetrical beam, in effect, act as if combined at the centre point of the beam. (this 'in effect' just means, if we weigh this contraption supporting it at this point around which it is symmetrical, the result will be the combination of all the distributed weights, as if they were there.) If we now combine this subgroup at their sub groups balancing point then this shouldn't make any difference to the balance of the original beam because that point is where the uncombined group was (or is) in effect acting anyway. Although our randomly combined subgroup may appear to make an A-symmetrical distribution on the original beam.
But now I have tried to put this in a logical argument I suppose it will be thought what happens in the case depends on logic. But it doesn't, it depends on things continuing to act in a way. From their existing at any time, or acting at any time, nothing logically follows about their existence or action at any other time. And it isn't our having a universal idea of their existence or action that we can apply to a new time or opportunity for acting, that makes what happens occur, but their continuing in the new situation, with those properties.
In the context of measuring weight, Archimedes himself is also famous for his demonstration of the law of the lever, which uses a way weights can be compared, but we could also describe it as producing a principle for comparing weights. But all this only works if weights and volumes continue. According to the axiomatic method we are supposed to list all our assumptions at the start of our demonstrations, but Archimedes does not mention this assumption. So it seems he must have overlooked it as something that is too obvious to mention--this is surprising.
But further, in passing, raising the water level, or the level of a fluid, IS raising a weight; the weight of the fluid raised. And the distance a weight is moved is work. We can also raise a larger weight a smaller distance, by arranging for a smaller weight to move a larger distance in the opposite direction, as in the law of the lever, or as in hydraulics. And this seems a principle made use of in pulleys (pulleys don't necessarily move a large distance in the opposite direction to the direction of the load, and also the screw) and the Archimedes screw. (Also, it seems Aristotle held the law of the lever was linked to the perfection of circular motion, but if raising a fluid weight by submerging a weight is a balance, like a lever is a balance, this does not involve circular motion.)
But all this is much too quick for philosophy, and for rigorous mathematical demonstration. Archimedes and his bath involve comparisons and continuation of volumes. It also involves the comparison and continuation of properties. It will be no good if the weights of objects continually change for no reason, and it will be most helpful if they continue unchanged. The volumes wont continue if their objects dissolve, compress, evaporate, or are porous. Because we are only considering volumes that don't change for no reason, or for any of other reasons listed. This can seem as if we are making it definitional what sort of objects and properties we are considering. But this is a confusion, because definitions don't make things happen. On the present view we are restricting ourselves to a particular sort of object by our 'definition', but it is the existence of these sorts of object together in a situation that makes the result come about, not a definition.
As an example of issues involved in deciding what shape something has, and so what volume it has, let us ask why we think a round coin is round? After all a round coin will look lozenge shape from nearly all angles. I think this is because we don't want to draw conclusions beyond objects, as situations unfold, or develop, we want the same unaltered object to continue through the various variations we may notice regarding it. To this end, if we supposed the coin was lozenge shape, then although we could manipulate a lozenge so it looked round, unless we used lenses, the round size would appear smaller than the lozenge, just as a lozenge is smaller than its round coin, because the perspective and angle cut the apparent size down. But on the other hand if the coin is round we can easily account for its various lozenge appearances by perspective and the changed angles from which we look at it. And this sort of thing can be checked using geometry, others testimony, and comparison with other objects that are supposed to remain the same. This sort of principle will also be involved in judging if a lever, for instance, is symmetrical, although the view supposed is normally one where it is obviously symmetrical. (wrong again!).
Although it doesn't really apply to the normal experience of a coin, geometry can show why objects appear to change relative position at different distances from the observer, if they remain the same object. For example, the moon seems to follow you along if it is near the horizon and you move, say in a car. This is because the further away an object is the smaller the angle it changes for any distance moved, as you can see by a taller or shorter triangle with the same base. The taller it is, the smaller the angle at its top. So the moon, being at the top of a very tall triangle, does not seem to move relative to yourself although you move a large distance, and although the roadside scenery, being a lot nearer speeds past, showing large changes in apparent relative position.
Hume would try to explain this by coherence, and the way the mind runs along the different possible perceptions of such a coin, these principles of convenience making us regard the differently perceived states as one object for pragmatic reasons. But, on the contrary, if we don't have to go beyond the same state as that varies in its appearance to us, this claim does not have anything to do with the imaginations principles of connection.
I can further illustrate how we don't like things coming in and out of existence, because we don't understand it, with the childhood trick two little dickie birds sitting on a wall, where bits of paper stuck on fingers are made to disappear and re-appear, by swapping protruding fingers. Also the magicians trick of pulling a rabbit from an empty hat seems to work on the principle that obviously an empty hat is insufficient to produce a rabbit, and the case of the miracle of the feeding of the five thousand is similar. But it is not just that we don't like this sort of thing. In these cases we can't just suppose what is already there produces the difference, so the developing situation, apparently, can't be self sufficient. But if on the contrary we can see what happens as the result of factors already present, continuing, such situations will appear self sufficient. If situations do appear self sufficient then they can't appear to need to depend on anything else, so they will appear to be independent of ourselves and 'our understanding'. Nevertheless mighty oaks grow from small acorns and so the natural world can seem full of cases where the situation is miraculous from this perspective. It seems possible that some attempts at understanding are attempts to meet this apparent challenge of the discrepancy between situations apparently not appearing themselves sufficient, and our incorrigible naive realists objective to see how they are. In this way we can have an objective that is not based on any guarantee, or probability as to what will happen, although success towards this objective will give a reason as to what further should happen and why.
Another example illustrating this aim of seeing how a situation is self sufficient is provided by evolution through natural selection, which, especially originally, wasn't very good at providing any predictions. But because it showed how the natural world was itself sufficient to produce life forms and their relationships as currently observable it made the need for any grand designer god to account for these things, redundant. And explained the phenomena just by this 'showing how the environment was itself sufficient'.
Lets start again by noticing how to compare weights, and how we can know if any object has a weight. It seems that a weight can only be known by its effects . Such effects would be by squashing or stretching other objects, or by balancing other objects (or weights), or by feelings of heaviness when we try to push, pull, or lift an object. This last set of cases seem different from the others in that they involve qualitative feeling, perhaps with some movement, while the others involve quantities of movement only. Feelings and motions seem, on the face of it, completely different things; we could for instance see something move without any feeling being involved, and we can probably imagine, or dream, a feeling of weight, or heaviness, without seeing anything move (or close our eyes). Nevertheless, it may be that feelings of weight are a natural sign for the sort of interactions an object will have, just as words can be artificial signs for things completely different from the words. If the feelings of weight were such a naturally occurring sign or indication for how an object will behave, this might be very useful, and also very convincing as to how the object will behave. But for all that the connection would seem intellectually unsatisfactory because the feeling will just be found conjoined with something completely different--a motion--and how could we know that on other occasions it will also be found like that? Or why should it be the case if things are found like that?
These effects that I have mentioned are sorts of happening to other objects that are found to occur in the presence or application of an object. This is the sort of conjunction that Hume requires for his 'constant conjunction' theory of causation, except that we don't need the 'constant' element in that theory to supply the motivation or cause for our supposing the conjunction will happen again on a new occasion. And we don't need the constant element to supply the motivation for a universal idea, or law, from which we can deduce what will happen in a new instance. --I don't know whether this may seem a disastrous move from an empirical point of view, which is why no-one makes it.-- But this is because we are TRYING to see how that very object that was involved in such a conjunction, could produce, by continuing to act in that way, the occurrence in this new situation. This is so we can make progress towards our (incorrigible naive) objective of seeing how the contents of the situation could themselves be sufficient to bring about what happens. It is true though that we often can suppose how objects act will be as similar objects have acted. In this sort of case the objects will not have continued into the new situation being considered. But a different reason we might suppose a similar object should be found conjoined with a similar effect is, again, derived from thinking that the contents of a situation should be themselves sufficient to produce what happens. Because, if we do tend to think in this way we may also feel that (even if we don't know how they do it) if the contents of a situation THEMSELVES produce what occurs, and if we suppose we we have another situation with identical contents, then it should produce the same results, or there should be some difference between the two situations after all--which will give us a motivation to re-investigate both situations. Or else we'd have to admit we can't see how both identical situations could themselves produce different results (of course, it would not be logically impossible for identical situations to be found giving different results.) A related basis for inductions of this sort are arguments from symmetry. For instance, in the law of the lever, it is supposed that if both sides of a lever are symmetrically identical to each other, they should balance, as there could be no reason why one side would fall or rise more than the other. Philosophers don't normally seem to mention this sort of thing as a way of reasoning inductively, which apparently gives a reason why what happens on one occasion should happen on another and so does not just assume that the past will resemble the future. To repeat the reason is derived from causal realism; that the contents of a situation should themselves be sufficient to bring about what happens, and we can't see how this could be the case if identical states issue in different results (as with symmetry), even though that is perfectly imaginable from the point of view of what is logically possible.
There may be several reasons why philosophers never mention such a basis for induction, although it at least seems different from supposing the future will resemble the past. Firstly, perhaps they think if symmetrical arrangements produce identical effects this is a prime case of something that must be learnt from experience. I agree that experience can show similar states don't produce similar effects. We could also find it easily the case that similar states--or symmetrical states-- are obviously producing similar effects. But none of this shows we can't suppose symmetrical arrangements should produce similar effects because they should each be self sufficient, but how can we produce a different result when there is nothing different to produce it? Secondly, they don't think we can make sense of anything itself bringing about anything-- but the basis works even if we don't know how anything could actually itself produce anything. It relies on having any chance to to progress towards the objective of seeing how the contents of a situation could themselves be sufficient to produce what occurs. Thirdly they are looking for some increase in probability as to what will happen, or at least some probability for the alternative basis for induction. And fourthly it must seem a bit a-priori, and a-priori principles that have any meaningful content seem un believable and to raise questions about themselves that are just as awkward as what they are supposed to resolve. But symmetry, or causal realism, doesn't come with any guarantee, or probability as to being true. It does not come with a knowledge that it is true. But, if it were true that would give a self sufficient reason why e.g. symmetry, should be true, and should be a useful basis for making inductions. (This sentence may seem circular but if there were a self sufficient basis for something to happen, that could explain why it happens. That is not circular. Symmetry might be one of the things explained in this way. That is not circular. Symmetry might be used to judge a degree of self sufficiency, as what is symmetrical should in one case produce what is produced in the other. This is about the degree of self sufficiency apparent. Perhaps exact similarity, or perfect symmetry in constitutive reductions, might be as far as we can get towards apparent self sufficiency.)
But it may be that philosophers don't recognise symmetry as a different basis for inductions. Perhaps they think 'One side acts in a particular way, then we suppose we have another side that looks symmetrical to the first, so on the basis that a new instance will resemble a previous instance in a respect, when it resembles it in another (i.e. that the future resembles the past), then the second side should act the same as the first. So 'symmetry' is just another case of supposing the future will resemble the past.' However if we suppose there is a self sufficient reason for something to happen then it is not just the similarity between events that makes them act, or result in the same thing. A self sufficient reason for something to happen is different from a similarity of occurrences, although, if present, it should produce similar occurrences on similar occasions.
Hölder, Mach, and the Law of the Lever: A Case of Well-founded Non-controversy (openedition.org)
The above links to a discussion worth considering involving the nature of proof in mechanics, focusing on the proof of the law of the lever of Archimedes. But the discussion centres round the adequacy of the proof (or reasoning)' whether or not it assumes what is proved, or the assumptions contain what is proved; and the origins of the premises/assumptions, i.e. are they known a-priori, or derived from experience. However my question is "does the reasoning show how objects continuing to act as supposed WOULD act in the way "deduced", or described?" --I'm not concerned whether our 'knowledge' or thought that the objects have weight and continue 'with' it--continue to exhibit it, is known a-priori or by experience, but whether, if they do continue to act like that together in a situation, what the result would be. It is difficult to separate out this question. They are looking at origins and logical certainty, I am looking towards the result of the origins continuing to act as originally, in various situations, in which case those new situations can be seen as self sufficient in terms of that continued original behaviour.
Mach does not seem worried about allowing that things being symmetrical should produce the same results (balance). What he finds raises the question of 'how we could know that?' is when the proof moves from the symmetrical arrangements of weights along a suspended or balanced beam, to an A-symmetrical arrangement at reciprocally differing distances from the original balancing point. But, if weights symmetrically arranged around a point balance at that point then we can take any sub group of the originally arranged weights, find the point around which they are symmetrical and they will balance at that point. Since they balance at that point, that is the point at which their combined weights in effect act, just as the distributed weights on the original symmetrical beam, in effect, act as if combined at the centre point of the beam. (this 'in effect' just means, if we weigh this contraption supporting it at this point around which it is symmetrical, the result will be the combination of all the distributed weights, as if they were there.) If we now combine this subgroup at their sub groups balancing point then this shouldn't make any difference to the balance of the original beam because that point is where the uncombined group was (or is) in effect acting anyway. Although our randomly combined subgroup may appear to make an A-symmetrical distribution on the original beam.
But now I have tried to put this in a logical argument I suppose it will be thought what happens in the case depends on logic. But it doesn't, it depends on things continuing to act in a way. From their existing at any time, or acting at any time, nothing logically follows about their existence or action at any other time. And it isn't our having a universal idea of their existence or action that we can apply to a new time or opportunity for acting, that makes what happens occur, but their continuing in the new situation, with those properties.
Re: Philosophers on Baths
objectives;
1) To understand how the contents of a situation could bring about what occurs
2) To produce successful predictions of what will happen
3) To find axioms that are certain from which everything else must follow
All these three seem distinct although pursuing 2) might incidentally result in something that seems like 1) and visa versa pursuing 1) might produce an effective way for making predictions. On the other hand 3) is liable to seem a priory, and proof that 3) is impossible has been taken to show that 1) is impossible. (And, independently, the causal theory of perception may be taken to show 1) is impossible.) 3) seems the most systematic way to present the understanding of a subject. However that is; pursuing 1) is working towards a goal, as is 2), it is not necessarily, or obviously, working from axioms.
Pursuing 1); Going by Hume's habit hypothesis, we must be able to see if several occasions appear similar or not, or be able to tell what would happen on a new occasion if it is to be similar to what we have experienced. --It would be no good trying to suppose that the future will, or does, resemble the past if we can't tell if the future resembles the past or not. So, if an object behaves in a recognizable way on one occasion, we should be able to tell what would happen if that object were in another, similar situation, and behaved in that way. This may not give anything like an ultimate basis, or real being, for why what happens does so, but nevertheless we may see how the conglomeration of properties that constitutes an object on one occasion could produce what happens on another occasion, if it were in that situation and acted similarly, and without this being produced by habit, but from the motive of trying to see how the sort of thing found in a situation could produce what happens in a situation. This seems distinct from, but not inconsistent with a supposition that an object continues into a new situation, or from supposing that a indistinguishable situation should produce an indistinguishable result, or we wont have anything to work with to suppose the contents of the situation produce what happens.
For example, when geologists see particular structures on the surface of Mars they hypothesize that that is what would be produced if water had flowed on the martian surface. Or if astronomers can measure a dip in the brightness of a star they can suggest that that is what would happen if a planet orbiting the star passes between us and the start. This differs from using a habit to decide what will happen, or what we will believe, It is instead making comparisons and trying to match some actual occurrence with another actual occurrence or supposed situation.
1) To understand how the contents of a situation could bring about what occurs
2) To produce successful predictions of what will happen
3) To find axioms that are certain from which everything else must follow
All these three seem distinct although pursuing 2) might incidentally result in something that seems like 1) and visa versa pursuing 1) might produce an effective way for making predictions. On the other hand 3) is liable to seem a priory, and proof that 3) is impossible has been taken to show that 1) is impossible. (And, independently, the causal theory of perception may be taken to show 1) is impossible.) 3) seems the most systematic way to present the understanding of a subject. However that is; pursuing 1) is working towards a goal, as is 2), it is not necessarily, or obviously, working from axioms.
Pursuing 1); Going by Hume's habit hypothesis, we must be able to see if several occasions appear similar or not, or be able to tell what would happen on a new occasion if it is to be similar to what we have experienced. --It would be no good trying to suppose that the future will, or does, resemble the past if we can't tell if the future resembles the past or not. So, if an object behaves in a recognizable way on one occasion, we should be able to tell what would happen if that object were in another, similar situation, and behaved in that way. This may not give anything like an ultimate basis, or real being, for why what happens does so, but nevertheless we may see how the conglomeration of properties that constitutes an object on one occasion could produce what happens on another occasion, if it were in that situation and acted similarly, and without this being produced by habit, but from the motive of trying to see how the sort of thing found in a situation could produce what happens in a situation. This seems distinct from, but not inconsistent with a supposition that an object continues into a new situation, or from supposing that a indistinguishable situation should produce an indistinguishable result, or we wont have anything to work with to suppose the contents of the situation produce what happens.
For example, when geologists see particular structures on the surface of Mars they hypothesize that that is what would be produced if water had flowed on the martian surface. Or if astronomers can measure a dip in the brightness of a star they can suggest that that is what would happen if a planet orbiting the star passes between us and the start. This differs from using a habit to decide what will happen, or what we will believe, It is instead making comparisons and trying to match some actual occurrence with another actual occurrence or supposed situation.