The return of radical empiricism

zby Massimo Pigliucci

“All our knowledge begins with the senses, proceeds then to the understanding, and ends with reason. There is nothing higher than reason.” So wrote Immanuel Kant in his Critique of Pure Reason, one of the most influential philosophy books of all time. Kant is also the philosopher credited for finally overcoming the opposition between empiricism and rationalism in epistemology, as he realized that neither position, by itself, is sufficient to account for human knowledge.

Kant was notoriously awoken from what he termed his “dogmatic slumber” [1] by reading David Hume, who had written in his Enquiry Concerning Human Understanding:

“All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic … [which are] discoverable by the mere operation of thought … Matters of fact, which are the second object of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. … If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.”

The second part of the quote makes it clear that Hume, in turn, was reacting to the philosophical excesses of the Schoolmen, the medieval logicians who attempted to discover truths about the world by sheer power of mental analysis — an approach that, to be fair, goes back at the least to Plato himself, who was himself impressed by the effectiveness of mathematics in arriving at conclusions with certainty, and thought that the task of philosophy was to do likewise when it came to its own spheres of interest.

Why am I reminding you of all this? Because I am now convinced that we are witnessing a resurgence of what I call radical empiricism, the sort of thing that we thought we had left behind once Kant came onto the scene, and which, frankly, not even good ‘ol Hume would have endorsed.

Recently, here at Scientia Salon I published three essays — two by Robert Nola [2] and one by Coel Hellier [3] — that epitomize radical empiricism, more so in Hellier’s than in Nola’s case, I might add. Interestingly, Nola is a philosopher and Hellier a scientist, and indeed it is known by now that “scientism” — which is the attitude that results from radical empiricism — is being championed by a number of scientists (e.g., Lawrence Krauss [4], Neil deGrasse Tyson [5]) and philosophers (James Ladyman and Don Ross [6], Alex Rosenberg [7]).

Clearly, I find myself puzzled and bewildered by this state of affairs. As someone who has practiced science for a quarter century and then has gone back to graduate school to switch to philosophy full time I have a rather unusual background that, I think, makes me appreciate where radical empiricists come from, and yet which also precludes me from buying into their simplistic worldview.

In the remainder of this essay, then, I will try to do the following:

  1. Sketch out what I see are the logical moves attempted by radical empiricists;
  2. Show why they don’t work;
  3. Explain why this is more than an academic debate, and certainly more than “just semantics.”

Radical empiricists’ moves in logical space, and why they don’t work

My, by now, extensive readings of and conversations with radical empiricists have unearthed a number of standard moves they tend to make. I will briefly discuss six of them. Two obvious moves are (i) the use of an over-extensive definition of science and the assertion that other valuable disciplines — particularly (ii) logic and math — are “ultimately based” on empirical facts. Since radical empiricists do not seem to value (except for some degree of forced lip service when challenged) any other kind of inquiry or method of understanding (say, philosophy, literature, or the arts), it then follows that science really is all we should care about. It is as if they collapsed Hume’s already narrow distinction above between relations of ideas and matters of facts, arguing that the former are really a version of the latter anyway.

The concept of science, of course, has changed over time. The term did not actually exist as indicating a particular approach to knowledge of the world until recently [8]. Arguably, Aristotle (but not Plato!) was doing science, and so were some of the pre-Socratic philosophers, particularly the atomists. After the Renaissance, “natural philosophy” began to separate itself from philosophy more broadly construed, and finally a number of individual sciences became independent during the 18th, 19th and 20th centuries (most recently psychology, which was still a branch of philosophy until about the time of William James).

But modern defenders of radical empiricism don’t get to help themselves to the fact that what we understand by science has changed over the centuries, because if they did they might have to concede that, really, historically speaking it’s all philosophy.

Where could we turn for help, then? I’d say the dictionary, to get us started. Dictionaries are funny things. They play both a descriptive and a prescriptive role. They are descriptive of how — at any particular moment — a given culture uses a certain term; that, of course, can and does change over sufficiently long periods of time. But dictionaries are also prescriptive in the sense that, within a reasonably short time frame, they also tell us how we ought to deploy those terms. One doesn’t get to arbitrarily redefine words to suit one’s own ideological position or personal inclinations.

So, what are the dictionary definitions of science, mathematics and logic? Here they are (from my built-in Apple Dictionary):

science, the intellectual and practical activity encompassing the systematic study of the structure and behavior of the physical and natural world through observation and experiment. (Interestingly, the same dictionary also provides this alternative meaning: “knowledge of any kind,” but labels it as archaic.)

mathematics, the abstract study of number, quantity, and space.

logic, reasoning conducted or assessed according to strict principles of validity.

It ought to be clear even from these definitions — which are congruent with the vast majority of the specialized literature on the philosophy of science, of math, and of logic — that mathematics is distinct from but akin to logic, and that both of them are very distinct from (although very useful to) science. Hume was onto something, after all.

As I mentioned, the most common refrain from radical empiricists when faced with the above is that math and logic “ultimately” are rooted in empirical knowledge, a recurring example being that we believe that 1+1=2 because we can see that if we put side by side two objects of the same kind we get a total of two objects of the same kind. Another example is that standard practices in logic, say modus ponens [9] are adopted because they “work” in the real world.

Both responses miss the mark because they subtly but surely change the conversation. The first example tells us at most that human beings began to think about abstract objects prompted by elementary empirical observations. But the question at hand is not how mathematical reasoning originated in the Pleistocene, it is what kind of mental activity is modern mathematics. And much of it has nothing whatsoever to do with empirical groundings of any sort. Yes, math is deployed as a tool in science and in all sorts of other applications, but there are huge swaths of mathematical territory that neither describe anything in the world nor are pursued by mathematicians for any practical reason at all.

As far as logic is concerned, a similar reasoning holds there too. And the example of the utility of modus tollens is another red herring that derails the conversation: the question isn’t whether some principles or methods of logic are useful and therefore employed in other areas of application. Of course they are. But logicians — just like mathematicians — are concerned with the formal structure and internal coherence of their constructs, not with whether they do or do not map onto the real world. Many of those structures do not, in fact, map onto the world. When they do, it is only because the world as it actually is does not contain logical contradictions and mathematical inconsistencies, so math and logic are bound to describe the real world together with countless other hypothetical ones (this is true quite irrespective of the ontological question concerning abstract objects, i.e., regardless of whether one is inclined to be a Platonist or not).

Another common move employed by radical empiricists is to (iii) deny the existence of a priori knowledge. It cannot exist, because otherwise they’d have to admit that science (understood as an essentially empirical enterprise) isn’t the source of all knowledge. The most sophisticated of the new wave of radical empiricists sooner or later will cite W.V.O. Quine’s famous rejection of the difference between analytic (a priori, by reasoning) / synthetic (a posteriori, by observation) truths in his paper, “Two dogmas of empiricism” [10]. But I bet that a good number of them have not actually read it, and even more likely that they are not aware of the criticism it got and of the significant amount of backtracking Quine himself had to do throughout the rest of his career.

You see, Quine made ample room for a priori truths in his “rejection” by acknowledging two things: the special status of mathematics as a type of science because it has applications in science (but see above for why this is irrelevant), and the fact that tautological statements (the famous “bachelors are unmarried men” kind of thing) are indeed examples of analytic truths, but turn out to be “epistemically insignificant” according to Quine’s judgment [11]. Well, that’s his opinion, and given that much of logic and math are built on tautologies, a very debatable opinion at that.

A better example of what Quine was talking about are equations such as F = ma from Newtonian mechanics. He thought that this may look like an analytic truth, specifically a definition (hence tautological) of force. But in fact the equation is only true within a specific empirically-based theory of the natural world, its truth not deriving from mathematical reasoning per se. I have no qualms with that, but acknowledging this is a far cry from saying that there are no a priori truths and no difference between synthetic and analytic statements.

Radical empiricists’ next move is to (iv) point out that science uses the same fundamental tools — observation and reason — that we all deploy in everyday life whenever we want to know anything at all. This is just as true as it is utterly uninteresting. It would be surprising, in fact, if science as a human epistemic activity were to somehow transcend the basic intellectual faculties of our species and operate sui generis (just as it would be equally surprising if there were a philosophical method that was entirely distinct from normal human reasoning). Of course doing math, logic, philosophy, art, literature, navigating the New York City subway system, and plumbing use facts (whenever appropriate) which are analyzed by reason. Nevertheless there are tons of interesting distinctions among all those activities, distinctions that are lost by the quest for what I have come to call “explanatory monism,” the obsession with a one-size-fits-all epistemology. Epistemic pluralism is much more interesting and fecund, not to mention more accurately reflective of actual human practice.

The next move, then, is a partial retreat on the previous one, and goes something like this: (v) there are no sharp distinctions between the mentioned activities, so there is no principled way to distinguish among them. To which I can only reply in two ways: there is no sharp distinction separating a helicopter, a jumbo jet and a Saturn rocket, as they are all flying machines. But if you think there are no interesting differences among them you are sorely mistaken. Also, anyone seriously arguing that philosophy, math, logic and, say, biology, are more or less the same thing has clearly not read a single technical paper in more than one of those disciplines.

There is one more defense of radical empiricism, rooted in a kind of greedy reductionism: (vi) the idea that “ultimately” whatever it is we are interested in (poetry, art, mathematics) is made of physical matter or done by beings made of physical matter, so that it all comes down to neuroscience or, if the radical empiricist is particularly bold, to quantum mechanics.

This, again, is a move predicated on shifting the discourse without apparently realizing that one has done so. The issue isn’t what something is made of (ontology), but rather how we may best proceed in understanding it (epistemology). Epistemologists understand very well that for any particular problem X there is a usually small number of levels of analysis that are most informative and appropriate in order to understand X. These can be located one or two (loosely defined) levels of complexity below or above X itself, but the explanatory returns taper off very quickly after that. Let me give you an example.

Let’s say you want to understand the population dynamics of a species of plants, for instance belonging to an invasive species (this comes straight out of my work as an empirical scientist, as you might have guessed). It is of no use to point out that plants, “ultimately” are made of quarks. A quantum mechanical theory of population dynamics — even if possible in principle — is never going to be developed and it wouldn’t help anyway because it would be far too complicated (and unnecessarily so) for a human to comprehend. Instead, the population biologist looks at population genetics (circa one level of complexity below that of organismal biology) and at ecosystem theory (circa one level of complexity above).

Similarly, it is a good bet that to understand economies one needs to operate at the level of economics as autonomous science, plus at the levels of, say, human sociology and psychology. Neuroscience is not likely to be helpful, because it would be too detailed for the problem at hand, even though of course economies are inventions of the human mind, and of course the human mind is the result of the activity of the brain, and of course the brain is made of neurons and other cell types. If you are not convinced, try to go even further down the hierarchy of complexity. How likely is it that we could develop a useful theory of economies based on molecular biology (after all, the brain is made of molecules!)? What about fundamental chemistry (those molecules are made of atoms!)? And so forth until we get to the single wave function that allegedly represents the entire universe.

So, a crucial reason to maintain distinctions among fields of inquiry — even when acknowledging bridges, cross-pollination, and similarities — is that ultimate reductionism will always be a losing epistemic proposition, even if one agrees with the ontological statement that everything is made of quarks (or strings, or wave functions).

Why bother?

I find all of the above intrinsically interesting as an example of intellectual debate about matters of proper definitions, conceptual understanding of different human epistemic activities and so forth. In other words, as a professional philosopher this kind of discussion represents a worthwhile venture into the philosophy of science and in epistemology. But there are far more practical reasons why the assault of the radical empiricists ought to be resisted.

Two reasons in particular are of concern to me: the damage being done to non-scientific disciplines, and the damage potentially to be suffered by science itself.

For years now the humanities and any non-STEM (Science, Technology, Engineering and Mathematics) fields have been in retreat in colleges throughout the world, especially in the US. This retreat is the result of a number of factors, perhaps foremost among them the increasing importation of business-style models into academia and the resulting conviction that if studying a given discipline doesn’t have an immediate payoff in terms of employment then it is not worth studying. This is a false and perniciously instrumental view of higher (and lower, really) education, which has the potential to undermine people’s ability to develop into cultured human beings capable of reflecting on what they do, how they do it , of appreciating all aspects of life (not just jobs and livelihood), and of making informed decisions as members of a democratic polity.

The aggressiveness of radical empiricists and their dismissal of non-scientific fields exacerbates this problem, and in my mind, therefore contributes to undermining the very fabric of our democracy and to decreasing the quality of our life.

This may sound like “defending the turf,” and in a sense it is. But some turfs are worth defending against an all-encompassing cultural imperialism that risks to flatten the intellectual landscape in the name of Science (notice the capital S). And no, I’m not at all coming at this from the point of view of mystical or theological woo in constant entrenchment against science — as I hope is abundantly clear by the body of my writings.

The second worry may seem specious, but I think it is just as important to appreciate. I think that an over-emphasis on the powers and overall reach of Science will, in the long run, do harm to actual, good science. We are already facing a public that is increasingly unwilling to trust scientific findings (just think of the widespread rejection of the theory of evolution or the notion of climate change, or of the uncritical acceptance of a non existent causal link between autism and vaccines, to mention just a few examples). The more scientists are seen as arrogantly dismissive of any other dimension of human experience the more this distrust will grow and fester. And science, the real science done in countless laboratories and university centers across the globe, is just too precious an achievement of humanity to let it be damaged by an emotional reaction to the loud, radical statements of an overbearing but comparatively small number of highly visible public figures.

Isaac Asimov famously said that “The saddest aspect of life right now is that science gathers knowledge faster than society gathers wisdom.” Indeed, but we don’t get wisdom from science alone.

_____

Massimo Pigliucci is a biologist and philosopher at the City University of New York. His main interests are in the philosophy of science and pseudoscience. He is the editor-in-chief of Scientia Salon, and his latest book (co-edited with Maarten Boudry) is Philosophy of Pseudoscience: Reconsidering the Demarcation Problem (Chicago Press).

[1] As he put it, in Prolegomena to Any Future Metaphysics.

[2] Scientism: ‘Yippee’ or ‘Boo-sucks’? — Part I and Part II, by Robert Nola, Scientia Salon, 18 and 19 August 2014.

[3] Defending scientism: mathematics is a part of science, by Coel Hellier, Scientia Salon, 21 August 2014.

[4] Lawrence Krauss: another physicist with an anti-philosophy complex, by Massimo Pigliucci, Rationally Speaking, 25 April 2012.

[5] Neil deGrasse Tyson and the value of philosophy, by Massimo Pigliucci, Scientia Salon, 12 May 2014.

[6] James Ladyman on Metaphysics, Rationally Speaking podcast, 9 September 2012.

[7] Is science all you need?, by Massimo Pigliucci, The Philosopher’s Magazine, 2nd Quarter of 2012.

[8] The very word “scientist” was coined by philosopher William Whewell in 1833, in response to a challenge issued by poet S.T. Coleridge.

[9] Modus ponens.

[10] Two dogmas of empiricism, by W.V.O. Quine.

[11] Quine, W.V.O. (1991) Two Dogmas in Retrospect. Canadian Journal of Philosophy 21:265-274, see p. 271.

315 thoughts on “The return of radical empiricism

  1. Hi All,
    Just to say that my comment there didn’t use the word “batchelor” and was not about definitional tautologies, it was about even more basic logical tautologies.

    “Can an unmarried man be married?” is about the law of non-contradiction. Take the claim:

    (1) Our world has the property that there are categories P such that an element of P cannot also be an element of not-P.

    Whether (1) holds seems to me to be an empirical question about our world. If someone wants to argue that (1) must hold in all possible universes then I ask how do you know that? Can you present a proof of (1)? (No using any axioms in that proof unless you have previously proved those axioms!)

    Declaring that it must be true by intuition is not sufficient, since human intuition is a product of our world, and thus is not reliable about all possible worlds.

    I’m asserting that even a statement as basic as (1) is empirical, in that we arrive at it because it seems to hold in the world that we see around us. If anyone has any other justification for adopting it, please present it!

    As I also, said, observations of our world related to quantum mechanics and Bell’s inequalities seem to tell us that (1) is true on the macroscopic scale (where quantum superpositions always decohere) but is not true on the quantum scale. Any sniff of it not always being true is enough for me to declare that any truth in (1) must be empirical.

    Like

  2. Hi DM,

    Coel is entertaining the possibility that our reason is so constrained by this particular universe that we see tautologies where there are nothing of the sort.

    Exactly. The first half of that sentence is surely entirely correct. As for the “all possible worlds”, how on earth would we know about that given the first half of the sentence?

    This is equivalent to the hypothesis that we are deranged and incapable of thinking rationally.

    Well no, it’s more the hypothesis that our reason developed as a model of our universe. Which, if you think about where our reason comes from, more or less has to be true. We are not “deranged” in our thinking processes, we are simply using thinking processes that evolved to model *our* world, and which do that fairly well.

    But how do we get from there to statements about all possible worlds?

    Like

  3. Hi Robin,

    So it is a process which is not reducible to physics and shows how the automatic assumption of reducibility would lead to wrong conclusions, even if everything is physical.

    That statement depends on which conception of “reduction” we are talking about. You are right that it refutes the notions of “strong” reduction as defined by Aravis, but it does not refute the notions of “weak” reduction as the term is used by physicists.

    In “weak” reductionism there is no objection to emergent phenomena (and the utility of higher-level descriptions) and there is no objection to multiple realisibility.

    “Weak” reduction ( or “scientific” reduction, as opposed to “philosophical” reduction) I would define as: (1) a complete simulation at the N level can reproduce all phenomena at the N+1 level, and (2) part of properly understanding a phenomenon at the N+1 level is the requirement to understand how it is implemented at the N level.

    Like

  4. Hi Robin,

    For example if a spin-up electron could be a spin-down electron then there could be no superposition of spin-up/spin-down since it might equally be a superposition of “spin-up/spin-up” or “spin-down/spin-down” …

    But quantum mechanics does allow that, a “spin-up/spin-up” state is simply a decohered superposition, and quantum mechanics does allow spin-up/spin-down states to turn into spin-up/spin-up or spin-down/spin-down states.

    … and not even a fact of the matter about the probability of which it was.

    I don’t see how that follows. Stating that a superposition of spin-up and spin-down is possible is not the same as stating that there are no facts of the matter about the probability of being in the different states.

    How would you be able to do the maths of QM if every member of a superposition could be something else?

    So long as there are probability laws relating the different states, I don’t see a problem.

    There is a difference between there being a superposition of X and not X and X being not X.

    But the ending there is not “X being not X”, but “X having some probability of being not-X”. (Which is sufficient to refute “no unmarried man is married”.)

    Like

  5. Hi Robin,

    That is the difference between doubting that we have a physical body and doubting that a definitional tautology is a definitional tautology.

    We can doubt the first without also doubting that any knowledge or meaning is possible at all. The proposition that doubts the first does not entail doubt that the proposition itself carries any meaning, even approximate meaning.

    On that previous thread, I argued that 100% certainty is always impossible, we can only be very sure. I also argued that parsimony gives us enough reason to be very sure that we have bodies — so we can be about as certain of that as we can about anything.

    My argument was criticised by both Massimo and Aravis as missing the point, because I was taking for granted my ability to reason correctly and so to construct that argument from parsimony. The proper way to interpret the argument, I was told, was to be skeptical of my ability to reason. I agreed that that was legitimate, but like you, it wasn’t obvious to me that this had anything much to do with the argument in the post.

    Coel’s point is that there may be valid ways of reasoning which we cannot do for physical reasons and of which we are unaware because we can only perceive the logic that is consistent with this particular universe. This means that our ability to reason is fundamentally compromised, and there may be truths or possibilities we are forever incapable of perceiving for physical reasons. If Coel is right (and I don’t think he is), then anything is possible. What seems to us a straightforward contradiction may be as only an artifact of our faulty reasoning. So the point is not that a scrimpson-scrampson-scree could be needle-nardle-noo but that it really might be possible to have a married bachelor without changing the meaning of the terms. You can’t show otherwise because any proof you could demonstrate would be based on rational argument, and if rational argument is unreliable we can’t be sure of anything.

    Like

  6. Similarly we can see that there really is no possible world in which modus ponens is not a tautology. If it were not a tautology then the operators would not mean what we mean by them and therefore it would not be modus ponens.

    Like

  7. Massimo,
    I agree with your assertions about scientism, summarised below:

    (i) the use of an over-extensive definition of science
    (ii) logic and math — are “ultimately based” on empirical facts.
    (iii) deny the existence of a priori knowledge.
    (iv) point out that science uses the same fundamental tools — observation and reason — that we all deploy in everyday life
    (v) there are no sharp distinctions between the mentioned activities, so there is no principled way to distinguish among them.
    (vi) the idea that “ultimately” whatever it is we are interested in (poetry, art, mathematics) is made of physical matter

    Essentially, you are saying that scientism is a biased and incomplete view of the world that denies important aspects of human knowledge and experience.

    I agree with that but I also think you have missed the core of the matter, the one thing that defines the heart of scientism. That is a rigid view of scientific determinism. The best exponent of this view is Steven Hawking (Grand Design) while Brian Greene says something very similar(Hidden Reality). These quotes from Grand Design show the thinking:

    It is Laplace who is usually credited with first clearly postulating scientific determinism: Given the state of the universe at one time, a complete set of laws fully determines both the future and the past. … The scientific determinism that Laplace formulated is the modern scientist’s answer to question two. It is, in fact, the basis of all modern science, and a principle that is important throughout this book

    Since people live in the universe and interact with the other objects in it, scientific determinism must hold for people as well.

    Though we feel that we can choose what we do, our understanding of the molecular basis of biology shows that biological processes are governed by the laws of physics and chemistry and therefore are as determined as the orbits of the planets.

    It is hard to imagine how free will can operate if our behavior is determined by physical law, so it seems that we are no more than biological machines and that free will is just an illusion.

    This then is the belief that the laws of nature fully determine the past, present and future, that we are biological machines and our future is rigidly determined, thus we have no free will. Laplace’s Demon is another expression of this belief and so is Einstein’s block universe. We are just part of a gigantic machine inexorably grinding towards a predetermined future and we are cogs rotating in predetermined synchronism with the machine.

    There are many versions of this belief that vary in their details since scientism has no agreed definition. It is an attitude, more than a consistent body of beliefs. I will take Hawking’s view as the best accepted definition though I acknowledge that it lacks the rigour of the philosophical treatments. This is how science tends to think.

    I believe that this view is the core of scientism while your articles (1) to (vi) are properties of scientism. I call the view you described, ‘soft scientism’, while I call Hawking’s view ‘hard scientism’.

    What matters is whether this core belief is true. If true then the question of harm is moot. If not true then it is clearly harmful, as you outlined it.

    How might we know if it is true or false since science has overwhelmingly demonstrated the universal, exceptionless applicability of the laws of nature? At first sight it seems trivially true. It all comes down to the question of free will. Free will, if it exists, is the fault line in scientific determinism. If we possess free will we can generate knowledge that is not predetermined by the laws of nature. In that case scientism is an inadequate world view. If we do not possess free will, all the knowledge we generate is determined by the laws of nature and scientism holds everywhere.

    This then is the acid test of scientism, do we possess free will? I suggest that we clearly do, for the following reasons:
    1) it is a universal human experience and my critics will demonstrate it when they choose how to reply to this comment;
    2) our consciousness is strong evidence of free will. It is not necessary, serving no purpose in the absence of free will;
    3) in the same way, creating a costly illusion of free will serves no useful purpose;
    4) our ability to create new knowledge is open ended and nearly infinite, which would not be the case if we lacked free will.

    The counter argument is that scientific determinism has the consequence that free will is impossible. I reply that is an argument from ignorance. Our knowledge of how the brain and mind work is extremely limited and it is likely that future advances in science will uncover the mechanism that makes free will possible. “That must be so” arguments are not good arguments but a form of ideology. The most that any opponent of free will can claim is the matter is open and that it remains for future science to settle the matter.

    To summarise then. Scientism rests on a bedrock of belief in scientific determinism. Free will, if it exists, as I maintain, is a fault line in scientific determinism which has the result that not all knowledge is subject to scientific determination and that therefore scientism is an incomplete and inadequate view of the world.

    Like

  8. Hi miramaxime,

    While an end result does – in some (trivial) sense – depend on the starting point, the exact relationship is far from trivial and it’s precisely at the heart of the issue in this discussion.

    Agreed, but we are discussing the maths case where the end result is logically entailed solely by the axioms.

    A fictional novel, for instance, usually starts from or is at least inspired by empirical facts about the real world and from then on usually seeks to create a plausible storyline …

    But in a novel you cannot derive the story from those empirical starting points. With every sentence the novelist is adding information, information that is counter-factual and which adds to the real world inspiration. In contrast the mathematican is not adding new information, they are simply deducing ideas that are already entailed by the starting points.

    Put it this way. Could a second and independent mathematician, given the same starting points, predict the whole of the resulting edifice of theorems? Answer, yes.

    Could a second and independent novelist, given the same starting points, the same real-world inspiration, predict the whole of the resulting story? Answer, not a chance.

    You could even turn every story into an axiomatic system, where the next event would follow necessarily from prior events and some additional axioms (although it would get messy).

    No you could not, or at least, you’d have to specify so many contingent facts in the axioms that the set of axioms would be the same length as the story, containing the entire information content of the story. In other words the “set of axioms” would *be* that story (in which case the claim reduces to the story being predictable from the story).

    Now you would find it disingenuous if I would argue that therefore it is and will always be an (approximate) empirical description of the real world and when questioned on that would simply refer to its empirical roots. Your argument simply doesn’t do the work you need it to do.

    There is a vast difference. The mathematician is making statements such as: “If we consider a 7-dimensional cube then {such and such} about that construct”. Everything in that statement derives from the axioms adopted, there is no added information.

    The novelist is making statements such as: “John stared wistfully out of the window before returning to his book”. That is making statements that are not entailed by any empirical starting points. Every such statement is adding information. (You might say that, empirically, we know that there *could* be a person named John who was in that location and that there *could* be a window out of which John *could* stare wistfully, but that is not what the novelist is saying.)

    Mathematical systems, … are not supposed to be about the real world, … They are formal systems studied in pursuit of a better understanding of the formal structure and that is that.

    Agreed, but, again, if all the axioms are about the real world, and if all else follows tautologically from those axioms, then the theorems are still “about the real world”. The novelist is continually adding counter-factual information. The mathematician is not.

    Like

  9. Hi Robin,

    I agree with what you say, and indeed it’s not too far removed from what I was trying to say. We agree that the physicist might miss the significance of all this physical activity, but what is significant is largely subjective. There is no single correct answer to the question of what the machine does. The machine shuffles electrons. The machine moves bits. The machine computes primes. The machine inspires bafflement.

    So it’s not fair to issue a blanket statement like “He doesn’t understand the system” without qualifying it. There are multiple levels on which a system can be understood.

    Like

  10. Moving the post isn’t the crucial issue, it’s a question of how one moved it. Scientists also “move the post” when they refine their theories in the light of new discoveries, but clearly that’s not a problem.

    Like

  11. Hi Coel,

    Well no, it’s more the hypothesis that our reason developed as a model of our universe.

    Yes, I understand that. By equivalent, I mean it has many of the same implications. Of course, since our intuitions suit us very well in this world, it is not literally a sickness or a derangement.

    However, by reframing your argument as an appeal to the possibility of our irrationality, I hope to make the point clearer to those philosophers who already understand this kind of radically skeptical approach.

    Like

  12. Let’s unpack that.

    Suppose there was a world in which there was an algorithm to enumerate the digits of a Chaitin Constant.

    If so then those words have to mean what they mean in our world, otherwise it is just a world where there is a scrimson to scramson the needle of a nardle noo.

    And if so then “Turing Machine” and “probability” must have the meanings they have in this world.

    If so then, in that world, there is an algorithm which can tell if any other algorithm halts.

    And if so, then Turing’s proof for the Halting Theorem does not hold in that world.

    But this could only be the case if one of the terms in that proof had a different meaning in that world to the meaning it has in this world, in which case the concepts don’t have equivalent meanings in that world to this world.

    If all the terms are equivalent, on the other hand, then the theorem holds in that world and there is no algorithm to enumerate the digits of a Chaitin Constant in that world either.

    You may say that this is not real knowledge in that case. But I doubt that you were born knowing this fact and some of the greatest mathematicians before 1930 did not think that this would be the case.

    The it is true that there is no algorithm to enumerate the digits of a Chaitin Constant, it represents real knowledge and there cannot be a possible world in which it is false.

    And the same goes for all mathematical truths.

    Like

  13. Hi Massimo,

    Makes precisely no difference: un married man is by definition not married, so this is still a definitional tautology.

    But making any definitions at all in any meaningful way requires that the law of non-contradiction holds.

    So what is the proof or evidence that the law of non-contradiction is valid?

    Like

  14. Hi Robin

    <blockquote. If it were not a tautology then the operators would not mean what we mean by them and therefore it would not be modus ponens.

    Your argument, and what we “mean by” the operators, requires a theory of meaning. I assert that “meaning” is about real-world correspondence. What else do you mean by “what we mean by” the operators?

    Like

  15. Hi Coel,

    I’m asserting that even a statement as basic as (1) is empirical, in that we arrive at it because it seems to hold in the world that we see around us. If anyone has any other justification for adopting it, please present it!

    You are still trying to fill that broken straight. But as I point out, you cannot empirically test these axioms unless you first assume them.

    In this case you are assuming that if something seems to hold then it seems to hold – in other words you are again assuming the axioms you are presuming to test.

    If that is your reason for adopting the axioms then you have an absurd reason for adopting them.

    The reason we adopt the axioms of identity and non-contradiction is that we cannot begin to do any sort of reasoning, inductive or deductive without beginning with the assumption that they represent absolute truth.

    They are so basic that you are using and depending on them without even realising that you are doing so.

    As for the possible world in which they did not hold, if there was one then this could be it – they might not hold at all in this world.

    Like

  16. Hi labnut,

    If we possess free will …

    I presume that you’re talking about dualist/classical free will? (As oppose to compatibilist free will, where the decision is determined by the prior state of the physical system, plus possible quantum randomness.)

    If we do not possess free will, all the knowledge we generate is determined by the laws of nature and scientism holds everywhere.

    No, since, if there is quantum randomness, then many events are contingent, depending on the outcome of the quantum dice-throwing, and “knowledge” then includes an account of past outcomes of quantum dice-throwing.

    I suggest that we clearly do [possess free will], for the following reasons:

    it is a universal human experience and my critics will demonstrate it when they choose how to reply to this comment;

    That entirely begs the question of whether their response is compatibilist.

    our consciousness is strong evidence of free will. It is not necessary, serving no purpose in the absence of free will;

    That entirely begs the whole question. How do you know that consciousness is not a necessary aspect of our function? Have you ever been a p-zombie to experience what it is like?

    in the same way, creating a costly illusion of free will serves no useful purpose;

    Personally I don’t have an “illusion of free will” in the dualist sense (though I do in the compatibilist sense). Anyhow, repeat last question of how do you know it is not functional? Have you ever seen any functional p-zombies?

    our ability to create new knowledge is open ended and nearly infinite, which would not be the case if we lacked free will.

    See above answer about quantum randomness.

    Free will, if it exists, as I maintain, is a fault line in scientific determinism

    Now produce a *good* argument for dualistic/classical free will. All the above are merely question-begging reports of your intuition.

    Like

  17. Hi Robin,

    In this case you are assuming that if something seems to hold then it seems to hold – in other words you are again assuming the axioms you are presuming to test.

    I don’t see the problem. We *provisionally* adopt something and see if it improves our world model (in terms of explanatory and predictive power).

    If it does we retain it, if it doesn’t we reject it.

    The reason we adopt the axioms of identity and non-contradiction is that we cannot begin to do any sort of reasoning, inductive or deductive without …

    So we try out two alternatives. One, a model including the law of non-contradiction, the other a model without that law, or with the negation of that law.

    Then we see which works better. You seem to be agreeing with me about which works better!

    Like

  18. Hi Robin,

    If so then those words have to mean what they mean in our world, otherwise it is just a world where there is a scrimson to scramson the needle of a nardle noo.

    What I’m saying is that we have no way of restricting how “another world” behaves. It may (for all we know) behave in such a different way that we cannot apply any our-world statement to it. This would include not being able to apply our law of non-contradiction to it.

    In saying “it could enumerate the digits of a Chaitin Constant” you are applying an our-world statement to it, and what I’m suggesting is the possible existence of worlds in which no our-world statement holds.

    Like

  19. There is no proof, that’s just what it means, in the cases cited above. It’s a language stipulation.

    It which point I go the whole hog and declare that language cannot have any meaning without some connection (however indirect and remote) with a real-world reference.

    Like

  20. Coel,
    simply throwing around the label ‘question begging’ is plainly not responsive. If you can’t seriously engage with the argument, stay out of it.

    Like

  21. Labnut writes:

    I also think you have missed the core of the matter, the one thing that defines the heart of scientism. That is a rigid view of scientific determinism. …

    I believe that this view is the core of scientism while your articles (1) to (vi) are properties of scientism. I call the view you described, ‘soft scientism’, while I call Hawking’s view ‘hard scientism’.

    You nailed it. Coel only admits the possibility of quantum randomness. Others do not.

    Robin Herbert writes:

    This idea that QM contradicts the axiom of contradiction is a furphy.

    There is a difference between there being a superposition of X and not X and X being not X.

    Correct. It is possible to interpret some quantum experiments using some sort of quantum logic, such as many-valued logic or denying the law of the excluded middle. However that view is not particularly useful, and hardly any physicists subscribe to it. Even if it were more popular, it is just an interpretation and would not disprove the axiom of contradiction or the law of the excluded middle. Black holes do not contradict the Pythagorean theorem, and a finite universe does not contradict the infinity of primes.

    Like

  22. In “weak” reductionism there is no objection to emergent phenomena (and the utility of higher-level descriptions) and there is no objection to multiple realisibility.

    ————–

    Then you are not an epistemic monist. Indeed, you are not even an ontological monist. So, I have no idea what on earth we have been arguing about for all this time.

    Like

  23. Put it this way. Could a second and independent mathematician, given the same starting points, predict the whole of the resulting edifice of theorems? Answer, yes.

    The answer to this question entirely depends on what you mean with “starting points”. If you are talking about just a set of mathematical axioms, then the answer is clearly “no” or at least “not very likely” (qualitatively the same as in the case of a fictional novel, where the chance would be very small, albeit non-zero). Look, you might need to read some more actual publications, to get more familiar with the process of doing math.

    While the axioms provide a backdrop with respect to which the process of theorem-proving is judged, the actual content under study typically has to be defined into existence, be it a graph, a convex polytope or a calabi-yau manifold. There is hardly a chance that one will be able to predict which object another mathematician is going to define and study from any given axiomatic system, since the conceptional space is so vast (same reason as for the novel, by the way).

    No you could not, or at least, you’d have to specify so many contingent facts in the axioms that the set of axioms would be the same length as the story, containing the entire information content of the story. In other words the “set of axioms” would *be* that story (in which case the claim reduces to the story being predictable from the story).

    This is just untrue, unless you would label all additional definitions of “objects” or “characters” of the story as “axioms”, which would be odd and over more defeat your claim about mathematical axioms being all inspired by empirical facts.

    With respect to the information content: The definitions in combination with the axioms determine the whole informational content any mathematical analysis could ever reveal. So this describes the typical situation in math.

    There is a vast difference. The mathematician is making statements such as: “If we consider a 7-dimensional cube then {such and such} about that construct”. Everything in that statement derives from the axioms adopted, there is no added information.

    But the existence of a 7 dimensional cube is not entailed by the axioms.

    Agreed, but, again, if all the axioms are about the real world, and if all else follows tautologically from those axioms, then the theorems are still “about the real world”. The novelist is continually adding counter-factual information. The mathematician is not.

    Again. See above. Why is the mathematician not adding counterfactual information if he defines a 7-dimensional cube into existence? Or a symmetry group? Or a Khovanov knot? Or is she?

    Like

  24. Up to now, in a couple of different threads here, there are 34 occurrences of “tautology” (oops—just now 35).

    Would it be too much to ask that the term be given a definition (presumably more than one definition, depending on who is using it)? For me, the discussions are just a waste of time without more clarity.

    At the risk of ‘bringing coals to Newcastle’, recall that logicians do have such a precise, and purely syntactical, definition. This makes the confusion even worse, since an example bandied about from an earlier post, namely the proposition “1+1=2”, is not a tautology in the technical sense of a mathematical logician (nor is “x=x”, which I think was claimed to be earlier). They are what many of us call “logically valid in 1st order logic”, so it is perfectly possible that other, perhaps non-mathematician, logicians use the word tautology also for logically valid logic formulas. But let’s be clear.

    In this post, it is even worse when people think they know (and perhaps they do) what they mean when calling a sentence in natural language (e.g. about bachelors) a tautology, and they may even be able to articulate clearly the distinction between those which are “definitional” and others. It seems likely that people (even ‘thinkers’) 150 years ago or more believed they could use “tautology” accurately in natural language, but I seriously doubt that today.

    So can as many as possible of those who used the term up above please define it?

    If you don’t, I’ll have to assume you can’t.

    Like

  25. labnut: “Scientism rests on a bedrock of belief in scientific determinism. Free will, if it exists, as I maintain, is a fault line in scientific determinism which has the result that not all knowledge is subject to scientific determination and that therefore scientism is an incomplete and inadequate view of the world.”

    Fair enough. There are many problems with this grandiose scientism which advanced human happiness tremendously in the past a few centuries but is now a malignant tumor for the advancing the final knowledge. This article on ‘radical empiricism’ has done a great job on putting the scientism to its proper place, amen!

    labnut: “… you have missed the core of the matter, the one thing that defines the heart of scientism. That is a rigid view of scientific determinism. The best exponent of this view is Steven Hawking (Grand Design) while Brian Greene says something very similar (Hidden Reality). … This then is the belief that the laws of nature fully determine the past, present and future, that we are biological machines and our future is rigidly determined, thus we have no free will.”

    The ‘rigid view of scientific determinism’ goes way beyond being wrong; there is only one world for it (stupid). Every street walking person knows that his fate is not 100% determined by the laws of nature. All victims of war are not killed by laws of nature. All starving people are not suffering from the laws of nature. Anyone who comes to this great site is an educated person. So, for the stupid scientific determinism, enough is enough.

    I have showed that the empirical experience is very helpful for the ‘doubting Thomas’ to gain some knowledge. But, in principle,
    a. It (empirical experience) is not needed for gaining knowledge.
    b. The final truth is way beyond the reach by any empirical means.

    On the other hand, the ‘free will’ is totally empirical reachable fact. You wrote your comment with your will (free or not, I don’t know, but you should). I am writing my reply to your comment totally as the result of ‘my free will’. You might not have free will but I do.

    As the ‘free will’ is a part of this universe, it must at least ‘allowed’ by the laws of nature. That is, it must be the ‘consequence’ of the laws of nature. The laws of nature can at least be divided into two parts.
    I. The laws of creation (I will skip this for now)
    II. The laws of governing, and it consists of at least two parts: (1) measuring rulers, (2) a framework (power structure).

    Steven Hawking and Brian Greene are ‘famous’ physicists but both of them do not truly know about the ‘source’ of both measuring rulers and the power (energy) structure (distribution). That is, they do not truly understand ‘this’ universe yet. How can they make any statement about ‘free will’ which is the ‘emergent’ from that ‘source’? I have showed this ‘free will’ issue many times in terms of ‘laws of nature’ at this Webzine. The following are the links.

    https://scientiasalon.wordpress.com/2014/07/21/is-quantum-mechanics-relevant-to-the-philosophy-of-mind-and-the-other-way-around/comment-page-1/#comment-5018

    https://scientiasalon.wordpress.com/2014/07/24/clarifying-sam-harriss-clarification/comment-page-1/#comment-5122

    http://rationallyspeaking.blogspot.com/2014/03/this-isnt-free-will-youre-looking-for.html?showComment=1394690233246#c1832738504891602291

    https://scientiasalon.wordpress.com/2014/05/22/my-philosophy-so-far-part-ii/comment-page-1/#comment-2515

    Like

  26. Hi phoffman56,

    So can as many as possible of those who used the term up above please define it?

    Good question to ask. I (think I) was using the term “tautology” in the sense that something follows tautologically from X if it needs no further information input than we already have in X.

    Like

  27. Hi labnut,

    Coel, simply throwing around the label ‘question begging’ is plainly not responsive. If you can’t seriously engage with the argument, stay out of it.

    Sorry, but mine was a serious response. To me you were just making a series of assertions based on your intuition. From my intuitive standpoint your assertions were all unsupported and false. You might regard this response as mere assertion, but to me your whole comment was mere assertion. That’s what I meant by question-begging.

    Like

  28. Hi Aravis,

    Then you are not an epistemic monist. Indeed, you are not even an ontological monist. So, I have no idea what on earth we have been arguing about for all this time.

    Well I have, a couple of times, mentioned the possibility of miscommunication owing to different people using terms like “reductionism” differently. It is likely the case that some of these terms tend to be differently by physicists versus philosophers.

    As for whether I’m an epistemic monist or an ontological monist, I’d better await a definition of the terms before commenting, since I could interpret them both in ways that produced a “yes” and in ways that produced a “no”.

    Like

  29. Hi miramaxime,

    There is hardly a chance that one will be able to predict which object another mathematician is going to define and study …

    Agreed, but the issue of what the mathematician chooses to study was not what I was getting at. Whatever the mathematician does choose to study, the properties of it and the theorems about it then derive from the axioms.

    If you like, consider two mathematicians agreeing a set of axioms, and one saying: “I’ve derived a wonderful theorem telling me whether or not there are an infinite number of primes”, or “I’ve arrived at a proof telling me whether the square root of two is irrational”. The second mathematician can then, given only the axioms, go away and predict exactly what answer the first mathematician arrived at regarding those questions.

    Now take two novelists who have had the same empirical background. One says to the other: “I invented a story about a character Jim, and about whether he married his sweetheart.” Can the second novelist then predict the outcome of the story, in the same way that the second mathematician could predict the answers above? No, of course not. That’s because the novelist is adding information at each line of the story, whereas the mathematician is only exploring what is entailed by the axioms.

    In short, the properties of the 7-d cube (and thus anything the mathematician says about it) are set by the axioms. You could not have one 7-d cube having some properties and another 7-d cube having different properties, given the same axioms.

    In contrast, what the novelist says about Jim and whether or not Jim marries his sweetheart are not set by any “axioms” that the novelist starts with. You could indeed have myriad different stories arising from the same starting point.

    Or, to put this another way, there are a lot of non-determined contingent events in the story, such that the possible story lines diverge from the “starting axioms”, whereas there is no non-determined contingency between the axioms of maths and any theorem.

    Like

  30. To reply to miramaxime’s 1st point, and perhaps sharpen Coel’s, surely the difference is as follows:

    Two ‘independent’ computer programs, and so mathematicians, can in principle list all the deducible propositions from that mathematical axiomatic system, if the system is anything like acceptable to modern logic.

    By the latter ‘deducibility’, I am not referring to the (not totally silly but wildly unsuccessful) attempts to extend logic, e.g. by the relevance and/or the paraconsistency crews—but rather to standard 1st order set theory (say) logic as understood by mathematical logicians and many others. And I do wish philosophy profs would spend less time bothering students with the former kind of marginal stuff at a point where the students are barely able to formulate completeness, and certainly not expected to prove it, even for propositional logic. Get them at least to understand Godel’s completeness theorem in 1st order (I didn’t say INcompleteness) before trying to dazzle them even with modal logic and the reputable Kripke version of other worlds, much less with the nonsensically loose “other worlds” tossed around here.

    Those two lists above will of course have the same propositions, perhaps in a different order. That relatively easy result is of course in contrast to the absolutely fundamental fact (Church, Turing, Godel, …) that no algorithm can in general decide [deducible or not?] for a given input proposition; only, say by list inspection, a ‘non-halter’ that decides truth, not falsehood, so that the Hauptvermutung is ‘undoable’.

    As to the so-called ‘axiomatic’ input for a novelist, the notion is so loose as to be useless I think. Even if something remotely sensible can flesh this out, it seems unlikely (to say the least) that there would be anything like the above aspect of mathematical deducibility.

    Like

  31. Thanks, Coel. That gets somewhere. But clarity of the word ‘information’ might be a problem.

    This is mostly irrelevant to the issue here, but it is amusing to read, many times over the years, Jeff Shallit explaining how the “god-botherers” (sorry, ‘intelligent-designer-botherers) at the Discovery Institute have no idea what they mean by “information”, despite it being central to the ‘arguments’ of Behe and company.

    Like

  32. Hi Orwell,

    I’m sure you realized that my earlier response was mainly intended as gentle sarcasm, expressing reservations about the importance Massimo (who has been patient with my worse vituperations in the past!) attaches to scientism as a cause of STEM getting too much of the loot in universities.

    Implicitly it was secondly to suggest that some rather uncalled for opinions
    (by Krauss, for example) were maybe meant more as:
    ‘much which passes for research results by present day people in academic
    phil departments is bullshit’, rather than as: ‘philosophy is bullshit’ (close to what he said).
    I suspect that many philosophers themselves, those who are worthy of research
    support these days, feel that earlier sentiment towards a large proportion
    of the other philosophers in the same category;
    whereas that seems unlikely in physics or mathematics.

    The latter relates to what you had originally said. Thanks for the reference to your recent paper
    in the journal published by Pacific University library. I read it, but not its references, and will briefly comment. I must say it is hard to come down to earth and figure out how to express myself
    in the context of doubt expressed about the existence of atoms. When asked for what he would say
    to the layman as to a single most important discovery of science in the last century,
    Feynmann is said to have replied something like ‘Stuff is made of atoms’.
    But I hope I’m not completely reduced to argument from authority in this.

    I admit that I had been utterly unaware of the existence of two separate notions of existence
    (not abstract versus concrete here) which would lead some metaphysicians to believe
    atoms do not exist in one sense of the two. Were this the only argument against scientism
    (in a reasonable sense which I still cannot fully formulate precisely enough), I’d be a scientismist.

    For this little disputation, what is relevant is that point above about some, perhaps meaningless,
    subtleties concerning existence of atoms or other fundamental objects from physics theories,
    but not about your discussion on philosophy of mind, e.g. the”hard problem”.

    Is it really the case that philosophers to whom your paper make reference in this context think
    that the major scientists connected with the atomic theory (examples below) either have not
    thought about, or were/are naive about, these points—Rutherford,
    Einstein, Bohr, Heisenberg, Feynmann, Weinberg, Wilczek—? My worry
    is that most studying this purported philosophical problem on causation have read physics popularizations, rather than real scientific publications, by such people. The popularizations would
    likely use the words ’cause’ , ‘causality’, etc. But you even quote Norton:
    “When they need to be precise, fundamental sciences do not talk of causes…”, so the position of
    “Causal anti-realism .. .” which your article is about would not likely be relevant.
    Please look at what the scientists actually write, and also avoid conflating logical implication with causality.

    “For causal anti-realism, nothing is ontologically reducible to anything else because ontological reduction is a form of real causal explanation. “:

    With all due respect to philosophers, I seriously doubt that that popular phrase “ontological reduction” is of much value or has been well thought through.
    Maybe you could explain what it means here in a simplest of examples,
    the hydrogen atom, described as a mathematical structure
    (not just a set), whose underlying set has a proton and an electron
    (but there is much more mathematical structure).
    It is the explanatory wonders in this snippet (along with countless other ‘snippets’)
    which moves us closer to belief in the actual existence of electrons, not the reverse.
    The explanatory value of this piece of quantum theory, and even more, of quantum field theory,
    gives meaning to the word “exists” here. I think popular writing of Deutsch (despite what I said above about causal anti-realists possibly being deluded by popular writing) has considerable
    value in actually getting at this sort of existence (and despite Deutsch abjuring much of philosophers’ jargon).

    “…appeals to spectroscopic images and other empirical findings do not conflict
    with the philosophical claim that atoms do not exist in the absence of observers.”

    Sorry, I really do think that philosophers who seriously maintain that position
    are very unclear about what they mean by “exist” here,. They needn’t be if they
    spent more time reading what the scientists I mention above have written in their
    not-for-the-popular-press writings.

    And to remove the irony referred to in 1st paragraph above,
    were that the only argument against the academic
    vice-pres. redistributing more of the vacant positions to STEM,
    I’d be on her side to do that!

    Peter

    Like

  33. there are some issues that are not precise in these papers recently like the reference to mathematics and logic is always a rush one while the debate over there is so heavy and cannot be simplified in such one easy paragraph of 1+1=2….a simple thought is that the empirical equivalence of 1+1=2 , i.e. two objects added together is not the correct ideas in mathematics, for the number 2 only represents the class of couples which happen to correspond to objects that share the property of couples……..

    the problems always raise in dissertation of this kind as they invoke the authors own interpretation and philosophical culture. referring to a classical philosopher is always risky in such kind of context, out of the history of philosophical thought movements (and not the chronology). in a recent methodological readings, it was correctly pointed out by the authors that explaining a philosophical text should not invoke the writer’s knowledge and own culture to explain the text, the text carry its own meaning in its context and its own structure of argumentation, its own doctrine of the time etc…the dissertation or comments of the text however invokes heavily of the culture and knowledge of the writer but references to classical texts can be very risky when the author takes a side and defend a thesis based on very quick and short quotes from established classical philosophers to defend own’s position without due examination of the context of such quotes

    Like

  34. 1.Preaching the Good News from World 3 (aka the anti-science moves in logical space)

    i.Equivocation between an arbitrarily narrow definition of science (and the knowledge thereby obtained) and undefined other ways of knowing (and whatever they discover.)

    There is far more to the practice of science than observation and reasoning. Nonetheless, those are scientific methods even if they overlap (as they did historically) with daily life. Some scientific methods include mapping, change of perspective, observations by instruments, collecting, classifying, dissection, measuring, census, drilling cores, tabulation of data, graphing data, systematic comparison, drawing and photographing, models, simulations, statistical tests of generalizations, scientific polling, testing documents for authenticity, examination of witnesses for reliability, historical reconstruction and, of course, the whole breathtaking variety of controlled laboratory experiments. All this is a communal activity, neither organized nor carried out by a single individual nor even a small group, over an indefinite period of time over an indefinite geographical expanse in a variety of institutions and other social groupings. The fruits of the scientific endeavor are no longer wholly known to any individual and any individual account must to some degree be either personally impressionistic or a transmission from collectively accepted authority.Neither personal opinion and intuition nor communal religious dogma count as scientific authority. Note the partial listing of methods are carried out neither in daily life nor the other ways of knowing.

    Another aspect of the arbitrarily narrow definition of science is omitting that scientific explanations are materialist. Also, the arbitrarily narrow definition of science omits that it adheres to a correspondence account of knowledge, knowing what really is. A bonus here is confusion between realist and antirealist accounts of scientific knowledge.

    By contrast the other ways of knowing, which are rarely even listed, are left vague and undefined, so that it can be tacitly assumed they too can be as empirical as the science which uses observation and reason. It can also be tacitly assumed that whatever knowledge these discover are simply equal to knowledge of reality. And as the last implies, it can be tacitly assumed that study of any topic, regardless of its real existence, thereby produces knowledge.

    After using this rhetorical ploy the conclusion then that science is overreaching if it claims to be the only known way to find knowledge, or that its methods can be applied to study people as well as brute nature follow inevitably. It’s also true that this refutes as well the conclusion that nature is all that’s real, but it is a moot question whether this is really a problem for the anti-science.

    ii.Logic and mathematics assumed to be valuable for producing an unspecified but nonempirical kind of knowledge that may or may not be useful for mysterious reasons that need not be explained.

    a.There is a great deal of scorn heaped upon the proposition that mathematics may be ultimately empirical. Yet it is remarkably bold to claim that geometry is not empirical, given that the name! In any event, if mathematics is not empirical, it’s usefulness to all sorts of quotidian endeavors, such as measurement (and by the way, science,) is somewhat miraculous. Perhaps it’s the will of God? The secularized version, that mathematics give a priori knowledge of reality, suffers from the fatal fault that there’s too much it can’t tell us, such as whether space is Euclidean. And it tells us things that aren’t, such as that a pea can be unpacked to be the size of the Sun. (To be fair,I think there are many mathematicians themselves who don’t quite hold the extreme views attributed to their subject in this ongoing discussion, particularly in regards to actual infinities. I gather they don’t count philosophically?)

    A less extreme contention, that mathematics provides a coherentist kind of knowledge suffers the difficulty that coherence in any strong form implies (inescapably I think) solid foundations and consistency of the kind attributed to Euclid’s presentation of geometry. It is well-known that this is not the case. Despite the oddity, however, there are those those say lack of foundations and proof of internal consistency still do not matter, since the proofs otherwise are either trivial or irrelevant because some parts of mathematics are complete. (Frankly it was news to me that Godel didn’t really prove much of anything, but I’m told that’s where we are.)
    I don’t think weak coherentist claims can bear the burden of showing in principle that science is wrong or inadequate or inferior.

    In this presentation, the mathematician studies consequences of axioms as other criteria than the crassly empirical ones of science. It is merely a coincidence if this happens to be helpful to the scientist, but mathematics is deductions from axioms. Sometimes, it is said that mathematics is the study of abstract objects. I can see the appeal of such a definition but I don’t know what is so abstract about knots. In a different vein, Boole and de Morgan did logic (or The Laws of Thought) as mathematics. The thing there, in what sense is logic a mathematical object?

    I don’t believe mathematics as axiomatic deduction (or even as the study of mathematical objects,) is the case, not in ordinary life, not in the history of mathematics, and not in all parts of current mathematical practice. I’m not sure it is even universally true even for mathematicians working in the heavily axiomatized fields. In infancy, we use no Peano axioms to learn to do aritmetic. We do not even use Euclidean axioms to grasp the concept of space. Most of us use mathematics with no thought of writing proofs. Applied mathematicians may do proofs but they are unfortunately also using those dirty empirical methods. Historically, as in analysis, nonrigorous methods of a creative origin, preceded axiomatization. Whether the new methods were empirically justified caused great concern over the introduction of negative numbers, infinitesimals, non-Euclidean geometries, and Cantor’s transfinites. I’m not even sure that it makes genuine sense to define mathematics as writing proofs and ignoring the rest.

    I don’t know how you can separate mathematics from measuring even. And I don’t know what it means to say that you can prove that one sphere can be turned into two identical sphere by a set number of simple operations. If you define a sphere as a set of points and if you accept the axiom of choice…What kind of knowledge do you have about reality from such ifs? How is this different from knowing what Sherlock Holmes would do if he investigated a real crime? Or maybe it’s like knowing what moves must be made in the endgame of a chess match? Is it acceptable to have proofs without words? Why not? Why is the Greek geometry misrepresented as axiomatic when it’s also very much straight-edge and compass geometry?

    The easy assumption that mathematics is just knowledge, end of story, is too easy an assumption and I am doubtful that it can bear the weight of condemning in principle science as wrong or inferior or inadequate.

    b.As for logic? Formal logic is a branch of mathematics, to mention Peirce, Frege, Rusell and Whitehead as well as Boole and De Morgan. I do not know that anyone investigating reality found out something using formal logic. I do not believe modus ponens was hypothesized, demonstrated to be necessarily true, then applied to reality. We are informed that a bachelor is an unmarried married man, and that this is a necessary truth and therefore knowledge. Yet we do not always call an unmarried make a bachelor, as he may be a boy or youth living at home, divorced, engaged and presumed unavailable for another bride, or partaking in a common-law marriage. In practice, “bachelor” means not just an unmarried male of an age suitable for marriage but living alone. Widowed husbands are surely unmarried but who calls them bachelors? If you protest that you have just one meaning for bachelor, good on you, but I haven’t agreed to play that game. If the rules are rigged, what kind of knowledge do you have?

    There is an equivocation as to whether formal logic is part of philosophy or mathematics. Being vague on this point covertly allows allows philosophy to implicitly claim deductive rigor that constitutes an independent claim to knowledge prior to and superior to science, with, unlike empirically limited science, an unlimited scope and applicability. Quine may be right that what we “know” from this is epistemically insignficant but refuting him I think requires evidence. Or even, if that’s too crude, an argument.

    As for informal logic, that is a branch of rhetoric, the part devoted to the appeal to reason. As such, it is a part of the humanities. There are those who either deny that formal logic is mathematics or incorporate it into philosophy as the technical part, the demonstration of philosophy as a kind of scientia (not using the ineffective tools of the natural or social sciences) of thought itself, superior to all other forms of learning in scope and profundity, achieving knowledge of the eternal world beneath the trivial material manifestations. The problem for this view is the repeated failure of this scientia to agree on what is the eternal.

    iii.Assume not just the significance and importance of a priori knowledge but also that its origin and existence are not just separate from experience but superior to it.

    a.Following this ploy, one can assert the law of identity can be conceived logically therefore it could not be something learned from experience, even though infants did not know this. And since it can be conceived logically therefore it must be necessary to justify empirical reasoning or is even a requirement before experience can be understood. These sort of enormities are good philosophy. Closely related are the idea that any logical or conceptual distinction can be posited without regard to evidence as to whether it exists independently. Whether a distinction makes a difference is irrelevant. Any apparent contradictions in logical analysis can be resolved by creating a further distinction or positing another entity. Also, that hypothesized entities are superior conceptions if they are not just devoid of empirical existence, but even better if they are unchanging. Again, all are apparently good philosophy. I’m not sure that they aren’t, along with a commitment to the coherence notion of truth, definitive of philosophy as a mode of thinking.

    b.A closely related notion is that a resort to more and more different kinds of facts is equivalent to an infinite regress, to be rejected out of hand. This may be good philosophy, but I think that the truly unacceptable infinite regress is one in which the argument keeps appealing to the same category of assertions, especially those which unamenable to change or empirical confirmation. The specific, the determinate, the path from origin to destination, the functional, the structured are hallmarks of the real. The scientism of Ladyman and Ross seeks the opposite, deeming physics the fundamental science because it is closest to being ontology, study of being as such, without attributes. Other sciences are special, particular, inferior, instead of collectively approaching closer and closer to a full and systematic description where abstractions and details interact.

    c.So-called logical inconsistencies in empiricism are defined by reducing all possible knowing to mental events in individual minds. Personal observation and intuitive reasoning are part of daily life and also of philosophy but one key aspect of science is confirmation of observations by use of multiple viewpoints. The formulation of scientific knowledge as the view from everywhere may be logically equivalent to the view from nowhere privileged. But that is not the same as a view from nowhere. That implies only mental events are to be accepted as the stuff of experience. As has been pointed out, a view of induction as the personal association of two events cannot be sustained logically. But this same logic also cannot sustain the existence of the contuous existence of either the so-called outside world (as if there were an identifiable boundary between mind and body!) or even of a continuous consciousness. The plainly erroneous conclusions comes from the wrong starting point, from reducing everything to the philosopher’s naked brain.

    iv.Assume philosophical reasoning is the standard while ignoring the epistemic pluralism of scientific methods.

    A coherence notion of truth eschews foundations and proof of consistency,, a reduction of experience to individual mental events, the insistence that all conceptual distinctions must be signficant, the insistence that any definitions have only the meaning chosen, the preference given to eternal concepts shorn of material content, the general presumption that positing an entity is sufficient to endow it with meaning…it is not obvious that philosophical reasoning is actually the same as everyday reasoning, much less scientific reasoning. Both the collectivism of the scientific project and the insistence that entities should be in some sense material devalues the individual’s vanities about their rightness. To be honest, it appears that historically and in general philosophy devalues the common man’s intelligence and integrity, but it does so to exalt the wise man. Who among us can resist the temptation to think that we are in the inner circle?

    v.Assume that the differences in the way different kinds of learning are carried out fundamentally significant while differences in the reliability or nature of the learning are not.

    For mathematics and logic, the optional nature of their some of their conclusions, the if/then approach means that in order to know what your deductive knowledge means about anything other than the subject, you have to know more, from experience. You can read Ellery Queen’s The French Powder Mystery and deduce, know, who the killer was. You’ve won the challenge to the reader. In what ways are the knowledge from deductions in pure mathematics different?

    Philosophical knowledge seems to be knowing what are currently considered good arguments for or against any number of positions. How is this different from knowing what is currently considered good drama?

    The knowledge acquired by science may not be a logically necessary a priori deduction but it doesn’t need to be. It is validated by other people over a period of time and, incomplete and confusing though it may be, it is what the evidence shows things to be. Many facts are immune to further correction, while most interpretive frameworks for facts (the catch-all term “facts” has hidden subtleties of course!) may be suspected of needing many corrections. But however tediously empirical it all is, this knowledge has objectivity. In a glorious irony this gives its conclusions more permanence than the philosophical search for the eternal free of the dross of matter.

    vi.False and selective accusations of reductionism, while leaving emergentism undefined.

    a.There are different views of science, which means that epistemological, methodological and metaphysical scientism will be different according to whether the “science” is naturalist or materialist. Naturalism appears to be largely anti-realist and may even be opposed to materialism, as in structural realism or mathematical Platonism (the favorite position among mathematicians?). Blanket accusations of reductionism are therefore false. In metaphysical materialism, it is common to hold to an emergentism based on material entities or processes, instead of a priori constructs or purely logical deductions. (The latter are generally dismissed as “metaphysical” in the pejorative sense of the word.) This emergentism done backwards is reductionism. And reductionism backwards is emergentism.

    The point is that it be materialist emergentism or materialist reductionism.. The anti-science argument equivocates on emergentism, illogically condemning reductionism for an cloudy offense called greedy reductionism. This is not really a thing. There is a reductionism that imagines artificial entities. Once some scientists condemned atomism as reductionism, claiming that atoms were metaphysical not empirical. Today, some scientists condemn viewing wave functions are empirical instead of metaphysical. Collectively the search for definitive evidence will either find the evidence to confirm one view or the other, or it will not. But there is no definition of greediness that sets a limit in principle. Wouldn’t the insistence currency has to be reduced to a homogeneous physical kind to be a real thing an excellent example of genuine greedy reductionism?

    Hayek has been cited as a critic of scientism yet Hayek is one of those greedy reductionists. He denies that economic life can be viewed as anything but the actions of individuals. He is also an anti-emergentist, denying that there can be any emergent phenomena in society that could be called social forces or capitalism or such. As I recall he talks rather freely about markets, but such inconsistencies are to be expected from the anti-science. Of people, Hayek emphasizes ideas as a non-material causal force that constitutes the subject of the social sciences. Since his version of ideas do not come from schools or experience, it is pretty much free form philosophy. Hayek’s muddled thinking on reductionism (he uses different terminology by the way,) probably derives from its role in advancing a viciously reactionary political agenda, aimed at devising pretended limits in principle to the powers of (social) science. The anti-science critique of reductionism has been entirely useless.

    In popularizations of biology, it is hard to escape another reactionary agenda, this one set by the evolutionary psychologists. The problem is not just their genetic determinism/panselectionism, which seems to me to be inseparable in practice from the selfish gene presentation of gene selection. The evolutionary psychologists actually argue strenuously that they are not greedy reductionists and indeed deny they are genetic determinists. The real problem? According to them, modules emerge in the mind. Or alternatively they reduce the mind to a collection of genetically programmed modules that cause behavioral propensities subsequently acted upon by natural selection.. Six of one, half dozen of the other…As I said, there is no opposition between reductionism and emergentism. Sure enough, these modules are not required ever to have genes related to them or specific parts of the brain associated with their function or a life history with times of appearance or normal range of variations in a population or a possible critical period in development or defects of the same type from similar congenital or traumatic causes. And again the anti-science critique is wholly useless.

    b.It is quite common for anti-science critics to demand extremely reductionist proofs, then treat the impossibility of satisfying their arbitrary standards as some sort of disproof in principle. Perhaps one of the crudest yet amazingly popular examples of this was Popper’s reduction of science to falsification of predictions. History can’t make predictions, therefore it can’t be a science. This naturally led him to deny evolution, an historical branch of biology, status as scientific. This was so foolish as to give his game away so naturally someone tried to think of some convoluted form of falsification that doesn’t really have anything to do with the actual practice of evolutionary biology, starting with Darwin. There’s many a modern Popperian who has no need of a fig leaf to sneak back into public, however and the anti-science critique of scientism is widely accepted.

    There are similar problems in the study of mind, in which hypothetical entities called qualia are treated as causal without reference to their real existence. My qualia change all the time, which suggests to me they are effects, but not being a Lover of Wisdom, I suppose I must be wrong. I fell once and hit my head and for a few moments my thinking was scrambled. To me that suggests my brain state has something to do with my mind. But an undefined and unsupported emergentism says that Mind cannot be composed of brain states! Both historically and biographically language precedes grammar. Yet the critic of reductionism insists that language must emerge from the rules of syntax. Then they conclude that if you can’t demonstrate that to their eagle eye, semantics must be an emergent phenomenon. They only forget to add what it emerges from. (Naming for a start? But that is so dully mundane it can’t be so?)

    Part of this is a misplaced insistence on logical coherence according to preconceived ideas, I think. But as pointed out in the comments, there are problems in reducing certain phenomena. What is not pointed out is that this is not decisive. I don’t think it has been possible to reduce a cold front or a tornado to statistical mechanics either. But anyone who doesn’t think both are explicable in simpler, smaller physical elements would be grievously wrong. These counterexamples do not constitute a principled argument against reductionism (which is still emergentism backward.) After all, if it does, the critique applies to the anti-science as well! Claiming this is denying the efficacy of science to find knowledge according to a strict coherentist view. The thing is, I think the coherence approach is wrong because it is anti-materialist. The proper counterexamples are those which demonstrate non-material causality. These can only be seen in the light of faith so far as I know.

    2.A Short Cry of Defiance from the Bowels of Materialist Hell

    This has been ridiculously long because there’s been a lot of stuff said in the anti-science critique. But I think that in some ways we can boil this down to something less analytical and more informal.

    The basic charge is that the world is excessively rational and this is devaluing our lives. I have no idea how someone can actually believe this. It’s Tory politics and Mont Pelerin philosophy

    Another is that natural scientists are ruining the humanities in colleges. Sorry, I don’t believe that. Business interest in favoring the products of natural scientific research and student interest in employment prospects are much more important. Also, the assumption that the humanities depends on college humanities departments is a little self-flattering.

    Another is that somehow the humanities are not justified by our pleasure in sharing feelings but have to be justified as some sort of knowledge. Say what? So-called scientism may say the humanities may be learning but are not truth according to the correspondence account (save incidentally,) but that is an epistemological, methodological and metaphysical claim, not an attack…unless at some level you really do believe the humanities must be justified by some sort of philosophical utility. That said, I do think that our understanding of the arts should when appropriate take account of what we’ve learned about the social functions of art, including assertions about the world and society. Our understanding of religious art for example should be informed by what we know of the evidence for gods.

    Hume’s fork does not include logic as an acceptable form of knowledge as near as I can tell.

    Why assume the humanities aren’t opposed to philosophy as well? This whole discussion makes me want to find my copy of Aristophanes and re-read The Clouds, just to see how much more sympathetic I would be to Strepsiades.

    Like

  35. Hi Coel and phoffman56,

    Thanks for your responses.

    My point in raising the novel was not to claim that this would be in any way useful for novelists. Instead I wanted to highlight that a concept having empirical “roots” is usually insufficient for calling whatever follows from it empirical. We seem to agree on that.

    I anticipated that Coel might argue that in the case of the novelist the story doesn’t necessarily follow from any given scenario. I don’t find this argument convincing at all, but to defuse it right away I hinted at the fact that one could develop a novel in which all content follows necessarily from a set of axioms and precise definitions of characters. While this would be a lot of work, it is certainly possible in principle. Would this fictional story then be any more empirical?

    Coel:
    Agreed, but the issue of what the mathematician chooses to study was not what I was getting at.

    But the objects mathematicians study are at the center of the question if whether math is empirical. Wouldn’t you agree?

    What differentiates a science-fiction book from a history book is precisely that the latter typically comes with the claim that all characters and events really existed or have happened. It is in this sense that history is referred to as empirical and science fiction is not (notice that in history things do not follow necessarily).

    In a similar sense a physical theory differs from a mathematical theory in that the defined objects are usually claimed to really exist in the former case and not in the latter and that’s also why empirical experiment can prove the former wrong, but not the latter. I would say that’s what people mean when they say: “Math is not empirical” and that seems an important difference, don’t you think?

    Like

  36. Hi miramaxime,

    In a similar sense a physical theory differs from a mathematical theory in that the defined objects are usually claimed to really exist in the former case and not in the latter and that’s also why empirical experiment can prove the former wrong, but not the latter.

    But if the empiricism proved the *axioms* of math wrong then empiricism would have proven the resulting theorems wrong. In contrast, nothing about empiricism could prove a science-fiction book “wrong”.

    This is why it really does matter whether the axioms are adopted as real-world models, or whether the axioms are adopted as arbitrary and unrelated to the real world.

    If it is the latter, then you are right that empiricism could not declare anything about maths “wrong”, any more than in the case of the science-fiction book.

    But, my whole case here is that the axioms of maths are not arbitrary, they are adopted as real-world models. No-one has given any alternative origin of the axioms, or any alternative account of what leads mathematicians to adopt them.

    The idea that mathematicians just adopt arbitrary axioms at random, not caring at all about whether they model real-world behaviour, is not tenable.

    Like

  37. “In a similar sense a physical theory differs from a mathematical theory in that the defined objects are usually claimed to really exist in the former case and not in the latter ”

    No to “not in the latter”, not by most practising research mathematicians, nor many physicists and philosophers (another quadruple negative??).

    “But the objects mathematicians study are at the center of the question if whether math is empirical.”

    Again no: though many in a venue like this will write about the existence or otherwise of an ‘object’, say “3”, the real issue is the existence or otherwise of (say) the structure which is the (standard) natural numbers, or of some system of axioms for it (or a 1st order system for it and lots of non-standard structures in addition) and the system’s attendant language and proof system in logic.

    In that context there seems both here, and in Jerry Coyne’s not-to-be-called-a-blog, a lot of confusion about what people loosely call Peano’s axioms (and Godel incompleteness): e.g. do they mean the classical Peano postulates which are definitely more than 1st order, so that incompleteness implies the impossibility in a precise sense of any decent proof system for higher order; or do they mean 1st order Peano arithmetic?. Mis-statements abound of incompleteness, where you could easily disprove ‘it’ by just saying to take all and exactly the true statements of arithmetic as your axioms, so that obviously it would be false to claim that there is no proof of at least one such true proposition. I’ll leave it to the reader’s (if any) delectation to recall what is missing in these statements, by Coel for example, to sort this out (and missing is not just the assumption that the axiom set should be consistent).

    The last criticism even applies to the wildly popular and otherwise excellent old popularization of Godel’s famous result by Nagel and Newman. That error has in cases moved young people (who immediately see what looks like a counterexample as above) away from thinking they want to study logic but don’t have anybody knowledgable to ask about it.

    Like

  38. Coel,

    First you say about me:
    To me you were just making a series of assertions based on your intuition.
    and then you say about yourself
    From my intuitive standpoint your assertions were all unsupported and false.
    So all you are saying is that your intuitions contradict my intuitions. That is called argument by contradiction.

    Sorry, but mine was a serious response.
    Argument by contradiction is not a serious response.

    You might regard this response as mere assertion
    Indeed, you assert that your intuitions contradict my intuitions. That is the long and the short of it.

    to me your whole comment was mere assertion. That’s what I meant by question-begging.
    Question-begging has a well defined meaning and it is not what you claim. Please read it up here:http://bit.ly/1dSbz5j (hint, conclusion is implied in the premises used to justify the conclusion)

    Like

  39. Hi phoffman56

    If you don’t, I’ll have to assume you can’t.

    That displays a lack of critical thinking on your part doesn’t it? It didn’t occur to you that some people have other things to do?

    I have used this term to talk about, for example, Modus Ponens. Do I really have to explain to you what I mean by “tautology” when applied to Modus Ponens?

    Now your quibble appears to be that we cannot use “tautology” in this sense to apply to natural language but you don’t say why or give any references.

    Tautologies don’t just appear in first order logic, they are in classical logic too. A tautology is any expression which resolves to “True” irrespective of the truth values of the atoms (or ions as Kleene uses the term).

    Also, something that is valid is a tautology but not every tautology can be described as “valid”.

    When applied to natural language it can be the case that we are saying this somewhat informally, but I see no problem with that. When used formally calling something a tautology says that the truth of the expression follows from the definition of the terms. It means the same informally, such as in “a bachelor is unmarried”.

    We could formalise these things if we wanted to. For discussion on the formalisation of natural language statements see the first chapter of Kleene’s “Mathematical Logic” and his useful distinction between the observer language and the object language.

    I am not aware of any serious objection to Kleene’s remarks there.

    Like

  40. Calling something a definitional tautology simply distinguishes it from other uses tautologies, for example where an adjective is redundant because the noun it describes always has that that quality anyway. This is usually used jokingly – for example “corrupt politician”, “boring accountant”.

    Like

  41. Hi Coel,

    I don’t see the problem.

    Yes, I can see that you don’t see the problem – but nevertheless there is a problem.

    We *provisionally* adopt something and see if it improves our world model (in terms of explanatory and predictive power).

    Again, you are missing the point. If you have not adopted these axioms for the purposes of comparing the two approaches (adopting the axioms and not adopting the axioms) then you cannot make any comparison.

    Here is your procedure.

    1. Provisionally adopt I and NC and test model and get result A
    2. Provisionally drop I and NC and test model and get result B
    3. Test result A against B
    (where I is the axiom of identity and NC is the axiom of non contradiction.
    OK, so in order that you can understand the problem, explicitly answer the question – at step 3 have you adopted or not adopted I and NC?

    If you have neither adopted, nor dropped I and NC at step 3 then your base assumption for that step is that possibly more explanatory and predictive power is less explanatory predictive power and therefore you have no basis for a comparison.

    If, on the other hand, you are assuming at step 3 that more explanatory and predictive power is more explanatory and predictive power and not less explanatory and predictive power then you have implicitly adopted I and NC at step 3 and therefore have compared the two models under the assumption of I and NC.

    What you should do is:

    1. Provisionally adopt I and NC and test model and get result A
    2. Provisionally drop I and NC and test model and get result B
    3. Provisionally adopt I and NC and test result A against B
    4. Provisionally drop I and NC and test result A against B

    Now which model works better? You will find that model A works better against B in step 3 but not in step 4.

    In other words you have to adopt I and NC in order to empirically test I and NC.

    At this point, I don’t get what you don’t get about that.

    Like

  42. Hi Coel,

    Your argument, and what we “mean by” the operators, requires a theory of meaning. I assert that “meaning” is about real-world correspondence

    Your argument here requires a theory of “real-world” and a theory of “correspondence” and a meaning of “theory” and a theory of “theory” 🙂

    Like

  43. As I always say, those who ignore philosophy are doomed to repeat it.

    Talk of theories of meaning was always rendered absurd by the fact that in order to have a theory of meaning you would have to be able to state that theory in some language.

    But if a theory of meaning was necessary in the first place then how could you say that the statement of the theory of meaning had any meaning unless you first had a theory of meaning?

    Like

  44. “The basic charge is that the world is excessively rational and this is devaluing our lives. I have no idea how someone can actually believe this.”

    Love this. Well said.

    Like

  45. The quality of the arguments goes to to the validity of statements, not whether they are or are not within the realm of science. I mean, in math, you can have false statements which clearly fall within the realm of math (like 2 + 2 = 5).

    Like

  46. Hi Robin,
    The difference here is whether we adopt a heirarchical approach to model building or a web approach.

    In the former, we adopt Base Idea 1, then we add Ideas 2 and 3, and proceed from there. We can’t revisit Base Idea 1 because everything from there depends on it. I don’t think that this is how science works.

    In the web approach we *provisionally* accept Idea 1. Then we adopt Ideas 2 and 3 and build a model. We can then ask about Idea 1. Can we then improve the model by swapping out Idea 1 and replacing it by Idea 1b, propagating all consequences through the web. If swapping in 1b improves the overall model then we do so, if it doesn’t then we don’t. That process tests Idea 1.

    3. Provisionally adopt I and NC and test result A against B
    4. Provisionally drop I and NC and test result A against B

    Now which model works better? You will find that model A works better against B in step 3 but not in step 4.

    So the best, overall, considering all outcomes of 3 and 4, is that I+NC+A works best. It works better than B and better than (~I)+(~NC)+B. We simply swap I and NC in and out and see if they improve or worsen the overall model.

    This is a suck-it-and-see approach in which we do indeed *provisionally* adopt I and NC to see what happens, but the process is still empirically testing I and NC. The question is simple: does throwing I and NC out improve the model’s explanatory and predictive power?

    The only way you could refute that is if you can show that adopting ~I and ~NC could produce an outcome with the same explanatory and predictive power. In *that* case we could not decide between I+NC and (~I)+(~NC).

    This web model of science gets round all the usual complaints that science has to adopt certain axioms to get going. It only has to adopt them provisionally, and it can then test them.

    Like

Comments are closed.