Popper on Logic and Truth

by Mark English

It is often said that the foundations of logic are the conventions that we (as users of logic) agree upon. I see problems with this view.

For a start, the word ‘logic’ is used in different ways. It is often used to refer to formal logic and applications and developments thereof, but it is also used to refer to the principles of sound reasoning in ordinary informal contexts.

In the case of formal or symbolic logic, agreed-upon sets of axioms do indeed determine how each system operates. In this sense, logical systems are relative and malleable. They can be seen as tools, which may be applied to various subjects and activities. Different applications call for different systems or modifications of the system (or tool) being used.

The problem is that such a view seems to suggest that logic is radically relative, and this could be seen – as it often is, in fact – to justify a broader kind of relativism that would encompass science and possibly validate non-rational modes of thinking. I would want to argue against this view and say that the foundations of logic run deep.

Certainly, it is not satisfactory merely to say that the foundations are conventions we consciously decide on. One reason we know this is because certain logical principles are built into natural language such that an intuitive grasp of something very like what we call logic is a prerequisite for communicating linguistically. In other words, this intuitive understanding of what we might choose to call logical principles precedes any conscious decision we might make about adopting principles, much less sets of axioms. A young child – to the extent that the child uses language – gets it.

‘Not’. ‘Or’. ‘And’. ‘If … then’ Such words and idioms – and perhaps the pre-linguistic intuitions that lie behind them and their equivalents in other languages – are arguably the source of (and are closely related to) the various formal operators. [1]

Of course, there are big differences between natural and formal languages. For example, the meanings of the words and idioms of natural languages vary and are context-dependent, whereas the meanings of logical constants (which can be seen as being defined simply in terms of how they are used within a system) do not vary within a particular system and are not context-dependent in the way natural language expressions are.

Take the logical connective ‘or’, which is used in the propositional calculus to represent the truth-functional operator of inclusive disjunction. Its meaning/use is quite clear and explicit. When this operator is used, the set of operands is true if and only if one or more of the operands is true. So “Paris is the capital of France or Berlin is the capital of Germany” is true if (a) one of the two statements (operands) is true and (b) if both of the statements are true.  It is only false if both are false.

The English word ‘or’ is one of a number of coordinating conjunctions and normally doesn’t work like its counterpart in formal logic. It usually represents exclusive rather than inclusive disjunction. If someone says they wished they had become a doctor or a lawyer, they generally mean either/or, not either/or or both. The slightly awkward expression ‘and/or’ is often used to specify inclusive disjunction in English.

My broader point is that logical structures may often be complex and difficult to discern, but they are generally decipherable and are an integral part of any kind of symbolic processing. Some constraints always apply.  It is never a case of ‘anything goes’.

There are many ways you could approach these sorts of questions. You could focus on the relationship between natural and formal languages. Or you could probe into the logical basis of digital computing. But I thought it might be worthwhile here to present – mainly through selected extracts from a section of his book, Objective Knowledge – some of Karl Popper’s ideas on logic and truth. [2]

I disagree with many of Popper’s views (on the mind, for example) and I also have reservations about his apparent aversion to dealing with questions relating to natural language, questions which may well be pertinent to some of his claims. Nonetheless, I think his views on logic and truth are well worth taking seriously. Driven by a commitment to commonsense and scientific realism, he shies away from conventionalism and relativism.

Popper explicitly rejects the idea of logic being merely a set of more or less arbitrary conventions (whether consciously agreed upon or not). “I am opposed,” he wrote, “to looking upon logic as a kind of game. I know about so-called alternative systems of logic […] but alternative systems of logic can be discussed from very different points of view. One might think that it is a matter of choice or convention which logic one adopts. I disagree with this view.”

Popper sees logic as a theory of deduction or of derivability.

Derivability or deduction involves, essentially, the transmission of truth and the retransmission of falsity: in a valid inference truth is transmitted from the premises to the conclusion. This can be used especially in so-called ‘proofs’. But falsity is also retransmitted from the conclusion to (at least) one of the premises, and this is used in disproofs or refutations, and especially in critical discussions.

We have premises and a conclusion; and if we show that the conclusion is false, and assume that the inference is valid, we know that at least one of our premises must be false. This is how logic is constantly used in critical discussion, for in a critical discussion we attempt to show that something is not in order with some assertion. We attempt to show it; and we may not succeed: criticism may be validly answered by counter-criticism.

Popper is probably most famous for proposing to replace the verification principle of logical positivism with a falsification principle. This was his response to the problem of induction as described by David Hume. Popper’s “backwards” argument from false conclusion to a false premise is a logical notion (cf. modus tollens), but it also relates to science.  Indeed, logic is central to the practice of science.

Popper thinks that criticism is a crucial methodological device for the building up of a sound body of knowledge about the world and that effective criticism would not be possible if we could answer criticism by rejecting the logical framework of the critic; by saying, in effect, “Your logic may be all right for you, but I prefer a different logic, and according to my logic this criticism is not valid.”

He argues that strong logics (like classical logic) are to be preferred in critical contexts, “for we want our criticism to be severe [and in order] that the criticism should be severe we must use the full apparatus; we must use all the guns we have. Every shot is important. It doesn’t matter if we are over-critical: if we are, we shall be answered by counter-criticism. Thus we should (in the empirical sciences) use the full or classical or two-valued logic.”

What lies behind this concern is – in part – his rejection of subjectivist interpretations of quantum mechanics. “If we […] retreat into the use of some weaker logic – say, the intuitionist logic, or some three-valued logic (as Reichenbach suggested in connection with quantum theory) – then, I assert, we are not critical enough; it is a sign that something is rotten in the state of Denmark…” (His little joke about the Copenhagen interpretation.)

He recognizes, of course, the importance of these “weaker” logics in proof theory.

[I]f one can prove mathematical theorems with methods weaker than the full battery of classical logic, then this is extremely interesting from a mathematical point of view. Thus in proof theory we are interested in weakening if possible our classical logic, and we can, for example, introduce intuitionist logic […] and investigate how far we can get without using the whole battery. […] So if you wish to prove, or to establish something, you should use weak means. But for disestablishing it – that is to say, for criticising it – we may use strong means.

Alfred Tarski, he claims, introduced two important ideas into logic which are very compatible with scientific realism. The first (partly anticipated by Bolzano) is that logical consequence is truth transmission. The second, according to Popper, is a rehabilitation of the idea that truth is simply correspondence with the facts.

Of the three main theories of truth, the oldest [is] the correspondence theory, the theory that truth is correspondence with the facts, or to put it more precisely, that a statement is true if (and only if) it corresponds to the facts, or if it adequately describes the facts. This is the theory which I think Tarski has rehabilitated.

The second theory Popper discusses is the so-called coherence theory. It comes in many forms but in general terms holds that a statement is regarded as true to the extent that it coheres with the rest of our knowledge. The third theory is that truth is pragmatic utility or pragmatic usefulness: it says in effect that “we should accept a physical theory as true if it turns out in tests, and other applications, to be pragmatically useful, or successful.”

Our problem can be sharply formulated only by pointing out that the opponents of the correspondence theories all made an assertion. They all asserted that there cannot be such a thing as the correspondence between a statement and a fact. This is their central assertion. They say that this concept is meaningless (or that it is undefinable …). In other words, the whole problem arises because of doubts, or scepticism, concerning correspondence: whether there is such a thing as a correspondence between a statement and a fact. […] It is also quite clear that, but for these doubts, the upholders of the coherence theory and of the theory of pragmatic usefulness would really have nothing to argue against. Nobody denies that pragmatic usefulness and such matters as predictive power are important. But should there exist something like the correspondence of a theory to the facts, then this would obviously be more important than mere self-consistency, and certainly also much more important than coherence with any earlier knowledge (or ‘belief’); for if a theory corresponds to the facts but does not cohere with some earlier knowledge, then this earlier knowledge should be discarded.

Moreover, if there exists something like a correspondence of theories to facts, then it is clear that a theory that corresponds to the facts will be preferable to a theory that doesn’t. Or, as Popper puts it, “the pragmatist position will be superseded by a realist position if we can meaningfully say that a statement, or a theory, may or may not correspond to the facts.”

It is important to realize also that, while the coherence and pragmatist theories are generally taken to assert the impossibility or meaninglessness of a correspondence theory, the correspondence theory does not involve denying the importance of coherence or of pragmatic factors.

Popper sees the central issue with defending the correspondence theory as having nothing to do with defining ‘truth’ (he claims to have little interest in definitions), and remains focused on the question of whether or not a statement or a theory can plausibly be said to correspond (or not) to the facts.

According to Popper, Tarski rehabilitated the correspondence theory of truth by providing a simple but precise method of coordinating statements and facts. He did this by deploying the distinction between language and metalanguage in a particular way. A metalanguage is a language in which we talk about some other language (called the object language). Popper gives the example of a grammar of the German language, written in English, which uses English as a metalanguage in order to talk about German (the object language). But you can also use any natural language to talk about, i.e. make metalinguistic assertions about, itself, so that at certain points the language is operating metalinguistically and at other points not.

Here is the key part of Popper’s account of how Tarski’s theory of truth enables us to see how statements can be coherently seen to coordinate – or correspond – with facts about the world.

The characteristic thing about a metalanguage is that it contains (metalinguistic) names of words and of statements of the object language, and also (metalinguistic) predicates, such as ‘noun (of the object language)’ or ‘verb (of the object language)’ or ‘statement (of the object language)’. If a metalanguage is to suffice for our purpose it must also, as Tarski points out, contain the usual means necessary to speak about at least all those facts about which the object language can speak.  All this is the case if we use English as our metalanguage in order to speak about German [or English, for that matter] as the object language under investigation.

For example, we shall be able to say in the English metalanguage such things as: The German words ‘Das Gras ist grün’ form a statement of the German language.

On the other hand, we shall be able to describe in our (English) metalanguage the fact which the German statement ‘Das Gras ist grün’ describes. We can describe this fact in English simply by saying that grass is green.

We can now make a statement in the metalanguage about the correspondence of a statement of the object language to the facts as follows. We can make the assertion: The German statement ‘Das Gras ist grün’ corresponds to the facts if, and only if, grass is green. (Or: ‘. . . only if it is a fact that grass is green.’) This is very trivial. It is, however, important to realise the following: in our assertion, the words ‘Das Gras ist grün’, put within quotes, function as a metalinguistic (that is, an English) name of a German statement; on the other hand, the English words ‘grass is green’ occur in our assertion above without any quotation marks: they do not function as a name of a statement, but simply as the description of a fact (or alleged fact).

This makes it possible for our assertion to express a relationship between a (German) statement, and a fact. (The fact is neither German nor English, although it is, of course, described or spoken about in our metalanguage, which is English: the fact is non-linguistic, it is a fact of the real world, although we need of course a language if we wish to talk about it.) And what our metalinguistic assertion asserts is that a certain (German) statement corresponds to a certain fact (a non-linguistic fact, a fact of the real world) under conditions which are precisely stated.

Popper was attracted to the correspondence theory of truth because he saw it as a realistic theory:

[I]t makes the distinction, which is a realistic distinction, between a theory and the facts which the theory describes; and it makes it possible to say that a theory is true, or false, or that it corresponds to the facts, thus relating the theory to the facts. It allows us to speak of a reality different from the theory. This is the main thing; it is the main point for the realist. The realist wants to have both a theory and the reality of the facts (don’t call it ‘reality’ if you don’t like it, just call it ‘the facts’) which are different from his theory about these facts, and which he can somehow or other compare with the facts, in order to find out whether or not it corresponds to them. Of course, the comparison is always extremely difficult.

The coherence and pragmatic theories purport to present us with a method of deciding whether or not a given statement is true. But Popper emphasizes that his version of the correspondence theory (based as it is on Tarski’s semantic theory of truth) is not designed or intended to yield a criterion of truth. In fact, Tarski proved that in a sufficiently powerful language (and in every language in which we can formulate mathematical or physical theories) there can be no criterion of truth.

Although we have no criterion of truth and no means of being even quite sure of the falsity of a theory, it is easier to find out that a theory is false than to find out that it is true […]. We have even good reasons to think that most of our theories – even our best theories are, strictly speaking, false; for they oversimplify or idealise the facts. Yet a false conjecture may be nearer or less near to the truth. Thus we arrive at the idea of nearness to the truth, or of a better or less good approximation to the truth; that is, at the idea of ‘verisimilitude’.

Popper wants to incorporate this idea into logic. While his formal definition of verisimilitude (or ‘truthlikeness’ as it is often now called) has been challenged, the concept has proved to be a fruitful one. This is no surprise, really. Given the provisional and incomplete nature of scientific theories at any given point in time and the obvious phenomenon of scientific progress, this concept or something like it is clearly called for.

Seeing scientific progress merely in terms of effectiveness or some such pragmatic notion is possible, but seems unnecessarily restrictive. Whatever else it may be, scientific activity – encompassing both empirical and formal disciplines – also represents an attempt to understand the world of which we are a part. What’s more, within its self-imposed and natural limits, this quest for understanding can be seen to have been remarkably successful.

NOTES

  1. Clearly these expressions and the intuitions which underlie them have in turn arisen from our actions and interactions, and so are rooted in some sense in the physical world.
  2. Objective Knowledge: An Evolutionary Approach. Oxford: Clarendon Press, 1972. I am drawing on the final section (section 4) of the penultimate chapter. The entire chapter is available here.

78 comments

  1. Well-done, Mark. Nicely written, learned, and provocative all at once. A few things:

    1. The primary motivation here seems to be things that you (and Popper) “want.” Logical tidiness. Determinacy. The ability to say “Correct!” and “Incorrect!” with some real force. Realism. The trouble is, getting all these things is no reason to think that the account by which you get them is right. In genuine inquiry, the Rolling Stones had it right: “You can’t always get what you want.” This essay tells me more about the temperament of Mark English than about anything actually to do with Logic or Truth.

    2. Good luck with “facts” and “reality.” Those are sure-fire losers. (See, for example, Davidson’s take-down of “reality” in “On the Very Idea of a Conceptual Scheme”) And even better luck trying to define them independently of Truth, which, of course, is the whole point of invoking them in the first place.

    3. Truth is a “property” — it really isn’t a property — of statements. It is ill-applied to theories.

    4. There is a reason why most philosophers working in this area, since Quine, are deflationists of one stripe or another.

    5. The Tractatus was the best effort to make some sense of the idea of “correspondence” — that is, the idea that some representation can “map onto” some state of affairs that is not a representation. Wittgenstein ultimately rejected it himself. What do you know that he didn’t?

  2. I’ve always found Popper very helpful in understanding the nature of knowledge. I may have too much of an idiosyncratic (and perhaps incorrect) view of his ideas. Likely this is due to a lack of formal study of philosophy. I was introduced to Popper in a graduate biostatistics seminar. Our professor summed up Popper’s philosophy of scientific knowledge, approvingly, as “a scientist wouldn’t know the truth if he tripped over it”; I thought “I’ve got to read this guy.”

    I count as failures his proposed methodology for science (he seemed not to recognize that scientists behave as do other humans – as was pointed out by Kuhn) and the whole attempt at a theory of verisimilitude (I think David Miller argued, in essence, that all false hypotheses are equally false). But I do think he answered his initial question, which I take to be something on these lines: There is no logical method to establish the truth of a hypothesis (i.e., the problem of induction), yet it seems apparent that our knowledge has grown over time. How could this happen?

    He recognized the importance of the logical asymmetry between showing an idea to be true (impossible), and showing it to be false (possible in theory). Popper was quite aware that in practice it is generally not possible to show conclusively that an idea is false, but it is the asymmetry in the logic that opens the door to advances in knowledge. This of course gives the lie to the idea of knowledge as justified true belief – what we call scientific knowledge is the ideas that have survived so far; truth need not be involved. This seems to me not much different from pragmatism, though I think Popper would disagree.

    Now, because of my lack of formal philosophical training, it may be that I’m unaware that this argument had been around before Popper, or was common knowledge, but it’s always seemed to me that this was one of those insights that, like Darwin’s natural selection or Hamilton’s kin selection, once you hear it you say “Of course, how could anyone not see it?”

    Am I off the mark here?

  3. Thank you, Dan.

    I thought you would take issue with this. I am familiar with the tradition of thought to which you appeal but, for some reason, have never been entirely convinced by it. Some of the key arguments just don’t seem compelling to me. We have discussed Quine and Davidson to some extent in the past. I also recall an interview you did with Ian Ground. I could accept much of what you were saying but both of you seemed to me to be pushing the implications or significance of what you were saying too far. But perhaps sometimes it’s less a matter of simply disagreeing and more a question of what things we value or find worthwhile, like types of discourse or modes of understanding (art, math, sciences, etc..).

    You say my piece is provocative. Most people, I suspect, would say it’s boring. They would just think I and Popper are stating the obvious. This is in fact what I am trying to do.

    I think your comment distorts what I am saying (and what I am doing) here. I don’t have a set view on some of the things you touched on, and am resigned to uncertainty.

    On realism. I am defending commonsense realism and a particular form of scientific realism which assumes virtually nothing about how things are. It does assume *that* things are (a certain way or ways). Science (in my view) is all about answering the question of how things work and how things are in a more general and rigorous sense than the commonsense sense. I would want to say that one of its goals (perhaps its main goal) is a deeper understanding of the world of which we are a part – especially in terms of fundamental and underlying processes. (I realize there are different *ways* of understanding.)

    “Truth is a “property” — it really isn’t a property — of statements. It is ill-applied to theories.”

    There are theories that are out of whack with how things are or how things work and can fairly easily be shown to be so (like astrology or homeopathy) and then you have theories which can be shown to make very accurate predictions, etc.. Like Popper, I’m interested in maintaining this sort of distinction. We could express it in different ways, but I agree with you that saying that a theory is “true” is not only an awkward but also a misleading (i.e. too strong) way of putting the point.

    “The Tractatus was the best effort to make some sense of the idea of “correspondence” — that is, the idea that some representation can “map onto” some state of affairs that is not a representation.”

    It was an attempt. But it was ill-conceived, and it failed. The “mapping” metaphor is part of the problem. We don’t need a comprehensive “mapping”. I’m open to the idea that we should stop talking about “correspondence” also. We just need to be able to talk about how things are – as indeed we do all the time. “The cat is on the mat.” “Where did I put my phone? Oh yes. I left it in the bedroom.” What’s the problem?

    And I would have thought that the bits of Popper I quoted on language/metalanguage are quite in accordance with this commonsense view.

  4. August West

    I wouldn’t put Popper’s ideas on how science progresses in quite the same category as the scientific theories you mention – natural selection, and Hamilton’s theory. These had never before been formulated and they each provided an important foundation for or stepping-stone to further scientific work.

    To my knowledge, nobody before him had made explicit what Popper made explicit but it was not a scientific discovery nor necessarily something upon which others could build. The way I see it, he elaborated an insight. Some of his claims and elaborations are overstated, but the basic insights (such as those concerning the nature of that logical asymmetry you refer to and which I touch on in the essay) are, I think, sound.

  5. Thank you Mark for a fantastic blog post!

    Popper writes in A World of Propensities (page 3) that Gödel accepted Tarski’s priority to what Popper calls “a theory of objective truth”.

    Could you please help explain if that reference implies there is a link between Popper’s theory of objective truth and Gödel’s incompleteness theorems? And if it does, explain how are they linked? Could you make a simple mapping of the word “incomplete” (in Gödel’s sense) onto the word “falsifiable” (in Popper’s sense)? I.e., could an amateur like me reasonably claim that there is “mathematical proof” for the “theory of truth”?

    I would of course love the answer Yes! 🙂

    Best regards.

    //Erik

  6. Mark:

    Upon re-reading your answer, I find it rather unsatisfying. You seem to want to punt on every difficult question raised by your essay. Saying for example that some theories are just “out of whack with how things are or how things work” is not a serious or even a useful reply to a very well-rehearsed problem with the notion of theories “corresponding” to “reality.” And to respond to very well respected and oft repeated criticisms like Davidson’s by simply saying that “they just don’t seem compelling to me” is simply not going to fly, in a discipline like philosophy. It makes it look as if either (a) you don’t understand the criticism (or haven’t read it) and are trying to conceal that fact or (b) you don’t think you need be bothered, and neither is a good way of working in territory in which a lot of very sophisticated work has already been done.

    As you know, I myself am very much a fan of preserving as much of our common sense within the framework of philosophy as is possible, but it cannot be done in the hand-waving way you do here.

    I also want to reiterate the point that while the expression of one’s temperament is unavoidable in philosophy — a feature, rather than a bug — it cannot be all that philosophy is about. In this regard, the section on logic strikes me as the most problematic. The fact is that there *are* multivalent logics. The fact is that it is *true* that if you change the axioms, the starting assumptions, the “hinge propositions”, as Wittgenstein might have put it, you get entirely different formal systems. (And that’s as true in geometry as it is in logic.) The claim that natural language is the “source of” — whatever that means — the logical operators is *highly* controversial and cannot simply be asserted, with the odd peppering of a “surely” and a “clearly” around it. The primary argument seems to be that the reason why logic isn’t conventional is because if it is, it has implications that Mark English dislikes, and that, for obvious reasons, isn’t very persuasive.

    The frustration, then, is that it would be awesome to see a substantial defense of traditional notions of reality and truth, but all that we’re given here is a kind of teaser, with none of the meat. Part of the problem is that there are more quotations than there are arguments. Another part of the problem is that none of the objections — even the most standard ones — are even mentioned, let alone confronted.

  7. Mark – I had no intention of equating Popper’s work with Darwin’s or Hamilton’s in terms of scientific progress and importance. I was just expressing the similarity, to me, in the simplicity of the ideas once you hear them, and some amount of wonder at why it took so long for someone to come up with them. I just wanted to ask if this was the case with Popper, or if these ideas had been around and accepted long before.

  8. Dan

    “Saying for example that some theories are just “out of whack with how things are or how things work” is not a serious or even a useful reply to a very well-rehearsed problem with the notion of theories “corresponding” to “reality.” ”

    What I said there was, I think, perfectly clear, even if it was not directly addressing the issues which you want me to address. I was just stating what virtually everyone who accepts the basic principles of science accepts: that some theories or approaches are misguided and can be shown to be so (though not infallibly of course). There are people who would dispute these claims or, less radically, dispute a particular case (like astrology). I agree that, for the former at any rate, everything I have said here would be frustrating and unsatisfying. But they are not my target audience and I readily admit that I am not addressing their concerns. To do so I would have to write a different kind of piece altogether.

    You, I am guessing, would agree with my assertion that certain theories and approaches are misguided and can be shown to be so. You are saying, however, that I fail to engage with a particular body of philosophical literature dealing with the issue of whether statements or theories can be seen to “correspond” with “reality”. I realize this, but I was deliberately stepping back here and making an (as I see it) uncontroversial claim in order to indicate more clearly *what it is I am defending* – a very basic (attenuated?) form of scientific realism.

    Like Popper (or like Popper claims to be), I am quite flexible with respect to terminology. In fact, I agreed with you that the word ‘correspondence’ is not ideal in this context and I would be happy to drop it. But what I would insist on is that we can in fact talk about the world and how it is and how it isn’t in different respects: that is, in terms of ordinary life (“My phone is in the bedroom”), or in terms of scientific claims. That’s all I am arguing for here.

    I happened to base most of this on a text of Popper’s because I believe what Popper is saying here is intrinsically interesting. It also happens to reflect some of my own concerns and to correspond in significant ways with my own views. He says that what he is defending is basically an approach which “allows us to speak of a reality different from the theory” or to make statements (using language) which are about something which is not language.

    “… the section on logic strikes me as the most problematic. The fact is that there *are* multivalent logics. The fact is that it is *true* that if you change the axioms, the starting assumptions, the “hinge propositions”, as Wittgenstein might have put it, you get entirely different formal systems. (And that’s as true in geometry as it is in logic.) The claim that natural language is the “source of” — whatever that means — the logical operators is *highly* controversial and cannot simply be asserted, with the odd peppering of a “surely” and a “clearly” around it.”

    Again, you are seriously distorting what I said. I raised these issues and made a few tentative suggestions and then said that there were many ways you could address them but that here I was going to look at a few things Karl Popper wrote. I intend to develop some of my claims (relating to logical principles being rooted in natural language, for example) in the future. These claims are not something I have just dreamt up: they may be controversial but they have been argued for by reputable thinkers, including logicians and philosophers.

    I conceded the point about alternative logics etc. in the body of the essay. The question is: what do these undisputed facts about formal logic and geometry tell us about broader issues relating to the fundamental nature of logic and mathematics? This is not an easy question to answer (or even to frame satisfactorily) but it is a question and a topic which interests me and which I would also be happy to discuss, now or in the future.

  9. Mark,

    Great essay! Your comments below are spot on.

    “The problem is that such a view seems to suggest that logic is radically relative, and this could be seen – as it often is, in fact – to justify a broader kind of relativism that would encompass science and possibly validate non-rational modes of thinking. I would want to argue against this view and say that the foundations of logic run deep.

    Certainly, it is not satisfactory merely to say that the foundations are conventions we consciously decide on. One reason we know this is because certain logical principles are built into natural language such that an intuitive grasp of something very like what we call logic is a prerequisite for communicating linguistically. In other words, this intuitive understanding of what we might choose to call logical principles precedes any conscious decision we might make about adopting principles, much less sets of axioms. A young child – to the extent that the child uses language – gets it.”

    Children “get it” because Common Sense is the common logic we all develop early in life. Formal logic is as you developed it in the essay is a distillation of our nervous structure which is already highly integrated by early adulthood. Teenagers are notorious for their lesser brain development in the frontal lobes (which are less integrated into other brain structures) leading to more impulsive and less rule based behavior.

    In the lower mammals the olfactory sense is more highly developed and the frontal brain areas they dominate develop into our own primate brains which are more language based. From the mammalian olfactory pov, mind is highly dimensional or for a lower mammalian mind it is mostly their olfactory sense as opposed to ours which is more logic and language based.

  10. Hi Erik, thanks.

    “Could you make a simple mapping of the word “incomplete” (in Gödel’s sense) onto the word “falsifiable” (in Popper’s sense)?”

    No. For a start, Gödel’s proof is concerned with formal systems (and incompleteness has a very specific technical meaning within that context: roughly, that there are nonprovable (within the system) true statements in the formal system in question), whereas Popper’s falsifiability idea relates (mainly) to scientific theories and empirical claims (although it also draws on logical notions).

    Falsifiability is for Popper basically a criterion to distinguish science from non-science, and the process of testing or criticizing or falsifying empirical scientific claims is definitely not a formal process (nor can it be satisfactorily formalized).

    With respect to the different notions of truth, Popper makes the point that both the coherence and the pragmatic theories incorporate a criterion of truth (coherence and effectiveness respectively) and that the correspondence theory doesn’t, and he suggests that this is a plus for the correspondence theory. (He references Tarski in this connection, but I must confess I don’t know enough about Tarski’s work to say anything useful.)

    With respect to your more general point about theories of objective truth there is probably more to say but remember that the way Gödel interpreted his results may be a bit problematic and is not necessarily the way other people interpret them.

  11. Victor: Putting “certainly” in front of a sentence is not an argument.

    http://plato.stanford.edu/entries/logic-manyvalued/

    Also, the claim that logic comes from natural language is highly controversial. Coincidentally, I am currently teaching Ayer’s “Language, Truth, and Logic” in my Introduction to Philosophy course. Ayer’s remarks on the A Priori are worth considering in light of this conversation:

    “The analytic character of the truths of formal logic was obscured in the traditional logic through its being insufficiently formalized. For in speaking always of judgements instead of propositions, the traditional logic gave the impression of being concerned in some specially intimate way with the workings of thought. What it was actually concerned with was the formal relationships of classes, as is shown by the fact that all its principles of inference are subsumed in the Boolean class-calculus, which is subsumed in its turn in the propositional calculus of Russel and Whitehead. Their system, expounded in the Principia Mathematica, makes it clear that formal logic is not concerned with the properties of men’s minds … but simply with the possibility of combining propositions by means of logical particles into analytic propositions, and with studying the formal relationship of these analytic propositions.”

  12. Mark, I’m going to address your last reply in pieces.

    First, you wrote:

    “I was just stating what virtually everyone who accepts the basic principles of science accepts: that some theories or approaches are misguided and can be shown to be so (though not infallibly of course).”

    I agree with you that virtually everyone accepts this. But it implies no particular view of logic, truth, or “reality.” Nelson Goodman could agree with this.

    Then you wrote:

    “I realize this, but I was deliberately stepping back here and making an (as I see it) uncontroversial claim in order to indicate more clearly *what it is I am defending* – a very basic (attenuated?) form of scientific realism.”

    Scientific Realism notoriously has a raftload of definitions. You’d have to be more specific about what you mean by it, for it to be very informative.

    After this you said:

    “But what I would insist on is that we can in fact talk about the world and how it is and how it isn’t in different respects…”

    Again, taken a certain way, no one would disagree with this. But if you mean by “the world” something that is completely mind-independent, in the sense that it comes already pre-categorized — i.e. that there is some privileged frame of reference — then you have to say a lot more than you have in order to avoid hand-wavery. Again, see Davidson, and Kant, and Quine, and about 25 other people.

    As for the claim that I distorted what you said, regarding logic, I don’t think that’s fair at all. Here’s what you said:

    “In the case of formal or symbolic logic, agreed-upon sets of axioms do indeed determine how each system operates. In this sense, logical systems are relative and malleable. They can be seen as tools, which may be applied to various subjects and activities. Different applications call for different systems or modifications of the system (or tool) being used.

    The problem is that such a view seems to suggest that logic is radically relative, and this could be seen – as it often is, in fact – to justify a broader kind of relativism that would encompass science and possibly validate non-rational modes of thinking. I would want to argue against this view and say that the foundations of logic run deep.

    Certainly, it is not satisfactory merely to say that the foundations are conventions we consciously decide on. One reason we know this is because certain logical principles are built into natural language such that an intuitive grasp of something very like what we call logic is a prerequisite for communicating linguistically.”

    So, yes, you accept that there are multi-valued — i.e. non-classical — logics, but you then immediately proceed to defang them; to suggest that they don’t indicate anything about the ultimate conventionality of logic. Logic — and it should be added, geometry — were once considered by some to be formal descriptions of the world — i.e. of thought and of space — and one of the things that multi-value logic and non-Euclidean geometries show is that this cannot be the case. Now, you seem to want to reject this conclusion, but the only reason you give for rejecting it is that if we do, relativism follows. That’s exactly what I characterized you as saying and given what I just quoted from your essay, it seems a perfectly fair characterization.

    Again, I think you *can* make a case for the things you want to assert, here. I just found this piece to be mostly quotation and hand-waving and very little by way of actual case-making.

  13. Dan,

    Thanks for the comment. “Certainly” was from quoting Mark. It just seems to me from Ayer’s that the brain practices Natural Science just as it practices Natural Logic. Hebbian learning in brain networks or natural learning causes the brain to build its own library of natural objects and classes. Going back to my previous comment for olfactory sense, human learning is more visual which is why we are more prone to visual illusions or animals are less likely to be tricked by plastic fruit. Human symbolic learning itself is a system of illusion or learning based in more layering in our brains and manipulation in our frontal lobes so things stand in for other things and can be logically manipulated?

    1. This strikes me as committing the genetic fallacy or something like it. The fact that logic is “done by the brain” doesn’t mean that logic is *of* the brain, as it were.

  14. Let’s split hairs here or more precisely say it is under your hair (or where it used to be for us), or the center of your brain has the two mirrored lobes of the motor cortices which are the efferent and afferent nerves flowing through the spinal column. Logic is inside the part of the brain that controls and feels the movement of the over 650 voluntary muscles or 325 plus pairs. The sensorimotor structures are physically and metaphysically the center and centerpiece of brain evolution.

    Why does Billy Preston like Ray Charles famously did, “look back” through the entire optical chasm? If you study the optical structure with the dorsal and ventral path you can understand what is going on here, along with the dancing and hand clapping by the backup singers and audience. Its the integration of all of the brain structures including the emotions from the limbic system.

    https://youtu.be/XQ08DF8KlWY?list=RDXQ08DF8KlWY

  15. Hi Dan

    You quoted me (“But what I would insist on is that we can in fact talk about the world and how it is and how it isn’t in different respects…”) and then responded:

    “Again, taken a certain way, no one would disagree with this. But if you mean by “the world” something that is completely mind-independent, in the sense that it comes already pre-categorized — i.e. that there is some privileged frame of reference — then you have to say a lot more than you have in order to avoid hand-wavery.”

    It is not necessarily hand-wavery just because I don’t explicitly discuss this in the terms you want. For a start, I would never talk about a “mind-independent” much less a “completely mind-independent” world. I just wouldn’t use those terms. “Pre-categorised”? Well, obviously the physical world – including our brains – has a lot of structure. It is not amorphous. Categorizing is something we do, however.

    I am deliberately making my claims minimalist – because I don’t want to claim more than I have to claim. As you say, even Goodman would agree. But I’ll tell you who wouldn’t agree – a huge swathe of contemporary philosophers, continental but also many analytic philosophers who not only have little knowledge of or interest in science but who are hostile to it for various – sometimes obscure – reasons.

    Don’t get me wrong. I think that this Kantian and neo- or post-Kantian tradition (for want of a better label) encapsulates some important insights. But those insights have often (from the 19th century on, actually) been distorted – by being isolated from the broader (scientific-philosophical) context in which they arose – and used to push an anti-science agenda.

    I emphasize again that this fact (as I see it) does not invalidate the genuine insights and the genuinely interesting questions raised and discussed within this tradition.

    Of course I will need at some stage to elaborate on and defend my claim that logic (in language use, for example) does not arise solely from principles or axioms we *consciously* decide on. (I used the word “certainly” because I feel I am on *very* solid ground here – and frankly I thought most people would intuitively agree with this.)

    I may also try to flesh out further the nature of the “scientific realism” I am committed to. The trouble with these sorts of inquiry is that they can easily degenerate into sophisticated labelling exercises involving a proliferating number of labels and/or can become a sort of intellectual game (the sort of thing Popper – quite rightly, in my view – warned against).

  16. Interesting essay and interesting debate in the comments.

    I’ve read Open Society and a couple of Popper’s essays,. but never thought of him as a particularly deep thinker; Falsification theory has problems. Consider evolution: While one can frame its predictability in such a way as to appear ‘falsifiable’ (eg., ‘finding human remains at the same level as dinosaur remains would definitely require pause for thought’), but somehow that just misses the point. Verification theory works better for it; but the real problem is that evolution really stands on its ability to account for a wide variety of phenomena, and thus seems to allow a variety methodologies to justify it. Also, at the macro level, evolution cannot make the kind of predictive claims on the future that can be tested – its predictive power has to do with phenomena we’ll likely discover about the past, rather than evolutionary events in the future (what will, say, tigers evolve into? in what kind of environment?). More than any other theory of the natural sciences, evolution is primarily historical.

    Which leads me to the problem of whether there are indeed “non-linguistic facts about the world.” If you mean this in the sense that a fact is a fact whether anyone knows about it or no – I can’t even imagine what such an entity would look like. A tree falling in the wilderness with no one around it doesn’t even exist, let alone make a sound, as far as I’m concerned. I need the report, the recording, the articulation of the event for it to have any meaning for me at all.

    In theory of rhetoric, one sometimes reads the rule of thumb, ‘there is no fact without an argument.’ That’s as true of the sciences as for political journalism. Argumentation provides the articulation that builds the bigger picture in which an argued fact makes sense.

  17. I’ll continue the compliments on the essay and comments. It seems a bit above my pay grade as I tended to take logic at face value compared to other subjects. But let me see if I can add something without accidentally subtracting from the quality.

    I think I am more sympathetic to Mark’s position and endeavour than Dan’s worries about its deficiencies. I tend to take (what I consider) a pragmatic approach to metaphysical or ontological questions, including language about it.

    This all seems to boil down to how to make sense of, or interpret, our sensory experiences and the reports of those made by others. I think I am on the same page with Mark in believing there is a use, and perhaps accuracy, to distinguishing and discussing facts as they relate to theories based on our experiences. It seems to me this has to be true even if one is not a realist. At the very least if one is not a realist and also not a solipsist. Anyway, let me define my terms/concepts.

    Logic to me is simply a toolset for arriving at consistency in explanations. It does not distinguish “true” from “false” claims, without having established some framework where one has identified a category of relations called “true” and “false” about claims. All it can deliver is an assessment if one idea is consistent with another idea or train of ideas. Whether consistency lends value to anything is itself a choice one makes (it can’t be decided by logic), but people seem to seek it up to a certain point.

    Realism to me is not a position determined (delivered proof) by logic or investigation. It is a declaration one has chosen an axiom about the relation between experiences and what they seem to suggest about the world. And it is the simplest one. Our basic (built-in?) interpretation of experience is that it is delivering a report of some kind about external (and in some cases) internal phenomena, much of which relate to “physical” objects in a “physical” world. By physical I mean have causal properties (and so “existence”) independent of anyone experiencing them.

    Realism accepts this with the caveat that experiences (and our interpretations) may not always be accurate. This is helped by experiences of dreams, hallucinations, illusions where the only “coherent” explanation is to divide certain sets of experiences as inaccurate (due to certain conditions) compared to the majority of experiences which we take to be accurate. In short, whether one is a man dreaming to be a butterfly or vice versa is more likely determined by how much time one spends having to act as a man or butterfly.

    Once realism is accepted, then we can discuss the relationship between our interpretations of experiences (theories) with the actual causes of those theories (facts). As I’ve already mentioned “coherence” forms a part of our judgment about these relations. And as far as I can tell “correspondence” is simply an expanded version of “coherence”. That is to say we place greater trust that a specific relationship holds between theory and fact (it is accurate or inaccurate) based on its being coherent with/across different experiences over a sufficient period of time.

    Empirical investigations involve seeking out broader and/or more refined experiences to grow boundaries for which we can make statements that are “coherent”, and so evaluations of (yes presumed based on foundational axiom) greater “correspondence” (theory more accurately matching increasing details relating to fact).

    I was interested to see Popper distinguishing pragmatic from correspondence, since it is hard for to understand how (or why one should think) a theory has pragmatic value without some level of correspondence, without inventing means that one would have to believe are more likely.

    I am fine with terms like “correspondence” or “mapping” or “true/false” and even “real world” or “mind-independent” as long as it is understood that this relies on the founding axiom, which itself may or may not be true.

    And I am a bit skeptical about language approaches like Quine (which I have some knowledge about) and Wittgenstein (which I only know through Dan). Terms about the world do not require the world be divided up in any way at all. It only requires that the world can be divided in such and such a way by someone based on their experiences of facts about it.

    Ok this has gotten long, but I will end on an example. “The grass is green” should be a statement that I can make, which can be analyzed. After years of empirical investigations it may very well be the statement is “true” for me, and about my experiences, though it would be short for something like “the blades of plants I am looking at contain chemical compounds that absorb and reflect certain frequencies of electromagnetic radiation whose detection by photoreceptors in my eyes and functional capacities of my brain facilitate an experience I have come to call (through rules of language learned through social experience) green.”

    At this point it is “true” that green is not a property of the plant material, but the result of a system, which not all humans possess making the truth of “being green” contingent on the perceiver, whereas many underlying elements within the system will be true for most (if not all). The overall picture has become more coherent even as it has become more complex. And I am always curious to hear how anti-realists explain such a thing in a way that is more satisfying (and useful) than levels of correspondence.

  18. ejwinner

    “I’ve read Open Society and a couple of Popper’s essays, but never thought of him as a particularly deep thinker…”

    He may not be a “deep” thinker (whatever that may mean), and he got a few important things wrong (in my opinion), but he was a *serious* thinker, and that’s good enough for me.

    “Falsification theory has problems. Consider evolution: While one can frame its predictability in such a way as to appear ‘falsifiable’ (eg., ‘finding human remains at the same level as dinosaur remains would definitely require pause for thought’), but somehow that just misses the point.”

    Your claim here is too strong. It doesn’t miss the point. It shows that the theory is subject to being called into question on the basis of empirical observation.

    “Verification theory works better for it…”

    I am open to both falsification and verification playing a role.

    “… the real problem is that evolution really stands on its ability to account for a wide variety of phenomena, and thus seems to allow a variety methodologies to justify it.”

    Quite so. And even Popper accepted the significance of the explanatory aspect, I think.

    “… Which leads me to the problem of whether there are indeed “non-linguistic facts about the world.” If you mean this in the sense that a fact is a fact whether anyone knows about it or not – I can’t even imagine what such an entity would look like.”

    I was a bit confused by this because the phrase “nonlinguistic facts about the world” is not one I would choose to use. Looking back over the OP I see that there are a couple of paragraphs which should be in quotation marks or inset and are not. (In the version I sent in, I used quotation marks for all quotes but the editors replaced some with inset paragraphs.) I see that in one such paragraph – actually Popper’s words – the phrase “nonlinguistic facts” is used.

    By contrast, I talked in a comment about “making statements (using language) about something which is not language.” Do you have a problem with this?

    “A tree falling in the wilderness with no one around it doesn’t even exist, let alone make a sound, as far as I’m concerned. I need the report, the recording, the articulation of the event for it to have any meaning for me at all.”

    It goes without saying that it won’t have any meaning for you if you don’t know about it – but to claim the event didn’t happen just because no one saw it happen seems to be moving into strange territory.

    That said, the notion of a *universe* existing without even indirect observers (like scientists finding evidence of a multiverse) is, I grant you, somewhat difficult to get one’s head around. I am open to the idea that sentience or consciousness might play a role in the process of cosmic evolution.

    “In theory of rhetoric, one sometimes reads the rule of thumb, ‘there is no fact without an argument.’ That’s as true of the sciences as for political journalism. Argumentation provides the articulation that builds the bigger picture in which an argued fact makes sense.”

    As I said above, I am wary of talking about ‘facts’ as basic. It leaves one open to this sort of criticism. But my sense from what you say here (and also from your material on Hegel – which prompted me to write this piece, by the way) is that our differences are substantive and that we may have radically different pictures of how the world is and what constitutes it. I suspect we differ even on commonsense (i.e. non-scientific) claims, like about what we mean when we talk about the cat being on mat, or a lost umbrella.

  19. Dwayne: Your comment seems in many places to forget that the subject, here, is philosophy. In philosophy, we don’t just uncritically accept notions like “the world” and “reality” and “correspondence.” Of course, working scientists need not be concerned with such things, but Mark’s is not a scientific, but rather, a philosophical essay. And in philosophy, handwaving at all of these things is essentially leaving everything that’s important unexplained.

  20. Hi Dan, your point is taken but I think my position is not quite as bad as you make out.

    First, I didn’t forget that the subject was philosophy.

    Second, I was not in any way asking people to uncritically accept notions like “the world”, “reality”, and “correspondence”. Announcing I have adopted an axiom which allows one to use such terms for practical purposes (for example science), while caveating that it does not bring us any closer to verifying truth claims about such things (including the “truth” of the axiom), is not exactly bypassing critical reason.

    Third, I’m not seeing how that is so different than Hume’s answer to these kinds of problems. Basically he “handwaves” it goodbye on the way to the local tavern. My concept was to adopt a practical, if caveated, position about metaphysical/ontological claims which saves natural language (yes even about causation) so that we have a practical working model that *might* be valid. We can of course doubt its validity into *potential* non-existence, through radical uncertainty. Great. If the radical skeptics are right and it ends up only being useful in the tavern (and apparently the lab), then oh well. I don’t see a reason to give it up or not discuss it as a practical, potentially correct model to work from as long as it is properly caveated.

    (But I am curious if/why you think Hume’s approach which IIRC you call naturalism avoids your criticism)

    Fourth, that the use of such notions appear to provide valid results (again exampled by science)–by which I mean improved sets of actions available on entities not previously recognized–makes such radical uncertainty positions less satisfactory to me as philosophical positions. Is it invalid to mention (or ask about) the unlikelihood of certain successes without some level of “correspondence”? For example, how do we get cool electron microscope pictures of things previously unknown, and make proper use of such findings if there is no such thing as correspondence between our theories and the objects we posited?

  21. EJ: “A tree falling in the wilderness with no one around it doesn’t even exist, let alone make a sound, as far as I’m concerned. I need the report, the recording, the articulation of the event for it to have any meaning for me at all.”

    Mark: “It goes without saying that it won’t have any meaning for you if you don’t know about it – but to claim the event didn’t happen just because no one saw it happen seems to be moving into strange territory.”

    I forgot to respond to EJ earlier. I was also confused by this statement.

  22. Hi Dan… I should have also said in reply to this…

    “but Mark’s is not a scientific, but rather, a philosophical essay. And in philosophy, handwaving at all of these things is essentially leaving everything that’s important unexplained.”

    There are things being argued between you two regarding philosophy that is as I said in my first post “above my paygrade”. Mark seems to be making an argument for a “stronger” position than the one I outlined, but it is one I am sympathetic to.

  23. Mark,
    Yes, I agree that we seem to live in different realities, which is rather troubling to any theory of reality. A mild relativism just seems a safe bet.

    My point about dinosaur remains and human remains is that such a case is simply trivial – evolution just is not the kind of theory open ti falsifiability tests. I don’t deny that such a standard has value for scientific research. But evolution is a narrative redefinition of the nature of life on the planet as an historical process. As such, it cannot set up tests for falsification; it either explains the phenomena or it does not.

    Facts are articulations of things, events , relationships. They are always linguistic in nature. Things and events are meaningless without articulation, and relationships always require interpretation.

    The question here is what constitutes knowledge. Who cares what happens anywhere if there’s no human to experience it or articulate it for others?

    And yes, by the way, I do have problems with sentences like “the cat is on the mat” as an example of ‘common sense’ logic, since, lacking contextualization, they have minimal sematic value.

    Part of the richness of natural languages is that they embedded in the contexts of their use to such an extent that the logic of that use is hardly noticable. Formal logics are impoverished by comparison, and necessarily so if we wish to use them as tools – which of course we do, since they are designed intentionally for a purpose.

    Obviously I’m not going to convince you to either of these points here. But I did want to make a little more clear the reality I live in difference to that proposed in the essay.

    I’m all for Pragmatism, of course – it seems useful in accepting the variety of methodologies used in the making of knowledge.

    dbholmes,
    “Realism to me is not a position determined (delivered proof) by logic or investigation. It is a declaration one has chosen an axiom about the relation between experiences and what they seem to suggest about the world.”

    This is not Realism, in either its Classical, Medieval, or Modern variants. Once admitting that one has chosen an axiomatic approach to experience and the world, one by the way implies that neither experience nor the world impress themselves on us directly.

    As to the falling tree – I reject any ‘view from nowhere’ in epistemology or metaphysics. Knowledge is what *we* make of it. I’m sure that there are, every minute, a myriad of events happening through-out the universe, but they won’t become ‘facts’ until we learn of them and articulate them somehow

  24. ejwinner

    Just a quick response to your last comment. You said:

    “And yes, by the way, I do have problems with sentences like “the cat is on the mat” as an example of ‘common sense’ logic, since, lacking contextualization, they have minimal semantic value.”

    I meant it as a stand-in for fully contextualized statements of this kind.

    “Part of the richness of natural languages is that they are embedded in the contexts of their use to such an extent that the logic of that use is hardly noticable…”

    I totally accept this. I didn’t elaborate on it but the point about the young child and logic in the early part of the essay fits in perfectly with this view.

    “… Formal logics are impoverished by comparison, and necessarily so if we wish to use them as tools – which of course we do, since they are designed intentionally for a purpose.

    Obviously I’m not going to convince you to either of these points here…”

    Well, the first point I already accept. The second I’m not sure about because I’m not sure what it is exactly.

  25. ejwinner

    (I think I misunderstood your “point” demarcations.)

    “I’m sure that there are, every minute, a myriad of events happening through-out the universe, but they won’t become ‘facts’ until we learn of them and articulate them somehow.”

    Your point seems to be about the word ‘facts’ and what it means/how it should be used. As I indicated, I avoided using the word because it has (or could be seen to have) the sense you suggest. But I’m surprised by the first part of the sentence because in a way that’s all I want to insist on as far as my ‘realism’ is concerned. I’m surprised by the assertion (much as I agree with it). I thought you were denying this.

    “My point about dinosaur remains and human remains is that such a case is simply trivial – evolution just is not the kind of theory open to falsifiability tests.”

    But falsifiability seems to apply perfectly well here. Finding certain kinds of fossils would upset the theory. Therefore it is falsifiable. Isn’t it?

    “…it either explains the phenomena or it does not.”

    Okay. But if strange new evidence comes to light the theory may no longer explain the phenomena (and so be rejected). Looks to me like falsifiability applies.

    “The question here is what constitutes knowledge.”

    This question can be taken in different ways.

    “Who cares what happens anywhere if there’s no human to experience it or articulate it for others?”

    Caring – or not caring – *is* a personal matter, and a relative one. With that I agree.

  26. dbholmes

    Thanks for the kind words. I was interested in the point of view you were putting.

    You said to Dan: “Mark seems to be making an argument for a “stronger” position than the one I outlined, but it is one I am sympathetic to.”

    This seems about right, and I’m glad you’re sympathetic to what I’m saying – or trying to say. To tell the truth, I’m a bit unsure where I stand on a number of these issues, but some claims and approaches make sense to me – and ‘ring true’ – while others decidedly don’t. That’s my starting point.

  27. A few people (eg Hilary Putnam, Hartry Field) have suggested that Popper’s interpretation of Tarski as supporting a correspondence theory is not quite true (;)). And one can believe in the correspondence theory of truth and still be an Idealist. I like Popper because of his stance that a philosopher can make useful contributions to solving problems affecting other disciplines eg his pretty minimalist solution to the problem of induction and progress in science.

    As to the construction of theories, in his book on the Presocratics, his example of hypotheses (conjectures) that are much better than anything a simple empiricism would get you (at that time) are the atomic theory and Anaximander’s idea that the Earth is held up by nothing, “because it is equally distant from all other things”. He is attracted to this “rationalist” way of hypothesis generation as being the same way Einstein generated fecund theories from very simple mathematical principles. In the same way, he claims he liked W’s Tractatus because of the cosmology it implies.

    So, Darwinian evolution is a rationalist explanation making sense of a vast number of facts all at once (one explanation for its pretty rapid acceptance). Such a broad theory allows a similarly large number of tests, but no single one will be enough to refute it, but rather cause theory modification or evolution.

  28. Hi EJ,

    EJ: “I’m sure that there are, every minute, a myriad of events happening through-out the universe, but they won’t become ‘facts’ until we learn of them and articulate them somehow.”

    Mark: “… I’m surprised by the first part of the sentence because in a way that’s all I want to insist on as far as my ‘realism’ is concerned. I’m surprised by the assertion (much as I agree with it). I thought you were denying this.”

    I’m really on the same page as Mark here. Your original claim read to me as if you were denying the first part of the sentence.

    EJ: “This is not Realism, in either its Classical, Medieval, or Modern variants.”

    That could be why I wrote “Realism to me is…” and not just “Realism is”. The *to me* was there for a reason. Let me unpack that bag a minute…

    As far as I can tell (though I admit my knowledge is a bit out of date) the battles between Realism and Anti-Realism have ended in a virtual stalemate. Different forms of doubt (Cartesian, Humean, etc) have established a check on making any firm commitments either way. And I concede a lack of *absolute* knowledge regarding the nature of existence and our experiences.

    So a thoroughly stringent position on the question should be “I don’t know”. Yet Realists and Anti-Realists keep going at it. People claim to be one or the other. And when I have heard them talk (like the debate Victor Panzica recently linked to) it always seems to me that each has some starting foundational belief from which they are working. I don’t think that Dan would disagree with that for Realists, though he might for Anti-Realists. But to me the ARs must hold one just the same as Rs (again unless they are full blown solipsists).

    While I found Hume’s concession to lack of knowledge humorous, and a worthwhile read, it was a bit unsatisfactory. Maybe back then it would have been easier to roll with, but not given many experiences we have today that were not available back then. What I am talking about is predictive value well beyond the scope of our immediate experiences. I gave the example of the electron microscope to Dan.

    Yes, at the end of the day we can shake our philosophical doubts off and head off to the tavern, letting the constant flood of experiences and our necessary interpretations (like causation) have their way with us to simply get on with it (living). However, I found myself asking yeah but what concept are you using when you are out there “getting on with it”? And why do so many interpretations work so consistently, especially if you head to the lab rather than a party?

    So *to me* I am doing the same thing as Hume, only admitting that I am holding a functional, tentative Realism when I’m “getting on with it”. A Realism caveated with an acknowledgment there is a foundational belief (an axiom), which may or may not be true.

    To circle back to the first quote I gave from you. I don’t see how you can talk about “myriads of events happening through-out the universe” much less being “sure” of them unless you are holding at least the provisional, axiomatic form of Realism I discussed or the one Mark is advancing.

    EJ: “Once admitting that one has chosen an axiomatic approach to experience and the world, one by the way implies that neither experience nor the world impress themselves on us directly.”

    One axiom, acknowledged to be held for a practical purpose and can be removed for further deliberation. I’m not sure I’d call that an axiomatic approach. In any case, I’d be interested if you could unpack your last statement. I don’t see why it entails that as I take it the axiom I set out is a working assumption it does that very thing.

  29. davidlduffy

    What you say highlights the richness and dynamism of Popper’s view of science, both in terms of the freedom involved in the conjectures and also in terms of the explanatory side of things. Believing in the possibility of scientific explanation implies a degree of realism, does it not? That is, you are assuming that there are actually occurring processes that may be explained in their own terms – not just in terms of our thoughts and perceptions etc..

  30. dwayne: I’m afraid I see no help for Mark from Hume whatsoever. If Hume is a Realist, it is of the commonsense variety, a la Reid, and this is not at all obvious. The chapter “Skepticism with Regard to the the Senses” seems to imply a kind of philosophical phenomenalism, a la Berkeley, and a vulgar Realism, none of which provides a philosophically rigorous “reality” to connect to some robust notion of correspondence-truth.

    I don’t know what you mean by taking realism as an “axiom.” I would certainly accept Wittgenstein’s notion that depending on which language game we are playing, certain propositions function as “hinges,” and I would also agree that in scientific language games, statements like “there are celestial bodies” play such a role. But this is precisely the sort of framework relativism that Mark is trying so hard to eschew.

    This is part of the problem with being as hand-wavey as Mark has been. It’s not even clear what, really, the proposal is, so it’s very difficult to say what counts for or against it.

  31. dbholmes,

    If you set out to learn the world through the lens of an axiom, then you’ve already admitted that your experience will be mediated. If your axiom is “I will assume that the world comes to me directly through experience,’ this reduces to a presumption that one can decide beforehand how one will experience the world.

    It should be noted that even contemporary Realism looks little like Classical or Medieval Realism; Charles Peirce, who understood traditional Realism and wanted to find some way to resurrect it, pointed out that all modern philosophies are openly or covertly forms of traditional Nominalism, actually because of such ‘axiomatic’ approaches to reality; since Descartes, we have always begun inquiry into the nature of knowledge with the knower rather than with the world.

    Mark,
    I think davidlduffy gives a pretty good thumbnail sketch as to why evolution is not really very open to falsification. It can only be replaced by a stronger theory, which I don’t see happening any time soon.

  32. Dan

    (Addressing Dwayne) “I would certainly accept Wittgenstein’s notion that depending on which language game we are playing, certain propositions function as “hinges,” and I would also agree that in scientific language games, statements like “there are celestial bodies” play such a role. But this is precisely the sort of framework relativism that Mark is trying so hard to eschew.

    “This is part of the problem with being as hand-wavey as Mark has been. It’s not even clear what, really, the proposal is, so it’s very difficult to say what counts for or against it.”

    Okay, what about my (and Dwayne’s) observation that ejwinner’s statement, “I’m sure that there are, every minute, a myriad of events happening throughout the universe, but they won’t become ‘facts’ until we learn of them and articulate them somehow,” reflects the view I am putting? The statement is clearly not restricted to a scientific framework; and I acknowledge that ‘facts’ can be seen in this way. (Popper is using the word in a different sense.)

    Let me spell this out a little more. Astrophysics is theory-based and so postulates all sorts of specific entities and/or processes. My concern here is not with the existence of any specific entities or processes but simply to insist that the various sciences are dealing with *actual processes* which are subject to being investigated and (to a greater or lesser extent) described and explained.

    It’s almost as though you are wanting me to make a science-like claim which is vulnerable to falsification whereas my claim is not like this and *not intended to be like this*. It is simpler. It is — as I see it – stating the obvious (which is worth stating only because some people (often philosophers) deny it).

  33. Mark, I don’t see how even a metaphysical anti-realist need disagree with the claim that “sciences deal with actual processes which are subject to being investigated …” etc. As I said, Nelson Goodman could agree with this.

    So, I don’t see which philosophers would reject it.

  34. So is it just the use of the word ‘realism’ (or perhaps the word ‘correspondence’) that you are arguing against here. Why is what I have said and/or presented Popper as saying “challenging”? Is the problem just terminological? Take the bit about language/metalanguage, for example, which is at the heart of it but which no one has talked about.

    I would be pleased if there were no differences. But I think there are. And I suspect that what may lie behind them is a general take on science (and its epistemic authority). Many, many academics in philosophy and other fields want to question the epistemic authority of science. Like Rorty. (And most continentals, I would have thought.)

  35. “Believing in the possibility of scientific explanation implies a degree of realism, does it not?”. Hi Mark, yes absolutely. In Popper’s contribution to the symposium on Tarski (visible via Google Books), he specifically says he was worried that his first book depended so heavily on “truth” and “facts”, and was so happy to see Tarsky’s formalism. He remains better known than say Goodman because he is a scientific realist and suggests a nice simple framework that fits in with how science works and how statistical analysis of experiments proceeds — see Deborah Mayo’s website
    https://errorstatistics.com/
    This is though the usual Neyman-Pearson “p value” approach is explained the opposite way around ie as rejecting a strawman “null hypothesis” which is usually not what we believe, as opposed to “strongly testing” a conjecture. In real life, we take small p values as support for the idea that our conjecture has survived refutation. Obviously, statistical testing and decision theory currently lean upon classical logic.

  36. Thanks for answering my question Mark, but feel there was a bit more in it that I need help with addressing before I can let go.

    Natural and formal languages are of course different, but apparently lojban can be used in both formal and natural contexts, so saying a formal process (Gödel’s realm) is not the same as an informal process (Popper’s realm) is not saying very much.

    It’s not the differences between the contexts that is my problem, my problem is that there are similarities between the contexts that makes my mind invent a common structural feature. And once “seen”, it’s very hard to get rid of!

    I guess what we’re doing here is playing with such similarities, so here goes: Just as Gödel assigned all formal system statements a prime, Borges assigned all natural languages sentences a prime. Borges ends up with understanding the meaning of “Axaxaxax mlö” (i.e, he claims that that sentence belongs to a natural language) even if that sentence looks like white noise gibberish to most people. Borges also has this guy being able to read a sacred sentence written in the picto-logo-graphical language of leopardskinspottish.

    Btw, would feeding an graphics AI with endless pictures of school children’s integer long division homework lead to the discovery of graphical rules that could then do long division with aztec numbers and get the right answers without knowing what math it was doing? What about arbitrary symbols like pictures of oranges and apples (i.e not numbers)?

    Anyway, it’s not me who (perhaps) is irritating, it’s Popper who says that Tarski’s Theory of Truth is both “the great bulwark against relativism”[1] and “trivial”[2]! 🙂

    “On the other hand, triviality might reasonably have been expected, since after all everybody understands what “truth” means as long as he does not begin to think (wrongly) about it.”

    That sentence is as hard to ignore as it is to understand.

    Best regards.

    //Erik

    [1] A World of Propensities, page 3
    [2] Unended Quest: An Intellectual Autobiography, page 165

  37. I am busy today and will have to reply later (definitely have some things to say), but I want to reinforce Mark’s request for an explanation (from EJ or Dan) about EJ’s statement… “I’m sure that there are, every minute, a myriad of events happening throughout the universe, but they won’t become ‘facts’ until we learn of them and articulate them somehow,”

    That includes his follow up question if this is merely a problem with terminology.

    And to Dan’s last reply… ” I don’t see how even a metaphysical anti-realist need disagree with the claim that “sciences deal with actual processes which are subject to being investigated …”

    What is an “actual process” for an anti-realist compared to a realist? This may be where we hit my paygrade but it was my impression ARs would reject “actual”, whereas Rs accept it.

  38. HI Dan, I want to sort out a few different issues we are dealing with…

    1) Mark is (as he and I both acknowledge) making a case for a “stronger” Realist position than I am. I did not say I was completely convinced the target was reached, but that I was sympathetic with his attempt to hit that target and thought his method looked reasonable (or as he described “sounded good”). You have suggested things are left unaddressed and that may be true. However some of your references to where there might be problems were less appealing to me and so would have to be fleshed out.

    2) My position is not that I adopt Realism as an axiom. Rather it is that when I say I am acting as a Realist, or taking a Realist approach, I am admitting that I have adopted an axiom (relating experiences to sources of experience) which allows me to do that. Without that axiom Realism as an approach would become (when push comes to shove) philosophically indefensible… that is until such time people like Mark make their case. Then again I see ARs in the same position.

    3) So my discussion of Hume was not to defend Mark. I agree he would not help with that. I only mentioned him given your criticism of my position, since I do not see how Hume would escape the same criticism. Perhaps I made it confusing whose position I was defending by using “hand-waving” to describe what Hume was doing. Most of your reply regarding Hume’s position seems to support my case. One can call what I am talking about “commonsense” and “vulgar” and that would be fine with me (actually I sort of like the ring of vulgar Realism) and captures what I am getting at… which is definitely *not* a “philosophically rigorous “reality” to connect to some robust notion of correspondence-truth.”

    I agree that Hume was not clear, which is why I brought up his being “hand-wavy” himself. I am very skeptical he was advocating a Berkeleyian position, even if his arguments mean it can’t be discounted. But I do agree he was suggesting, after shaking off philosophical skepticism to get back to living, that he was taking on a kind of common sense (or vulgar) Realism.

    I just wasn’t happy with how he ended on that (not being clear), and think one can explore what that means/requires and what one can build from that, even if it is not conclusive or air-tight rigorous.

    I think there is value to be had there, especially in light of activities and experiences coming out of science which simply would not make sense if one had adopted a solid Anti-Realist approach.

    1. I’m sorry, Dwayne, but I just don’t see how my account of Hume supports your case. I think it does exactly the opposite. He most certainly is *not* hand-wavey — that misunderstands his metaphilosophical position — and the chapter I cited from the Treatise, one of the most important chapters in Hume’s work overall, most certainly can be seen as supporting a kind of philosophical phenomenalism. Indeed, when I was at Michigan, I took an entire Senior Seminar on just the first book of Hume’s Treatise and wrote a paper on Humean Phenomenalism. That is not to say he *is* a phenomenalist — he isn’t — but that’s because of his metaphilosophical position, concerning the limits of reason, what nature compels us to believe, etc.

  39. Hi EJ,

    “If your axiom is “I will assume that the world comes to me directly through experience,’ this reduces to a presumption that one can decide beforehand how one will experience the world.”

    I’m not sure why it says anything quite so strong, especially if you keep in mind it can be wrong. It is a working assumption, and if it seems to keep working then how is that a problem? I already agree (as Dan has argued) it will not deliver a rigorous account, nothing air-tight against all doubts. But it allows an obvious way forward for action and further investigation, as well as easier ways of talking about one’s experiences based on most common (arguably built-in) interpretations.

  40. Hi Dan, maybe I should have said “position” instead of “case”.

    Outside of the phenomenalism bit, your description of what position he could be considered as taking (though you say is not obvious) is what position I was suggesting he was taking (and what I would essentially be taking).

    I am sure you have more time into this and so may have a much better read on Hume. But I will say that my prof had a totally opposite position as you on whether he could be read as “supporting a kind of philosophical phenomenalism.” The fact that you end by saying he isn’t one may account for that. That it is credited to a “metaphilosophical” position is not something I am seeing detracts from my point, unless we have to ignore that?

    It was my reaction to Hume’s position, as I took it and how it was taught, that led me to expand/explore in the direction I described.

    We can leave Hume out of it I suppose, but this does seem to be getting into a situation of where different people (even profs) have different interpretations.

    1. The point is just that nothing philosophical — or theoretical — can be done with Hume’s brand of commonsense realism. And Mark *is* trying to do things with his realism.

      As for your prof, I can’t speak for him. I was taught Hume by Louis Loeb and David Velleman, at the University of Michigan, and the orientation was generally the naturalistic reading of Hume a la Norman Kemp Smith.

  41. Hi Dan, well we are in agreement (I thought I said this) that nothing philosophical (at least nothing counting as rigorous philosophy) can be done with Hume’s brand of Realism, Mark seems to be trying for that level of rigour, and so Hume does not help.

    Again, I only brought Hume up regarding your comments about my position which I totally admit (again I thought that was stated) is not striving for some rigorous philosophy.

    This does raise the question if you totally discount any utility in less than air-tight, rigorous, philosophy? We may very well agree that when put through the absolute wringer, only certain limited accounts are possible. But isn’t there some worth in pursuing philosophical questions in less constrained ways?

    I feel there is. By easing constraints and testing, we can generate “concerns” or “questions” about the more rigorously acceptable accounts. You may have good reason to disagree but I am interested.

    On that point I am still interested in an explanation about the difference between AR and R accounts of “actual processes”. This dovetails with the comments made by EJ on ‘myriad events in the universe he is sure are occurring’. So far there have been no answers on this, which I (and likely Mark) feel would be useful and relevant. Right now they seem inconsistent with such wholesale rejection of Realist positions.

    “I was taught Hume by Louis Loeb and David Velleman, at the University of Michigan, and the orientation was generally the naturalistic reading of Hume a la Norman Kemp Smith.”

    I have no idea who these people are (exhibiting my pay grade). It is totally possible these people are the best. I have read at least one paper of yours on a naturalistic Humean account and I had no problems with it. I don’t even see that last point as conflicting with what I was taught. I was just pointing out (which you also seemed to be saying with mentioning Reid, and then calling his ideas into question) that there are other reads out there, and in my case kind of strongly about how much Hume would “support” Berkeley.

    1. I myself accept that Hume is a commonsense realist, so it seems that we have no disagreement. I read your early comments as supporting Mark, though, which is why I criticized them.

  42. Hi Dan (though perhaps to be clear for other readers), I still, by myself with no invocation of Hume, support Mark’s position in the sense that I sympathize with his target and thought his arguments sounded ok… but yeah it is up to people with bigger investments of time and energy in philosophy (the bigger guns) to hammer that one out to test its robustness. On that question I must withdraw.

    So we’re good. 🙂

  43. dbholmes,
    my remark on the myriad events I thought to be quite clear. No serious philosopher in the Modern era denies an external reality. To the extent that Mark suggests this, he is ‘straw-manning.’ The issue has *never* been whether there are things or events, but whether our interpretations of those can be trusted; to what extent; and on what basis. And finally, what it is it that we do with those interpretations – how do they fit into a larger view of the world, what are their material implications, how can they be used to ground further research or improve our lives, etc.

    Mark is also just wrong that the Continental tradition somehow poses a threat to the “epistemic authority” of the natural sciences. The “epistemic authority’ of the sciences has been an issue of concern since Descartes. There are currently some social-relativists who say silly things about the sciences. But most in the Continental tradition have pretty much left the hard sciences alone.

    At one point Mark suggests that he wrote this essay partly in response to my piece on Hegel. If Mark thinks that Hegel is the source of his problems, the originator of ad-hoc explanations that seem to suck every unexpected counter-example into them, or that Hegel is a solipsist or a relativist in any way whatsoever, he couldn’t possibly be more mistaken. And although Nietzsche wrote that truth was merely a deployment of metaphors so overused that it had been forgotten that they were metaphors, he also wrote admiringly of the modern sciences and the technologies they spawned as providing the means for a future poiesis of human culture divorced from the superstitions of the past. Finally, it may come as a surprise to discover that two of the most important figures in the Continental tradition – Husserl and Heidegger – both considered themselves traditional Realists, like Peirce (whom they both had read), trying to find a language that would articulate a direct knowledge of reality (“Being’ as Heidegger liked to call it), providing a ground for the sciences – for mathematics and the natural sciences for Husserl, for the social sciences and philosophy itself for Heidegger. But Peirce’s Realism collapses into (the decidedly Nominalistic) semiotics, Husserl ends up with so much bracketing that we can no longer distinguish the bracket from the reality (das ding an sich) we wish to know, and Heidegger deludes himself that he can know the ‘reality’ of Nazism better than the Nazis themselves, and suffers the consequences.

    Look, traditional Realism just no longer works. It was a beautiful idea, it helped ground Aristotle’s empirical research (such as it was for its time), and an almost earthy trust in the essential goodness of God’s Creation in such as Thomas Aquinas. But once scientists began to discover that ‘the world is not only stranger than we suppose, but stranger than we can suppose;’ and once philosophers stopped asking ‘what can be known? how can the world make itself known to me?’ and began asking “what can I know? how can I know anything at all?’ the jig was up. Reality does not come to us directly and never has.

    BTW, and certainly related: if I understand you aright, your continuing clarifications – and moderations – of your preferred take on Realism, tend to sound more and more like a rather moderate Pragmatism – an experimentalist ‘ok, let’s believe this for now, and see what comes of it.’* That’s not at all the kind of (scientific) Realism Mark is advocating. He wants to say that the theories of the natural sciences are purely descriptive of actual events and processes *just as they are* – I don’t see how this successfully evades the problems of interpretation.

    —-
    * Somewhat reminiscent of Dewey – Popper’s real adversary here, although I don’t know if the two thinkers ever acknowledged each other.

  44. dbholmes,
    I forgot to clarify – from the perspective I am writing from, ‘facts’ are the results of argumentation that begins when someone makes the claim (such as) ‘It is the case that -.’ Once the argumentation has convinced us of the truth or reliability of the claim then the ‘case’ is agreed to be a fact. (The reason why interpretation is so important here is because such argumentation has to present a strong interpretation of the case to be convincing. However what grounds a strong interpretation is itself a matter of interpretation, and so we have discussions and arguments such as this one.)

  45. DanK,
    Well, I think traditional Realism was long panting from exhaustion, but there’s no doubt that Kant drove a spike through its heart.

  46. Hi Erik (and others)

    Borges! Right. Now I have a better sense of where you are coming from. I am operating on a much more pedestrian level however.

    On the issue of the distinctions between natural, constructed and formal languages, this is complicated and I’m no expert. But the point I would want to make is that a formal system is one in which every element (symbol) is specified in advance with precise and explicit rules for the way they may be combined into well-formed formulas, a set of axioms and rules of inference. If a language is actually used in the real world in the way natural and various constructed languages are it is not (or is no longer) formal. Given this gap (or gulf?) between formal systems and ordinary language, it’s little wonder that there are various conflicting interpretations of, say, Gödel’s proof.

    It’s funny you should highlight that point about Popper’s use of the word ‘trivial’. It struck me also as not only interesting but absolutely central to what he is saying. And it ties in with my recent replies to Dan.

    It is not clear from the OP because (as I previously noted) the editors have stripped off some of the quotation marks from the version I sent in (Dan explained why) but they did not indent all of the quoted paragraphs. So I have reinserted the quotation marks here. *Popper’s* words:

    “We can now make a statement in the metalanguage about the correspondence of a statement of the object language to the facts as follows. We can make the assertion: The German statement ‘Das Gras ist grün’ corresponds to the facts if, and only if, grass is green. (Or: ‘. . . only if it is a fact that grass is green.’) This is very trivial. It is, however, important to realise the following: in our assertion, the words ‘Das Gras ist grün’, put within quotes, function as a metalinguistic (that is, an English) name of a German statement; on the other hand, the English words ‘grass is green’ occur in our assertion above without any quotation marks: they do not function as a name of a statement, but simply as the description of a fact (or alleged fact).

    “This makes it possible for our assertion to express a relationship between a (German) statement, and a fact.”

    So, yes it is trivial in a sense. But making the object language/metalanguage distinction gives us a kind of ‘dual perspective’ which allows us to “express a relationship” (as Popper puts it) between a statement (language) and things that are not language.

    As I said previously, Popper is using the word ‘fact’ in a different sense from how most philosophers want to use it; but I think that it does, like many words, have different senses and can be used in subtly different ways. Sometimes it refers to information or ‘processed input’; but often it simply refers to what is ‘out there’. Think of the common idiom, ‘The fact of the matter is …’ meaning: ‘This is how things really stand (in respect of the topic under discussion)’. (Notice also that at one point Popper says “… fact (or alleged fact).”)

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