Criticism of Salmon on Popper

Wesley Salmon wrote a critique of critical rationalism in which he claimed this it could not explain why it is rational to use the predictions of scientific theories to help us make decisions. First, note that Salmon does not and cannot refute Popper’s criticism of inductivism. There is a very simple reason for that: the criticism is valid.

Second, Salmon states (p. 11) that Popper once wrote that a realist will think there are regularities in the world. Realism, by Popper’s lights, is a conjecture and should be treated by the standards of any other conjecture: that is, it should be retained if it can withstand criticism. To be an inductivist, Popper would have to hold the opinion that observations imply something about the future, but of course this is not implied by the statement that there are regularities in the real world. Observations plus the laws of physics may imply something about the future, but of course that cannot tell us about the status of our knowledge of those laws.

Finally, critical rationalism does say things about what sort of predictions are rational: those predictions should be made in ways that have so far withstood criticism and should be easy to criticise if they go wrong. Furthermore, we should take steps to make our predictions and practical actions easy to criticise. We should also take steps to respond to the criticisms we receive. So, for example, when planes are built the best available theories of aerodynamics will be used to constrain the design. Why? Because if we didn’t we would have an unexplained discrepancy between our explanation of why we chose a specific plane design and the best available theories about the real world in which that plane will operate. Those aerodynamic theories are in turn retained because they stand up to criticism, solve problems, explain things that other theories don’t explain and so on. Some of the components, or models of those components, may be tested in wind tunnels. The plane carries a black box that collects information about the plane during flight in case something goes wrong so that it will be easier to criticise the performance of the plane’s components. All of this involves only conjecture and critical argument and it is rational by Popper’s lights.

This procedure is not rational by Salmon’s lights because he is a justificationist – he thinks that decisions can and should be proven right or made more probable to work or something like that. However, he doesn’t produce any proposal for how such justification could be had and there is a straightforward logical argument that indicates that this is impossible. That is, any argument uses premises and rules of inference and its conclusions are only proven or probable if those inputs are proven or probable. How are we going to show the inputs are proven or probable: another argument with more premises and rules of inference that have to be proven or shown to be probable? Seems to me that would lead to infinite regress and to no decisions ever being made. This is supposed to be practical?

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68 Responses to Criticism of Salmon on Popper

  1. Peter D Jones says:

    “Second, Salmon states (p. 11) that Popper once wrote that a realist will think there are regularities in the world. Realism, by Popper’s lights, is a conjecture and should be treated by the standards of any other conjecture: that is, it should be retained if it can withstand criticism. To be an inductivist, Popper would have to hold the opinion that observations imply something about the future, but of course this is not implied by the statement that there are regularities in the real world. ”

    In fact:
    1: X’s have observed to be F in the past
    2 Past regularities will continue into the future
    3 Therefore,, X’s will continue to be F’s.

    Is a valid deductive argument. The problem of induction
    is not the problem of just deductively justifying induction,
    it is also the problem of epistemically justifying the deductive
    argument — particularly premise 2

    It seems that a Popperian who conjectures premise 2,
    the Uniformity of Nature, is then entitled to carry on using induction blithely — that a Popperian in fact only ever needs to make the one conjecture

    “Finally, critical rationalism does say things about what sort of predictions are rational: those predictions should be made in ways that have so far withstood criticism and should be easy to criticise if they go wrong.”

    And Salmon has a particularly pertinent criticism here: Popperians
    cannot offer the justification that other well-tested conjectures have
    proved reliable in the past, since that is an appeal to induction. It is also difficult to see what deductive argument they could be appealing to. It is also not helpful for them to say that is is obviously and intuitively rational to make use of well-tested theories, since the inductivist can also appeal to psychology and intuitiveness to support induction.

    ” aerodynamic theories are in turn retained because they stand up to criticism, solve problems, explain things that other theories don’t explain and so on”

    There’s always an infinity of theories which aren’t refuted by the facts. Salmon criticises Popperians for having no consistent
    grounds for making the choices they make.

    “However, he doesn’t produce any proposal for how such justification could be had and there is a straightforward logical argument that indicates that this is impossible. That is, any argument uses premises and rules of inference and its conclusions are only proven or probable if those inputs are proven or probable. How are we going to show the inputs are proven or probable: another argument with more premises and rules of inference that have to be proven or shown to be probable? Seems to me that would lead to infinite regress and to no decisions ever being made. ”

    We typically curtail such regresses with appeals to observation. I can justify “there are two bottles of milk in the fridge” by opening the door and looking. If Popper
    has facts that are firm enough to refute a theory, he has facts that are firm enough to stop a regress.

  2. Lee Kelly says:

    Peter,

    I do not believe you appreciate the extent of the Popperian rejection of induction, and neither, I suspect, did Salmon. Of course, Popperians, like others, make generalisations, and sometimes these are motivated by previous experience. The contention, however, is that such matters are irrelevant to methodology and epistemology. Our goal is not to describe how people think, per se, but the growth of objective knowledge.

    In any case, while you present a valid argument, it does not “deductively justify induction.” The conclusion of a valid argument cannot be justified by its premises, regardless of whether the argument is sound. What follows is a simple metalogical proof.

    Let x be a metalogical variable, i.e. a variable that stands in place of some logical formula, and let A be a non-empty set of such formula. Here is our only premise:

    1. A |= x

    In words, the set of formula in A entails x. From the law of identity and the premise (1), we can immediately get the following:

    2. A |= A, x

    Leaving (2) aside, we can return to the original premise (1) and get this:

    3. A, x |= x

    From (3) this follows:

    4. A, x |= A, x

    And finally, from (4) we get:

    5. A, x |= A

    All this should be quite elementary. But notice (2) and (5). Together we get a semantic equivalence:

    6. A, x =||= A

    If (6) is true, then any instance of “A” can be substituted with “A, x” and still mean the same thing. Thus, we get:

    “A |= x” is equivalent to “A, x |= x”

    Since the latter formulation of the argument is question begging, so must be the former. The difference is merely that one is more obviously question begging than the other. This result holds for all valid arguments that proceed from any non-empty set of premises A to any conclusion x.

    Since convention has it that the premises of an argument (valid or not) do not justify their conclusion if they assume (implicitly or explicitly) the conclusion in the premises, it seems to me that the premises of a valid argument can never justify their conclusion. It is important to add here that “question begging” depends on what one intends an argument to achieve. One can avoid the charge of begging the question merely by repudiating the intent to justify one’s conclusion. Logic need not serve that end.

  3. Peter D Jones says:

    It is rather well known that all valid deductive arguments are in a sense question begging. A common response is to restrict fallaciously question-begging arguments to those whose conclusion is explicitly stated in their premises, such as “Socrates is mortal because Socrates is mortal”.

  4. Lee Kelly says:

    Peter,

    Such a restriction presents a peculiar situation. Are complex and abstruse arguments preferable to simple and precise arguments, because the former are less obviously question begging? Would such a rule not encourage obscurantism?

    In any case, regardless of whether one’s question begging is explicit or implicit, the premises cannot justify the conclusion. The argument is merely an exploration of the logical consequences of the premises. Even if someone already accepts the premises as true, they are under no logical compulsion to accept the conclusion. If they persist in believing the premises are false, one could use the conclusion to “justify” rejecting the premises.

    Besides, no valid arguments are not question begging, per se. Whether an argument begs the question depends on the intent of the person arguing. If one does not intend for the premises to justify the conclusion, then nobody is begging the question.

  5. Lee Kelly says:

    Correction: “no valid arguments are question begging, per se.”

  6. Alan Forrester says:

    You say that “past regularities will continue into the future”. But many regularities noticed in the past have not continued, e.g. – Newtonian mechanics. A Popperian who conjectured that “past regularities will continue into the future” would have to abandon that conjecture because it is false.

    “Finally, critical rationalism does say things about what sort of predictions are rational: those predictions should be made in ways that have so far withstood criticism and should be easy to criticise if they go wrong.”

    And Salmon has a particularly pertinent criticism here: Popperians cannot offer the justification that other well-tested conjectures have proved reliable in the past, since that is an appeal to induction. It is also difficult to see what deductive argument they could be appealing to.

    I don’t have to say that well-tested conjectures will be reliable. Any particular conjecture is either right or wrong. If I refute a conjecture, then I have eliminated a bad idea. So I have a means of controlling my ideas.

    There’s always an infinity of theories which aren’t refuted by the facts. Salmon criticises Popperians for having no consistent grounds for making the choices they make.

    Being strictly logically compatible with the facts is not the only constraint. The theory also has to be easily criticisable. It also has to be a good explanation: that is, the details of the explanation should be related to the thing to be explained. “Poseidon causes the sea to be rough” is a bad explanation because it doesn’t explain how Poseidon does this, or why only Poseidon should be relevant and so on.

    “However, he doesn’t produce any proposal for how such justification could be had and there is a straightforward logical argument that indicates that this is impossible. That is, any argument uses premises and rules of inference and its conclusions are only proven or probable if those inputs are proven or probable. How are we going to show the inputs are proven or probable: another argument with more premises and rules of inference that have to be proven or shown to be probable? Seems to me that would lead to infinite regress and to no decisions ever being made.”

    We typically curtail such regresses with appeals to observation. I can justify “there are two bottles of milk in the fridge” by opening the door and looking. If Popper has facts that are firm enough to refute a theory, he has facts that are firm enough to stop a regress.

    A purported fact, like an experimental observation, say, is a conjecture. Let’s suppose I do an experiment and it seems to contradict my favourite theory about cheese. There are many possible explanations of this: (1) my cheese theory might be wrong, (2) I may have performed the experiment in a way that didn’t fit the specifications, (3) the specifications for the experiment might be wrong. I can try to come up with conjectures that fit each of these scenarios and test them independently of the problem they were originally supposed to solve. I don’t have to prove anything in order to do any of this, which is just as well.

    When you think you’ve looked in the fridge and seen the milk and so you think you have milk, you could easily be wrong. Perhaps you looked in the fridge yesterday and have done so every day before that for years and you got mixed up about whether you looked in the fridge today. Or perhaps you dreamed you looked in the fridge and saw milk.

  7. Peter D Jones says:

    Lee,

    “Such a restriction presents a peculiar situation. Are complex and abstruse arguments preferable to simple and precise arguments, because the former are less obviously question begging? Would such a rule not encourage obscurantism?”

    No,because even simple arguments like…

    Socrates is a man
    Men are mortal,
    Therefore, Socrates is mortal

    …are not question-begging in the sense I have defined. The idea is that one
    has to avoid explicit repetion of a premiss in a conclusion, not that one
    has to make things as complictated as possible.

    “In any case, regardless of whether one’s question begging is explicit or implicit, the premises cannot justify the conclusion. ”

    That is what is under discussion — it has yet to be established

    “The argument is merely an exploration of the logical consequences of the premises.”

    If the premisses are true — albeit for exta-logical reasons — any validly drawn conclusion will be true,

    “Even if someone already accepts the premises as true, they are under no logical compulsion to accept the conclusion. ”

    I can’t imagine why you would assert that. If someone accepts the premises,
    andthe validity of the netailmentof the conclusion, how can they not be rationally be obliged to accept the conclusion?

    “If they persist in believing the premises are false, one could use the conclusion to “justify” rejecting the premises.”

    People do sometime sreject premisses becau the don’t like the conclusions
    they lead to, but I donn’t see how that relates to your point above — where
    the individual does in fact accept the premisses

    “Besides,no valid arguments are question begging, per se.”

    No valid arguments are fallacioulsy question begging. They may still be question begging, “in a sense” that does not entail fallaciousness. It is not
    helpful, at this stage of the argument, to treat question-begging-ness as uniform.

    “Whether an argument begs the question depends on the intent of the person arguing”.

    Logic is all about explicitness. I don’t think it is any good to pin fallaciousness on anything as doubtful and inacessible as psychological intent.

    “If one does not intend for the premises to justify the conclusion, then nobody is begging the question”

    In a valid argument, the premises must entail the conclusion — otherwise it is non-sequitur. The problem with fallacious question-begging is that the entailment is trivial and uninformative. (Being informed, explicitly, that something is an entailment of ideas you already accept is still being informed. We are not in a position to instantaneoiusly figure out the consequences of all our beliefs).

  8. Lee Kelly says:

    Peter,

    If by “justified” you merely mean “is entailed by some premises that may or may not be true,” then you will get no more argument from me. However, I believe “justification” is traditionally defined more strongly, and expected to do far more than stand in place of “entailed.”

  9. Peter D Jones says:

    Lee,
    I can take “deductively justified” to mean “entailed by true premises” and that will not be affected by the “question begging” argument.

  10. Lee Kelly says:

    Peter,

    That definition is not the target of my criticism. Indeed, such a definition seems misleading, at worst, and at best, useless. The matter of whether a conclusion is “deductively justified” is an objective property of an argument, more or less identical to the concept of soundness, that cannot be established by fallible beings. That is fine, in my opinion, because I am contented with fallibilism. But people usually intend their “justifications” to do more, normally to carry the weight of some incorrigible authority.

    In any case, by your own definition, the original “deductive justification” of induction that you provided does no such thing. I have some objections regarding its validity, though here I merely wish to say that premises 2, “past regularities will continue in the future”, is false when interpreted as a universal. If not universal, then the conclusion does not follow deductively.

  11. Peter D Jones says:

    Lee,

    “That definition is not the target of my criticism. Indeed, such a definition seems misleading, at worst, and at best, useless. The matter of whether a conclusion is “deductively justified” is an objective property of an argument, more or less identical to the concept of soundness, that cannot be established by fallible beings. “

    That we are fallible does not mean we are never able to know anything. (If it did, it would be a disater for Popperians, as they would never know if they
    had refuted a conjecture). Fallibilism only implies a lack of certainty, and it is quite compatbile with justificationism. That it is possible to lend positive support
    to an argument does not imply that it is possible to lend certain support.

    “But people usually intend their “justifications” to do more, normally to carry the weight of some incorrigible authority.”

    I don’t think that is the case at all, at leat as far as informed opinion goes. Every contemporay inductivist seems to regard induction as problistic, for instance.

    “In any case, by your own definition, the original “deductive justification” of induction that you provided does no such thing. “

    You mean it isn’t incorrigibly true? I suppose not. It is only needs to be as good
    as any other deductive argument in this fallibilistic world.

    “I have some objections regarding its validity, though here I merely wish to say that premises 2, “past regularities will continue in the future”, is false when interpreted as a universal. “

    What would constitute a counterexample? When did a law of nature ever stop working?

  12. Rafe says:

    Peter, what would the inductivists regard as a successful outcome of their program?

  13. Kenneth Hopf says:

    Peter,

    One of Popper’s earliest concerns about scientific methodology was that it is always possible to hold a position as true come what may. Your comments about induction and justification seem to illustrate this point once again. Clearly, critical rationalists are not suggesting it is impossible to arrange one’s definitions so as to be able to continue talking about induction or justification without contradiction.

    You can always say, well, I’ll call that thing there induction, and that thing over there justification. Indeed, this is precisely what Ellery Eells does in response to the proof, given by Popper and Miller, that probabilistic support cannot be inductive (i.e., ampliative) support. What we are told by Eells is that even deduction is, in a strange way, inductive! Why? Because we can learn something from a deduction that we didn’t know before. And that’s induction. Shazam! Induction is suddenly everywhere.

    I notice that you also identify such a move as justificatory. But let me ask you this: do you really think all these academic philosophers agonizing over epistemic justification and Gettier problems simply haven’t noticed that mathematicians solved the problem of justification centuries ago (e.g., Euclid)?

    My point here is that even philosophers who repudiate critical rationalism entirely don’t think that you get epistemic justification out of a deductively valid inference. If they did, they would’ve folded their tents a long time ago. Why bother with Gettier problems? So let’s not get too excited by the possibility of using these immunizing tactics. Yes, yes … we know that you can shift labels around. But that’s really just another way of conceding defeat.

    It seems to me that induction at least has been long since driven from its ancestral homelands. Still, critical rationalists perhaps have not been perfectly clear about what it is they object to. Prolific, perhaps, but not perfectly clear. After all, one might still say that theories do come from experience in the sense that our brain or mind evolve in response to our environment. So if we invent a theory, there is still some sense in which we must give priority to experience, as inductivists would have it.

    My response to all this is that it may have been a fair criticism before Popper and Miller published their critique of probabilistic induction in 1983; but that once this paper was published it can no longer be doubted what exactly critical rationalists are talking about when they reject induction, because now it can be put in coldly logical and mathematical terms.

    Consider, for example, that we have some hypothesis, h, some evidence, x, and some background knowledge, b. Then the proof offered by Popper and Miller suggests the following definition of inductivism, i.e., the view that the following expression is true:

    (Ex)[p(h <- x, xb) – p(h <- x, x)] = (Ex)[s(h <- x, x, b)] > 0

    What Popper and Miller prove is that there can be no evidence satisfying this equation. You can find a short and sweet proof of their result on page 73 of David Miller’s book, _Critical Rationalism, A Restatement and Defense_. It is perhaps worth noting that, even if one finds fault in some way with assertions about the significance of the finding, the expression given above may still serve perfectly well as a definition of inductivism.

    Of course, this leaves the matter of justificationism out of account. I hope you agree, however, that it simply will not do identify justification with deductively valid inference. This makes nonsense out of the history of justificationist epistemology, as noted above. What can we say on a more positive note? To me it seems that Bartley has been extremely vivid about what exactly constitutes a justification. All the talk of Archimedes’ Lever and so forth is memorable. I’m tempted to say, if you don’t get it after all that, you just don’t want to get it. Still, it never hurts to push for more.

    My guess would be this: anti-justificationism is the view that there can be no objective criterion of verisimilitude. This amounts to saying that, while we may be able to obtain a realistic ordinal ranking of competing theories, there can be no realistic cardinal ranking of them. In other words, we cannot ascertain non-relative values for degree of corroboration. We can only compare one theory to another declare a relative ranking in terms of, say, degree of corroboration. We cannot obtain any non-relative measure of a theory’s closeness to the truth.

  14. Peter D Jones says:

    Kenneth,

    One of Popper’s earliest concerns about scientific methodology was that it is always possible to hold a position as true come what may.

    Nevertheless, some historical positions were rejected

    Your comments about induction and justification seem to illustrate this point once again. Clearly, critical rationalists are not suggesting it is impossible to arrange one’s definitions so as to be able to continue talking about induction or justification without contradiction.

    I don’t think there is anything non-standard about the claim that a sound argument justifies its conclusion.

    I also don’t think Popperians are immune from shfiting definitions. They don’t seem to be employing the dictionary definition of “corroboration”, for instance (“To strengthen or support with other evidence”)

    I also don’t think it is always a bad thing. I have no problem with the fact that we stopped defining atoms as indivisible after splitting them

    do you really think all these academic philosophers agonizing over epistemic justification and Gettier problems simply haven’t noticed that mathematicians solved the problem of justification centuries ago (e.g., Euclid)?

    I never said that all justification is mathematical, just that sound deductions justify their conclusions. Other forms of justification may be more problematical.
    But do you think all those academic philosophers are too stupid to realise that wholesale abandonment of justification is the answer? Perhaps they are smart enough to realise that whatever objections can be levelled against justification (or at least warrant) , parallel ones can be levelled against refutation (or at least criticism).

    So let’s not get too excited by the possibility of using these immunizing tactics. Yes, yes … we know that you can shift labels around. But that’s really just another way of conceding defeat.

    Fine..then you have no corroborated theores..

    After all, one might still say that theories do come from experience in the sense that our brain or mind evolve in response to our environment. So if we invent a theory, there is still some sense in which we must give priority to experience, as inductivists would have it.

    The objection that indictive arguments do not justify their conclusions is no hindrance to using repeated observation as a source of conjecture. I don’t believe KP puts any restrictions on where you get your conjectures from.

    What Popper and Miller prove is that there can be no evidence satisfying this equation. You can find a short and sweet proof of their result on page 73 of David Miller’s book, _Critical Rationalism, A Restatement and Defense_. It is perhaps worth noting that, even if one finds fault in some way with assertions about the significance of the finding, the expression given above may still serve perfectly well as a definition of inductivism.

    Every account of that argument has seen has summarised it as concluding that
    induction is actually deduction — music to the ears of those inductivists who thought that all along. If Hume had thought induciton entirely distinct from deduction, why would he have worried that is not deuctively justified?

    Of course, this leaves the matter of justificationism out of account. I hope you agree, however, that it simply will not do identify justification with deductively valid inference.

    I didn’t. I was using the “is” of predication (or set membership) not the is
    of identity.

    >This makes nonsense out of the history of justificationist epistemology, as noted above. What can we say on a more positive note? To me it seems that Bartley has been extremely vivid about what exactly constitutes a justification. All the talk of Archimedes’ Lever and so forth is memorable. I’m tempted to say, if you don’t get it after all that, you just don’t want to get it. Still, it never hurts to push for more.

    My guess would be this: anti-justificationism is the view that there can be no adequate theory of verisimilitude. This amounts to saying that, while we may be able to obtain a realistic ordinal ranking of competing theories, there can be no realistic cardinal ranking of them. In other words, we cannot ascertain non-relative values for degree of corroboration.

    That is a rather weak claim, and does not really contradict what I have been aiming at, which is just that there is some sort of positive support or warrant
    beyond lack of refutati0n — which is still contra Popperism.

  15. Lee Kelly says:

    Peter,

    I do not accept your definition of “justification” as conventional. The usual end of justification is to provide a method of identifying sound arguments. The attempt normally involves selecting some proposition or set of propositions that are apodictic, self-evident, or come from an authoritive source. Such propositions are considered inherently justified, without reference to further premises, because they are necessarily true or probable. Arguments are then identified as sound (or probable) because they are justified by such premises. A valid argument with true premises may pass as unacceptable because it cannot be justified by any special propositions or authoritive source.

    If justification cannot furnish arguments with something like what is described above, then it is an even more useless concept than I realised.

  16. Kenneth Hopf says:

    Peter,

    The claim is not that people never say a sound argument justifies its conclusions. Of course they do. People say that all sorts of things are justified. For instance, if you’re late for a meeting, your boss may ask if you to justify your tardiness. “Oh, I got into an automobile accident.” That’s justification in a vernacular sense as well. Well all know this. Further, if this is your response to the observation that ‘justification’ clearly means something else in history of Western epistemology, then you’re merely playing shell games with words.

    Once again, nobody who participates seriously in the epistemological debate about knowledge as justified true belief thinks that epistemic justification consists of a deductively valid inference. Further, there is a vast (entirely sterile) literature in which this simple fact is taken for granted. Just looking at my own bookshelf, for instance, I spy the following boring tomes: _Warrant: The Current Debate_, by Alvin Plantinga; _The Possibility of Knowledge, Nozick and His Critics_, edited by Steven Luper-Foy; _Problems of Knowledge_, by Michael Williams; _On Knowing and the Known_, edited by Kenneth G. Lucey. I could on citing references for hundreds of pages.

    So there is nothing strange about the use to which critical rationalists put the term ‘justification’. Nor is there anything unusual about the observation that a deductively valid inference isn’t what the current epistemological debate is about. If this plain fact on the ground cannot be honestly faced, then it seems unlikely to me that there can be much of a discussion. Perhaps you prefer to call it warrant, or something along those lines. That’s perfectly fine: warrant it shall be. As Popper always emphasized, words do not really matter. We’re trying to talk about the things to which words refer.

    Now you mention that “Popperians” are also not immune to shifting definitions. But shifting definitions per se is innocuous unless it serves to evade criticism. If anyone does that, including “Popperians”, then they ought to be called on it. Most critical rationalists I know try to make a point of not doing this sort of thing. In fact, not doing this was one of Popper’s methodological proposals in LSD. So it’s rather ironical that you should bring this up.

    The example you choose to illustrate the alleged malfeasance of critical rationalists in this respect backfires on you rather badly. Specifically, you mention the dictionary definition of corroboration. If you look at chapter 4 of _Realism and the Aim of Science_ you will see that Popper 1) goes on for pages about how he intends to appropriate the term ‘corroboration’, how he doesn’t like to do it but sees no more practical alternative — emphasizing that we could call it something else if we like, and 2) presents an extensive theory of corroboration, a theory which, if you look what it actually says, completely knocks the pins out from under your passing remark that, by abandoning justification, we abandon corroboration as well. In any event, none of this even remotely qualifies as evading criticism.

    Corroboration doesn’t depend in the slightest on justification. And if you care to go into the details we can illustrate why this is the case. Corroboration is not a form of justification. It is true, however, that Popper made a mistake in this connection. He suggested, in several places I believe, that corroboration should be a prerequisite for acceptance, or that the best corroborated theory is the most acceptable theory. This is incorrect. But it is a minor flaw that is easily corrected, and was corrected even by Popper.

    The reason Popper investigated corroboration, and presented a theory of corroboration, is that he wanted to clear up a muddle created by mistaken views on inductive probabilities. In this he succeeded admirably. More importantly, once we correct the insignificant error that corroboration has something to do with acceptance, Salmon’s whole critique falls apart. Salmon says that corroboration is either empty or it’s induction. The correct answer to Salmon is that it’s empty: corroboration plays no epistemological role whatever. It is simply the result of a failed attempt at falsification.

    Salmon’s only response to this is that, without using corroboration to promote theories, the falsificationist is left with no way of producing a leading candidate for the truth. This is what I would call epistemological Lamarckism, the view that criticism, though perhaps necessary, is not a sufficient means of finding true theories. The picture Salmon presents is that, without something like induction, we would be drowning in a sea of possible explanations. But this is simply absurd. Most of the possibilities we can think of fail immediately, or clash with other theories. Many more can be eliminated for strictly logical reasons. Long before we get to corroborating anything, we’re typically left with nothing at all, and when that is not the case we’re lucky to have one or two candidates in any particular field. Salmon talks as if falsification is the only thing that falsificationists care about, because if he didn’t do that it would be immediately obvious that his description of the actual problem situation in science is ludicrously unrealistic.

    Now you ask if I think that “all those academic philosophers are too stupid to realise that wholesale abandonment of justification is the answer”. My answer is No; it’s not that they’re too stupid to realise something; it is rather that they’re asking the wrong question. Critical rationalists do not say that the wholesale abandonment of justification is “the answer”. What they say is that there is no answer to the question being asked, and that one ought to abandon that question as misguided.

    What is the question? It is basically the question asked by Plato in both the Meno and the Theaetetus (among other places): how can we distinguish genuine knowledge from true opinion? This is the central project of Western epistemology. Plato himself initially accepted but later rejected the idea that knowledge is distinguished from true opinion by being justified (by a logos, or, as Plato says in the Meno, tethered — so it would not fly away like one of the statues of Daedalus).

    Clearly, Western philosophy consists of more than Plato’s question about genuine knowledge and true opinion. There is, for instance, a whole development around methodological questions, and this starts to a large extent with Aristotle’s work on logic. That is all important from the point of view of critical rationalism. The question about true opinion and genuine knowledge, however, is rejected. This cannot be overemphasized: critical rationalism rejects the central project of Western epistemology.

    So it is not that all these academic philosophers are too stupid. It is rather that their project is defined by this question about the distinction between true opinion and genuine knowledge, which is itself simply defined as justified true belief. If they abandon justification they abandon the whole project. They do not thereby accept that such abandonment is “the answer”. Do you see the point?

    Suppose your project is to build a ladder to the moon. You try and try, but always fail. Finally, Robert Goddard says: stop trying to build a ladder to the moon. Just build a rocket ship instead. You do that, and it works! You get to the moon. Now is building that rocket ship “the answer” to your original problem? Not really, because you were trying to build a ladder to the moon. That’s the situation. It’s not that critical rationalists suggest an abandonment of justification is “the answer”. Rather, they say that the original problem is bogus, and that you should drop it. And that’s why academic epistemologists persist: it’s not that they’re too stupid; it is rather that they cannot bring themselves to abandon the whole project. One must remember as well that many of them have tenure!

    Next you trot out the old war horse that “whatever objections can be leveled against justification can be leveled against justification (or warrant)…” But this is simply wrong, and it is so in strictly logical terms. Critical arguments differ from justificatory arguments in not being circular, i.e., not repeatedly begging the same question. That is, while critical arguments do beg questions, they need not do so regressively. It is really rather amazing that the academic community of Popper critics have been repeating this silliness for several decades now. I’ve finally been forced to the conclusion that they are not seriously interested in the truth about this particular circumstance.

    Finally, the proof given by Popper and Miller does not lead to the conclusion that “induction is actually deduction”. Rather, it leads to the conclusion that evidence is never ampliative, that it is always question begging. That pretty much puts an end to inductive inference.

  17. Rafe says:

    Peter, I still want to know what the inductivists expect to deliver to working scientists that will be helpful. Can you please explain that? If you can provide a satisfactory answer I will be more interested in inductive logic or inductive probability, or whatever you think we should use.

  18. Peter D Jones says:

    If working scientists are already using induction and don’t care about its philoosphical unerpinnings, they are going to find inducutivsm as uninteresting as other areas of philosophy. That kind of scientists is probably going to be uninterested in Popper too. That philosophy isn’t useful odesn’t invalidate it as philosophy.

  19. Peter D Jones says:

    On the other hand, the kind of scientist who uses induction and DOES dare about its underpinning might say “Hurray! At last my doubts about the validity of induction have been assuaged” (cf the situation with infinitessimal calculus, which was cheerfully used for a couple of centuries before being given foundations by Abraham Robinson).

    And what will Popper bring? Either he tells science that for all its apparent success it is broken and needs to stop using induction forthwith – a proclamation that is unlikely to get a warm reception — or he tells scientists they never were using induction and it was really C&R all along.

  20. Rafe says:

    That the philosophy of science is not useful to scientists I think invalidates it as the philosophy of science. Why else would you do it?

    But you have not answered the original question, what would count as a successful outcome of the inductivist project?

  21. Peter D Jones says:

    Lee,

    I do not accept your definition of “justification” as conventional. The usual end of justification is to provide a method of identifying sound arguments.

    I think that is the wrong way round. The usual way of formulating sound arguments is to select premisses that have already been justified in some way,
    and use them to justify a novel conclusion. Justification is by no mean restricted to arguments, either as input or output. Scientific data are justified by the employment of correct methodology; witness statements are justified by honesty, and so on.

    A valid argument with true premises may pass as unacceptable because it cannot be justified by any special propositions or authoritive source.

    I think it is implicit in the notion of a sound argument that the premises are knowledge, and not serendipitous guesswork. For instance, we typically
    stop regresses by using empirically based premisses, and we typically regard empirical data as true by default, so they question of how they get to be justified
    is backgrounded, since we typically do not offer justification for them beyond “it has been observed that…”

    If justification cannot furnish arguments with something like what is described above, then it is an even more useless concept than I realised.

    I don’t think there is any widespread problem of people putting forward arguments with unjustified premisses. I think justification is often tacit,
    which is not the same as being non-existent.

  22. Peter D Jones says:

    Rafe

    That the philosophy of science is not useful to scientists I think invalidates it as the philosophy of science. Why else would you do it?

    Philosophy is the “love of wisdom”, or pursuit of knowledge for its own sake. The philosophy of aesthetics probably isn’t useful ot artists either., so its business as usual.

    But you have not answered the original question, what would count as a successful outcome of the inductivist project?

    Insight into the nature of induction.

  23. Lee Kelly says:

    Every apparent induction can be described in an alternative context.

    A critical rationalist would say that a scientist was inspired or motivated by some particular observations to conjecture a universal hypothesis. If the observations could have went against the hypothesis, then it was, in a sense, pre-tested before being conjectured. The scientist merely discovered that an already tested hypothesis existed, and then proposed it as the solution to some problem.

    From a critical rationalist perspective, inductivists are trying to shoehorn abstract logical categories into subjective thought processes. The physical and psychological causes of beliefs, notions, and opinions are not the premises of logical inferences. The causes of thoughts, feelings, and creativity are properly the realm of psychology. Knowledge may be contributed to by the random mutations of DNA, even though the causes of such mutations cannot sensibly be considered the premises from which the tacit knowledge of organisms it derived. Likewise for our psychological processes.

    If one is concerned with the abstract objects of thought, propositions, theories, ideas, their logical relations to one another, problems and potential solutions, then our explanations bypass the subjective world of certainty, confidence, belief, and thought processes, and instead focus on correspondence and relation to the physical world.

  24. Peter D Jones says:

    Kenneth,

    Once again, nobody who participates seriously in the epistemological debate about knowledge as justified true belief thinks that epistemic justification consists of a deductively valid inference.

    Firstly, let me repeat that I never offered “sound deductive argument” as a DEFINITION of justification, just an example.
    Secondly, you substituted “valid” for sound. THat is an important difference

    Corroboration doesn’t depend in the slightest on justification.

    Corroboration by attempted refutation by evidence does require justification or warrant or something like it. The Popperian method of conjecture-and-refutation assumes that conjectures will be refuted if the evidence is against them. If an observation is a conjecture in exactly the sense that a
    theory is, there is no justification for that manoeuvre. One might as well discard the fact and keep the theory. A conjecture is being tested because it is not known to hold up; whatever is being used to criticise it must be true or probable or at least well tested. The Popperian could claim that well tested conjecture can serve that role — but tested against what? Other conjectures , which are tested against others still. Popperians have their own regress problem now. However, it is compatible with falliblism to regard an observation sentence as true by default, that is a standing in need of disproof. They would thus be in a position to refute conjectures without regress.

    Salmon says that corroboration is either empty or it’s induction. The correct answer to Salmon is that it’s empty: corroboration plays no epistemological role whatever. It is simply the result of a failed attempt at falsification.

    If corroboration isn’t guiding Popperians as to which unrefuted conjecture to base our predictions on — what is?

    we would be drowning in a sea of possible explanations. But this is simply absurd. Most of the

    possibilities we can think of fail immediately, or clash with other theories. Many more can be eliminated for strictly logical reasons.

    Who’s “we”? Unless you can demonstrate that scientists are already using Popperian methodology you cannot appeal to de facto science.

    In any case, all other things being equal, non-Popperians are better equped to cut down
    a plethora of theories than Popperians because they have an extra tool: they can apply all the critical tools a Popperian applies (it is not that non-Popperians are opposed to criticism) and then rank theories according to their level of positive support, which Popperian of course cannot do.

    So it is not that all these academic philosophers are too stupid. It is rather that their project

    is defined by this question about the distinction between true opinion and genuine knowledge, which is itself simply defined as justified true belief. If they abandon justification they abandon the whole project. They do not thereby accept that such abandonment is “the answer”. Do you see the point?

    But you have been presented with two arguments for Positive Support that have nothing at all
    to do with distinguishing knowledge form true belief. My argument is that it is needed to prevent a regress of unrefuted conjectures; and Salmon’s argument is that scientists methodologically need to
    sieve theories more finally than Popper allows.

    But this is simply wrong, and it is so in strictly logical terms. Critical arguments differ from justificatory arguments in not being circular, i.e., not repeatedly begging the same question.

    Firstly, I have already argued that not all circularity is fallacious:

    If a an argument is not a non -sequitur, its conclusion follows from its premises. Some argue that, this being the case, an argument is always invalid, either through circularity or through non-sequitur. The idea is that valid arguments, as it were, are fallacious because they are valid.

    Everyone objects to some circular arguments, such as “Socrates is mortal because Socrates is mortal”. Since the truth of the conclusion in relation to the premise is not in doubt, the objection lies in the lack of informativeness. The conclusion to a valid argument is always implicit in its premises. Does that mean it is already known to someone who know all the premises? We all have thousands or millions of beliefs and they are shfiting all the time. We do not have the means to be instantenously aware of all their implications. So an argument can be psychilogically informative to a human subject even if it isn’t information-theoretically informative. This tells us something about the nature of logic. Whereas empiricism gives us information we didn’t have at all: logic
    makes explicit information we had but didn’t realise.

    Secondly, I have argued that their abandonment of positive support means Popperians face a regress of their own.

    Finally, the proof given by Popper and Miller does not lead to the conclusion that “induction is actually deduction”. Rather, it leads to the conclusion that evidence is never ampliative, that it is always question begging.

    That’s what you say.

  25. Kenneth Hopf says:

    Rafe,

    If inductive evidence is ampliative evidence, then it is clear what would count as a successful outcome of the inductivist project. Given some hypothesis, h, and some evidence, e, one must show that the evidence makes this probability, p(h <- e, e), greater than this one, p(h <- e). The evidence, e, can be anything one cares to name, including the usual repeated sightings of a swan or a raven.

    In our post-1983 world, this project is in a death spiral, and it is clear why: Popper and Miller proved that no evidence can satisfy this requirement. So if inductivists are going to pull it off, they have to invalidate that proof. Popper realized this before his death in 1994. That’s why he says what he says in Essay 10 of _The World of Parmenides_. I think Salmon also realized this shortly before his passing in 2001, and made a last ditch effort to attack the proof.

    Thus Salmon’s earlier criticism of corroboration, upon which this thread is based, is obsolete, for unless the proof is wrong, there is no longer any possibility that corroboration is a form of induction, covert or otherwise. Of course, this is no problem for critical rationalism as long as one maintains that corroboration is a matter of no epistemological significance. Salmon had earlier offered the alternative, that either corroboration is empty or it’s induction. But the answer is clear: it is empty. This doesn’t mean that corroboration doesn’t happen. It just means that corroboration is no reason to think a theory or hypothesis is true, which is precisely what Popper always said.

  26. Peter D Jones says:

    Alan,

    You say that “past regularities will continue into the future”. But many regularities noticed in the past have not continued, e.g. – Newtonian mechanics.

    Nothing changed about the universe to refute Newton. The regularities his
    theory was able to predict are still there. However, tehre are other regularities it cannot predict, and they were there all the time

    A Popperian who conjectured that “past regularities will continue into the future” would have to abandon that conjecture because it is false.

    That has not been demonstrated.

    And Salmon has a particularly pertinent criticism here: Popperians cannot offer the justification that other well-tested conjectures have proved reliable in the past, since that is an appeal to induction. It is also difficult to see what deductive argument they could be appealing to.

    I don’t have to say that well-tested conjectures will be reliable.

    You do if you are using them to build an plane. Reliable prediciton is not optional for scientists and technologists,.

    If I refute a conjecture, then I have eliminated a bad idea. So I have a means of controlling my ideas.

    But not as good a means. All other things being equal, non-Popperians are better equped to cut down
    a plethora of theories than Popperians because they have an extra tool: they can apply all the critical tools a Popperian applies (it is not that non-Popperians are opposed to criticism) and then rank theories according to their level of positive support, which Popperian of course cannot do.

    Being strictly logically compatible with the facts is not the only constraint. The theory also has to be easily criticisable. It also has to be a good explanation: that is, the details of the explanation should be related to the thing to be explained.

    Everyone in science already knows that, these criteria aren’t novel

    We typically curtail such regresses with appeals to observation. I can justify “there are two bottles of milk in the fridge” by opening the door and looking. If Popper has facts that are firm enough to refute a theory, he has facts that are firm enough to stop a regress.

    A purported fact, like an experimental observation, say, is a conjecture. Let’s suppose I do an experiment and it seems to contradict my favourite theory about cheese. There are many possible explanations of this: (1) my cheese theory might be wrong, (2) I may have performed the experiment in a way that didn’t fit the specifications, (3) the specifications for the experiment might be wrong. I can try to come up with conjectures that fit each of these scenarios and test them independently of the problem they were originally supposed to solve. I don’t have to prove anything in order to do any of this, which is just as well.

    If you are going to treat every observation-sentence which might refute a theory as a conjecture in need of corroboration in the sense of attempted refutation, you are going to incur a regress

    The Popperian method of conjecture-and-refutation assumes that conjectures will be refuted if the evidence is against them. If an observation is a conjecture in exactly the sense that a theory is, there is no justification for that manoeuvre. One might as well discard the fact and keep the theory. A conjecture is being tested because it is not known to hold up; whatever is being used to criticise it must be true or probable or at least well tested. The Popperian could claim that well tested conjecture can sevre that role — but tested against what? Other conjectures , which are tested against others still. Popperians have their own regress problem now. However, it is compatible with falliblism to regard an observation sentence as true by default, that is a standing in need of disproof. They would thus be in a position to refute conjectures without regress.

    When you think you’ve looked in the fridge and seen the milk and so you think you have milk, you could easily be wrong. Perhaps you looked in the fridge yesterday and have done so every day before that for years and you got mixed up about whether you looked in the fridge today. Or perhaps you dreamed you looked in the fridge and saw milk.

    Once more with feeling: I accept fallibilism. But facts can be regarded as both firm enough to stop regresses and ultimately corrigible.

  27. Kenneth Hopf says:

    Peter,

    You’re completely confused about corroboration and justification. So was Wesley Salmon. Critical rationalism does not face a regress problem. Consider the following:

    Suppose that you have a hypothesis, call it h1. You are called upon to justify h1, and so you cite h2. But then you have to justify h2, so you call upon h3, and so forth. However far back you go in this chain, h1 remains at issue. You have a regress problem in the sense that you continue to beg the same question. That’s what ‘regress’ means: you’re backing up on the same question.

    But now consider a series of critical arguments. Suppose I advance h1 as a hypothesis. You criticize it by deriving some consequence from it, e, and proposing that not-e is true. I respond by deriving k from not-e and claiming that not-k is true. You respond again by deriving j from not-k and claiming that not-j is true. Admittedly, this could still land us in a circle. But it need not do so, and that is the important point.

    In other words, each of not-e, not-k, not-j can be logically independent of h1. So while we are begging the question with each successive derivation, we are not continually begging the same question, i.e., h1. Thus we do not have a regress. Rather, we have a progress of unjustified conjectures. And this is how science actually works. In other words, it makes progress without justification.

    In contrast, you’re not even hearing the assertion that we reject the demand for justification. Rather, you’re just assuming that we need it, and then complaining that we don’t have it. Someone says to you: I reject the idea that everything must be justified. You respond: oh? .. How would you justify that?

    You simply don’t get it.

  28. Peter D Jones says:

    Regress isn’t the same thing as question begging — the fact that you have a regress of different conjectures does not stop it being a regress. The fact that there is no circle is irrelevant. What is relevant is that whatever conjecture
    I put forward to refute your conjecture does not count as refutation until
    it surives corroborative testing (otherwise there is just a symmetrical contradiction between two conjectures). However, my conjecture can only be tested against another conjecture, ad infinitum.

    The regress is in the “infinitum”

  29. Kenneth Hopf says:

    Peter,

    You also seem to have misunderstood my view of circular arguments. Ironically, I had a long argument with someone else on-line several months ago, with me arguing that question begging arguments are not fallacious. So we’re in total agreement about that. In fact, if you say that an argument is circular, you’re admitting that it’s not fallacious, i.e., that it’s valid.

    Now you add that the problem with question begging arguments is that they’re not informative. This is obviously a statement about personal awareness. Critical rationalism doesn’t care about that. Indeed, some mathematical proofs would not be informative to a person who was already well-versed in that material. From a non-subjectivist point of view, what matters is logical structure, and in this respect all valid mathematical proofs are question begging.

    If you’re going to say that the axioms of a mathematical proof provide epistemic justification for the theorems, you have a petitio principii, for the axioms are just a different way of saying all that they imply. In other words, you’re committed to the view that simply repeating an assertion constitutes justification, which is absurd.

    What you’re likely to say, of course, is that you learned a lot from the deduction. I don’t disagree, but I also don’t care: that’s not induction. Nor do I care if you continue trying to pin that label on it. That’s just a different way of conceding the argument.

    In short, deduction cannot provide justification, because it is always question begging. It is not fallacious, it is just question begging.

  30. Kenneth Hopf says:

    Peter,

    The absence of a circle is NOT irrelevant. It’s the whole point of saying “regress” instead of “progress”.

    At bottom, Peter, all you’re doing is reiterating the view that justification is always required. We say No. Truth is enough. Truth and some way of moving the argument along without fallacious arguments. Clearly, critical rationalism does that.

  31. Peter D Jones says:

    Kenneth
    Now you add that the problem with question begging arguments is that they’re not informative. This is obviously a statement about personal awareness. Critical rationalism doesn’t care about that. Indeed, some mathematical proofs would not be informative to a person who was already well-versed in that material. From a non-subjectivist point of view, what matters is logical structure, and in this respect all valid mathematical proofs are question begging.

    I have given a criterion of problematical question-beggingness which IS structural and according to which most arguments are not problematically uninformative.

    If you’re going to say that the axioms of a mathematical proof provide epistemic justification for the theorems, you have a petitio principii, for the axioms are just a different way of saying all that they imply. In other words, you’re committed to the view that simply repeating an assertion constitutes justification, which is absurd.

    I am commited to the view that explicily repeating an assertion is not justification, but making its implications explict is justification. All you
    are doing here is using vague language to blur a distinction I have made.
    Making the implicit explicit is NOT mere repetition, in clear, literal
    language

    What you’re likely to say, of course, is that you learned a lot from the deduction.

    I may or may not have done, but I have a structural criterion to go on in addition to the psychological

    I don’t disagree, but I also don’t care: that’s not induction. Nor do I care if you continue trying to pin that label on it.

    I have never claimed that all deduction is actually induction. However,
    Popperians have argued that there is no justification of any kind, including
    logical justification, and that is the point I was addressing.

    In short, deduction cannot provide justification, because it is always question begging. It is not fallacious, it is just question begging.

    Some arguments provide justification, and if all arguments are question-begging
    then some question begging arguments provide justification.(I’m begging the question by assuming some arguments justify? You’r begging the question by
    assuming question begging alwasy stymies justification. We’re both using logic,
    so…)

  32. Peter D Jones says:

    Kenneth,

    At bottom, Peter, all you’re doing is reiterating the view that justification is always required.

    My argument is explicity phrased in terms of C&R. However, the point
    is that asymmetry cannot arise from a set of unrefuted conjectures, and refuted
    conjectures cannot arise without asymmetry.

  33. Peter D Jones says:

    ..but i’m not using logic to contradict logic.

  34. Kenneth Hopf says:

    Peter,

    So if all you mean by justification is making implications explicit, you admit that you’re not talking about epistemic justification, the sense in which Western epistemology has been talking about for over 2000 years. Maybe somebody should have told all those benighted justificationist philosophers like Roderick Chisholm and Alvin Plantinga and Fred Dretske (who was once my teacher at the U. of W.) that they needn’t have spent their career trying to puzzle out epistemic justification. They could’ve just skipped on over to the math department and learned how to make logical deductions. Boy, were those guys clueless or what?

  35. Peter D Jones says:

    Kenneth,

    So if all you mean by justification is making implications explicit,

    That is what I mean by logical justification

    you admit that you’re not talking about epistemic justification,

    I have stated at least four times that logical justification is only one variety thereof

    Boy, were those guys clueless or what?

    For the fifth time: I am not offering sound deductive argument as a definition of justification

  36. Kenneth Hopf says:

    Peter,

    The problem is that, on the one hand, you imply critical rationalists are wrong about justification and, on the other, you insist that ‘justification’ in your lexicon has a variety of different meanings. So one never knows what you’re talking about, and it seems more and more evident that you don’t either. Clearly, critical rationalism doesn’t hold that there is no such thing as making implications explicit. Why you even raise that possibility in this context is a complete and total mystery to me, and I expect to some others as well.

    About the so-called regress issue all you say is that the difference between critical reasoning and the attempt to justify is irrelevant, though clearly it is not. About the proof that support cannot be inductive you say only that you’ve heard it summarized to the effect that deduction is induction, which is patently absurd. Beyond that you seem to be caught up in some kind of old-fashioned analysis about logical symmetry, as if this has something to do with critical rationalism. What exactly I do not know.

    All in all I get the impression that you’re engaged in some kind of verbal game of catch-me-if-you-can. Criticisms of your views are ignored, words change their meanings freely, and assertions arise that are evidently intended as rejoinders but which fail to connect with critical rationalism in any discernible way. At this point it is hard to tell exactly what your position is about anything, except that you evidently think that Salmon was right in some way.

  37. Peter D Jones says:

    I think “justification” has a lot of different meanings to everyone. I would rather discuss what I have been calling positive support.

    About the Popper-Miller argument: I have quoted their critics as saying that they conclude that induction
    is (somehow unacceptably) deduction — the converse of your statement about about deduction being induction.

    There is a lot of complicated argumentation on both sides regarding mathematical arguments for and against induction (as the Stanford Encyclopedia of Philosophy page attests, for instance). It is a typical philosophical problem with subtle and plausible arguments on both sides, not a question of a bunch of professional
    philosophers-of-science being to downright stupid to recognise a clinching “proof” when they see one.

    Since you have relentlessly go my arguments wrong (for instance, misattributing
    to me the claim that all justification is deductive, on at least five separate occasion), I do not think you are on the high ground here.

  38. Kenneth Hopf says:

    Peter,

    Look .. the Popper & Miller proof is every bit as much a mathematical proof as, say, the proof of the binomial theorem. It can be proven ab initio from the axioms of the probability calculus. Now, mathematicians do not go on for decades squabbling about such things. Sure, there are some very long and complicated proofs that need extensive checking, like Wiles’ proof of Fermat’s Last Theorem. But the Popper Miller proof is not in that class. Miller even mentions that the conclusion they come to is not original, but had been noticed before, though it did not excite any adverse comment until it began to threaten the holy citadel of probabilistic inductive logic.

    This is not a claim of infallibility. It is just to say that there is this proof .. and if you think it is wrong, please point out where in the proof the mistake is. Until you do that, however, the objective problem situation seems to be as Popper and Miller indicate: evidence cannot be ampliative.

    In LSD there is a passage which, I think, applies in this circumstance as well. Popper says: “In this post-rationalist age of ours, more and more books are written in symbolic languages, and it becomes more and more difficult to see why: what it is all about, and why it should be necessary, or advantageous, to allow oneself to be bored by volumes of symbolic trivialities? It almost seems as if the symbolism were becoming a value in itself, to be revered for its sublime ‘exactness’: a new expression of the old quest for certainty, a new symbolic ritual, a new substitute for religion. Yet the only possible value of this kind of thing — the only possible excuse for it dubious claim to exactness — seems to be this. Once a mistake, or a contradiction, is pin-pointed, there can be no verbal evasion: it can be proved, and that is that. (Frege did not try evasive maneuvers when he received Russell’s criticism.) So if one has to put up with a lot of tiresome technicalities, and with a formalism of unnecessary complexity, one might at least hope to be compensated by the ready acceptance of a straight-forward proof of contradictoriness — a proof consisting of the simplest counter-examples. It was disappointing to be me, instead, by merely verbal evasions, combined with the assertion that the criticism offered was ‘merely verbal’. (see p. 394)

    I fail to see how the situation here differs from the one described by Popper. There is indeed a high ground, but it appears to me that Popper and Miller took it a long time ago (these arguments are not mine, Peter — I’m simply trying to convey them accurately; I’m not the sort of person who can come up with this stuff myself). Further, I’ve been surveying the literature on this matter for months now, and I can tell you that there is a steady regress on the part of the critics over the past nearly 30 years. The most recent criticisms no longer maintain that the proof is incorrect. It is rather widely agreed that there is no mistake in it. As I said before, the result is that induction has been driven out of its ancestral homelands. The proponents of induction still around today resort to more and more ludicrous evasions. The thing is on its last legs. I’m just trying to let you know what I’ve found out.

  39. Peter D Jones says:

    “the Popper & Miller proof is every bit as much a mathematical proof as, say, the proof of the binomial theorem. ”

    No, the binomial theorem is a mathematical proof with a mathematical conclusion”
    The P-M argument has a philosophical conclusion. It is a mathematical proof
    embedded in a philosophical argument. The maths needs to be related to the philosophy, the symbols need to be given an interpretation, which is where
    typical philosophical counterarguments can kick in.

  40. Kenneth Hopf says:

    Peter,

    Not at all. Look at the proof in Miller’s 1994 book, Critical Rationalism, A Restatement and Defense. The conclusion of the proof is precisely that, in the context of probabilistic support function, evidence either countersupports the hypothesis or has no effect at all. Couldn’t get any less ambiguous than that.

    BTW, Wesley Salmon actually withdrew his assertion that corroboration is an instance of induction. Of course, he replaced it with an even bigger muddle, so there’s still no shortage of error from that quarter.

  41. Peter D Jones says:

    Oh good grief. Just because he can state his conclusion clearly doesn’t mean he didn’t make any shaky semantic assumptions on the way there.

  42. mlionson says:

    “Critical rationalism does not face a regress problem. Consider the following:

    Suppose that you have a hypothesis, call it h1. You are called upon to justify h1, and so you cite h2. But then you have to justify h2, so you call upon h3, and so forth. However far back you go in this chain, h1 remains at issue. You have a regress problem in the sense that you continue to beg the same question. That’s what ‘regress’ means: you’re backing up on the same question.

    But now consider a series of critical arguments. Suppose I advance h1 as a hypothesis. You criticize it by deriving some consequence from it, e, and proposing that not-e is true. I respond by deriving k from not-e and claiming that not-k is true. You respond again by deriving j from not-k and claiming that not-j is true. Admittedly, this could still land us in a circle. But it need not do so, and that is the important point.

    In other words, each of not-e, not-k, not-j can be logically independent of h1. So while we are begging the question with each successive derivation, we are not continually begging the same question, i.e., h1. Thus we do not have a regress. Rather, we have a progress of unjustified conjectures. And this is how science actually works. In other words, it makes progress without justification.”

    This is as clear a statement of how Popperian theory is enacted as I have ever seen. I do not think as many people would object to it if they read this, because it describes what people seem to do when they think about problems and even when they utilize experimentation. And yes, an observation emanating from an experiment is nothing other than another conjecture.

    Do I have your permission to use it, with appropriate citation?

    Michael Golding

  43. Peter D Jones says:

    “I respond by deriving k from not-e and claiming that not-k is true. You respond again by deriving j from not-k and claiming that not-j is true. Admittedly, this could still land us in a circle. But it need not do so, and that is the important pioint.”

    What’s going to stop it? If everything is equally conjectural, any statement to
    the effect that “hypothesis h is contradicted by observation o” can be
    countered by “keep h and reject o”. Simply saying that something somehow breaks the impasse doesn’t resolve the issue. Common-sensically one
    would of course expect the impasse to be broken, but common-sensically
    hypotheses and observations are not equally conjectural so the problem
    does not arise.

  44. Constantius says:

    According to Hume, General conclusions from specific premises or observation reports are invalid because we can’t know whether future observations of the same thing will produce the same results. Hume said that past experience can’t give us clue as to how future events will play out. Hume contends that our knowledge of objective reality is confined to our past and present sense experience, so future occurrences which are necessarily beyond experience can’t provide us with any knowledge. Until we empirically experience those happenings, we can’t be sure of their truth. According to Hume there is no connection between cause &effect, they are “Loose & separate………conjoined but never connected” (An Inquiry Concerning Human Understanding, 3rd edition).
    Popper said that he thought he had the solution. He said, “I believe I have solved the problem of induction by the simple discovery that induction by repetition does not exist” (UNQ 52; cf OKN 1ff & PKP2 1115). What really happens according to Popper is the application of Critical Rationality; the advancement of knowledge by conjecture & refutation. “……In my view there is no such thing as induction” (LSCD 40); “what characterizes the empirical method is its exposing to falsification, in every conceivable way, the system to be tested” (LSCD 42). Popper said that Hume showed that “There is no argument from reason that permits an inference from one case to another…..and I completely agree” (OKN 96). Elsewhere he referred to induction as a myth that was exploded by Hume (UNQ 80) He said that “There is no rule of inductive inference-inference leading to theories or universal laws-ever proposed which can be taken seriously even for a moment” (UNQ 146-7; see also RASC 31).
    Popper’s solution is certainly correct in one respect; the problem of induction will vanish if there is no such thing as induction. However it can be solved in much better way if Hume is proved wrong & if it is proved that there was no valid ‘Problem of Induction’ for Hume to elaborate upon. And in fact, this is the case. Induction does not have such a problem which renders it devoid of logical force as Hume contended. In spite of being a great writer & thinker, Hume totally missed the main point about ‘Inductive Inference’. Because Hume’s idea that induction depends solely upon observation is wrong. Inductive Reasoning instead depends on ‘The Law of Identity’. In Hume’s view there is no Objective Identity, only subjective Custom or Habits.
    According to Hume, then, there is no certainty regarding the hawthorns of English Hedge bearing grapes next autumn or the thistles in the field producing figs in future. However the same person wrote, “When any opinion leads to absurdities, it is certainly false” (An Inquiry Concerning Human Understanding, 3rd Edition); his ideas of grapes of thorn & figs of thistles are certainly absurd enough. According to Nicholas Dykes, “And false is what Hume’s opinions most certainly are. Left standing alone, they lead us to what he himself called “The flattest contradiction of all, viz. that is it is possible for the same thing to be and not to be” (A treatise of Human Nature, Book 1). Criticism of this idea of Hume’s began in 1916 by H.B.W.Joseph in his book ‘An Introduction to Logic’. For a thing to be means to be something and that something is only what it is. To assert a causal connection between some cause A & some effect E means to assert that A produces E because of what it is & so long as such identity exists, A must act in the same way it did before because, in fact, it is what it is; and to assert that A acts in a different way is to assert that the A being discussed is not the same as A which it was declared to be.
    The problem with Hume’s Problem of Induction is its denial of the implications of The Law of Identity. Existence implies being. It is not possible to be without being something. The attributes of something separates it from the rest of the objects that exist. And a thing can only be what it actually is; A is & always will be A. Each & every practical consequence rendered by something forms part of its identity; “The way in which it acts must be regarded as part of the expression of what it is” (An introduction to Logic, H.B.W.Joseph, 1916). This is the most decisive shortcoming of Hume’s Problem of Induction. The essence of this Law of Identity is that every object has its own distinct character or a set of characters which sets them apart from others; forming their identity and causal connection between them and effects produced by them is comprehensible by human beings. So as long as a particular thing remains what it is, it will continue to produce the same consequence(s) that is/are determined by its attributes.

  45. Peter Jones says:

    The problem of induction is essentially epistemological. A metaphysical
    posit, such as the Law of Identity (or the Uniformity of Nature or a number of others) can explain how induction works, but it can’t resolve the epistemic problem of reaching sure conclusions on the basis of limited evidence.
    We can say that it is in the nature of the Sun to rise in the east (or it is part
    of its identity to do so, etc), and we can reach a conclusion about what
    will happen on that basis. But a conclusion is only as good as its premise. In order
    to reach a sure conclusion about what will happen tomorrow, a sure premise is needed. So the metaphysical posit of Identity or Nature would need to be known
    surely. But how does one obtain sure knowledge of a thing’s nature or identity
    on the basis of limited evidence? That is itself the problem of induction! So nothing has been resolved epistemically.

    When one is talking about identity, it is tempting to think that identity is a simple concept of A=A. But such a simple concept cannot do the metaphysical
    work we need it to do. The fact that everything is self-identical tells us nothing:
    what we are actually appealing to is the idea that everything has a unique
    identity – A is not B is not C. (Even self-indentity is complex in reality: is the butterfly identical to the caterpillar?). The unique and individual natures
    of things are not given by the tautology A=A, they have to be strudied
    and learnt. So the problem of limited data is not avoided by identity.

  46. Alan Forrester says:

    In reply to Constantius: you start out not knowing what things are identical to one another. You can’t prove any idea you might have because the conclusion of an argument may be false if any of its premises are false, and since you don’t start out knowing the truth, any of your premises might be wrong. All you can do is propose conjectures and test them against one another.

    You write:

    “To assert a causal connection between some cause A & some effect E means to assert that A produces E because of what it is & so long as such identity exists, A must act in the same way it did before because, in fact, it is what it is; and to assert that A acts in a different way is to assert that the A being discussed is not the same as A which it was declared to be.”

    This is true. But the point you seem to miss is that you can’t make something into A just by declaring that it’s A.

  47. Constantius says:

    Mr. Forrester, The points you made is valid (to a limited extent), but all times such idea of starting logical argument by not knowing the truth of the premises is not a realistic one. Also what you Popperians do is emphasizing on the notion of ‘Conjecture’. According to the Chamber’s English dictionary, conjecture means ‘An opinion based on slight or defective evidence or none; an opinion without proof’; a guess’. All of our argumentation does not necessarily need conjectures, facts are knowable & attainable. Instead of this defective notion of conjecture we can use the word Hypothesis/assumption.
    As to Mr. Peter Jones’s comments, you surely make a strong point in favor of Hume’s idea. But you do not seem to take into account that though knowledge about reality outside our mind can be fallible (liable to err), it possible for us to know phenomena or objects in their totality in certain cases. In that kind of cases we can certainly predict their future behavior provided that they are allowed to function without disruption.

  48. Constantius says:

    I think I need to elaborate on this by mean of example. Dear MR. Jones, do you know a what a human being is? I’m pretty sure your answer will be well, of course, why not. Then the counter-question can be like this, “How did your conception of humans developed? Have you deciphered human nature completely in your short lifespan from finite numbers of observation of this specie of creatures?”. If your answer is positive, then induction is also valid.

  49. Alan Forrester says:

    Constantius wrote:

    “Mr. Forrester, The points you made is valid (to a limited extent), but all times such idea of starting logical argument by not knowing the truth of the premises is not a realistic one. ”

    Why? I can start an argument with the premise that life may exist somewhere else in the universe. I don’t know if it’s true, but I can postulate that it is and argue about that proposition.

    And if you do actual experiments you start out with the theory that the experimental apparatus works in the way described. You then look at the results of specific experiments to test whether the apparatus is working and how the readings on the output correspond to the input – this is called calibration. If the calibration looks very different from what you expected then you know that something has gone wrong somewhere: either the test system you’re using isn’t understood under the conditions in the lab, or the sample is contaminated, or the equipment isn’t working. You could then start testing all those hypotheses, e.g. – if the sample is contaminated other equipment will give weird readings, if the equipment is wrong then other known samples will give weird readings and so on. You don’t have to assume the truth of any particular idea to make progress.

    “Also what you Popperians do is emphasizing on the notion of ‘Conjecture’. According to the Chamber’s English dictionary, conjecture means ‘An opinion based on slight or defective evidence or none; an opinion without proof’; a guess’. All of our argumentation does not necessarily need conjectures, facts are knowable & attainable. Instead of this defective notion of conjecture we can use the word Hypothesis/assumption.”

    I’d be happy to use the word hypothesis. I agree that facts are knowable in the sense that you can have true hypotheses. I don’t agree that you can prove them.

  50. Peter Jones says:

    Constantius,
    Knowledge “in totality” is not the same thing as certain knowledge. We may be able to know all the properties of a fundamental particle such as an electron, but there can still be considerable confusion about the laws under which they operate.

    I know enough about humans to tell the difference between a human and a cat. I have not “deciphered human nature completely” and neither has anyone else. If I could predict human nature, I would be playing the stock markets, not discussing philosophy. To know a things nature sufficiently to categorise it is not to know
    it sufficiently to predict it. Those are very different kinds and degrees of knowledge. The limited and uncertain knowledge we have may be gained inductively (I am not a Popperian). Likewise, a thing’s nature may [b]explain[/b] its actions, without addressing any epistemological issues. However, the Hard Problem of Induction, that of obtaining [b]certain[/b] general knowledge from specific cases remains unsolved and unsolvable. Something has to give: induction, certainty or both. I differ from the Popperians in thinking the abandonment of certainty as a criterion of knowledge is enough.

  51. Alan Forrester says:

    Peter wrote:

    “Something has to give: induction, certainty or both. I differ from the Popperians in thinking the abandonment of certainty as a criterion of knowledge is enough.”

    That’s not Popper’s position.

  52. Peter Jones says:

    If that is supposed to mean that, according to P., abandonment of certainty
    is enough…whence the relentless hostility to probablistic defences
    of induction?

  53. Rafe says:

    They don’t work!

  54. Alan Forrester says:

    To Peter:

    I misinterpreted what you wrote as meaning that Popper said the abandonment of certainty was enough, but of course Popper didn’t just abandon certainty, he provided an alternative account of knowledge. However, I think that saying you have just abandoned certainty is an adequate summary of your position either. I think you say, rather, that uncertainty can be quantified and that the numbers fit the calculus of probability. Am I right about that?

  55. Constantius says:

    In reply to Peter Jones: I am sorry to mention the expression ‘human nature’, it was supposed to be ‘human identity’. Though you have answered about identity in a fairly impressive way. One thing I find awkward about critical rationalists is their general rejection of justification. Each & every conclusion of valid deductive argument can be justified by their premises, provided that the premises are true.

  56. Rafe says:

    The problem is to justify the premises. Hence the travails of justificationism (foundationalism) and the attraction of critical rationalism for people who like to make progress with problem-solving instead of bogging down in paradoxes and other dead ends.

  57. Constantius says:

    In the cases of scientific theories, I completely and certainly agree with Popper. But his insistence on the same ideas when dealing with other issues leads the discussion to self-refutation.

  58. Alan Forrester says:

    What issues are you referring to? And why is critical rationalism problematic when applied to those issues?

  59. Peter Jones says:

    There are vast numbers of premises that are justifiable providing one isn’t looking for certainty. Seeing a bear justifies “there is a bear”. Etc. Empiricism+fallibilism solves the Agrippa trilemma..

  60. Constantius says:

    I was referring to evidences on which Popper tells us to rely for the refutation of Scientific theories. If they are also conjectural, thus unreliable; then we have no right to call a ‘Conjectural’ theory false because it is contradicted by another ‘Conjectural’ evidence.

  61. Constantius says:

    We need to distinguish concepts like ‘Conjecture’, ‘Falsity’, ”Fallibility’ & ‘Certainty’ & ‘Tentativeness’. Otherwise this theory may one day face the consequences faced by ‘Logical Positivism’ or ‘Marxism’.

  62. Constantius,

    That follows if evidence is conjecture, and all conjectures are equal. Popperians
    would do well to treat evidence as a different kind of fallible thing to the fallible
    thing that is uncorroborated conjecture — a thing that should be considered true by default. For some reason, they are unwilling to do so.

  63. Rafe,
    Then induction is an epistemological problem that needs solving, and the hostility
    isn’t solving it.

  64. Alan Forrester says:

    Constantius wrote:

    “I was referring to evidences on which Popper tells us to rely for the refutation of Scientific theories. If they are also conjectural, thus unreliable; then we have no right to call a ‘Conjectural’ theory false because it is contradicted by another ‘Conjectural’ evidence.”

    Why not? The evidence and the theory contradict one another. One of them has to be false. Under some circumstances the best explanation, i.e. – the one that solves most problems, will be that the theory being tested is false. In those cases why can’t we guess that it’s false and then look for another theory?

  65. Peter Jones says:

    Most people hold to the idea that evidence is probably true, and that does allow
    them to use it to refute a conjectural theory. However, most people would
    not call such evidence conjectural, and a it cannot be seen how a conjectural
    theory cannot be refuted by equally conjectural evidence. The theory
    that you describe, Alan, is a good one, but it is not a theory where evidence is conjectural. Maintaining that evidence is conjectural is either a different theory or a misleading description of the same one.

  66. Michael Golding says:

    Kenneth made the following argument about arguments and implied that it can increase knowledge.

    “Suppose I advance h1 as a hypothesis. You criticize it by deriving some consequence from it, e, and proposing that not-e is true…”

    In this thread, Peter, you have been trying to point out the illogical consequences of Kenneth’s arguments. Do you see that you are using Kenneth’s style of argument as specified in the quotes above, when you try to point out the illogical consequences of his arguments?

    Presumably you think that you can gain knowledge by arguing this way, otherwise you would not do it. (Right?)

    So are you not implicitly assuming that the argument style specified in the quotes above grows knowledge?

    Why do you think it works?

  67. Lee Kelly says:

    “I was referring to evidences on which Popper tells us to rely for the refutation of Scientific theories. If they are also conjectural, thus unreliable; then we have no right to call a ‘Conjectural’ theory false because it is contradicted by another ‘Conjectural’ evidence.” – Constantius

    What “right” do we need? Who determines these rights? Do we need an epistemic authority? But won’t this authority be unreliable, and ultimately, conjectural?

    In any case, you misunderstand; theories and evidence are not in and of themselves conjectural. The conjectures are ours. When we conjecture that some evidence is true, then it has particular logical consequences; among these consequences may be the refutation of some theory. Thus the act of conjecture (i.e. a tentative assignment of truth) logically entails the falsity of some theories. It can be no other way. There are no guarantee of success; we may err by wrongly conjecturing, but the growth of knowledge always was and remains a risky business.

  68. Andrew Crawshaw says:

    I know this is going to be uninformative for you guys. But I will keep coming back to this post and the debate herein, simply because it is one of the best debates I have read and it was very informative.

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