• Can the existence of God be proved?
    Going to have to disagree with you here as it appears to me that all motion, including inertial motion (by which I understand you to mean constant velocity) depends to some degree on another. In fact, all motion is relative motion and insofar as it is relative to another, all motion, including inertial motion, depends on another. But then all that means is that the metaphysical foundation of everything, God, cannot be in motion.NotAristotle

    You seem to be equivocating between "dependence" as being a function of something else and being grounded in something else. And your conclusion doesn't seem to follow from anything.

    The point I was trying to make is that in citing the example of a billiard ball, you seemed to be satisfied that it can move of its own accord, as long as it doesn't alter its motion. That's the Galilean insight, which diverges from the Aristotelian doctrine that prevailed earlier.
  • Can the existence of God be proved?
    For example, when a billiard ball moves and changes position, it does not do so of its own accord, but because another billiard ball has imparted motion to it. Similarly, and in accordance with Newton's (1st?) Law, the billiard ball will remain moving unless it strikes another ball or hits the boundary of the table, or encounters friction. And so, all change (of some thing) really depends on another to change it.NotAristotle

    The orthodox thinking in Western philosophy used to maintain that what we now call inertial motion (such as that of a billiard ball rolling on a flat surface) required a motive force, like everything else. You seem to have internalized Galilean relativity, but otherwise retained the same intuitions regarding motion (change).

    But the Galilean revolution (I am using the term loosely) was more thoroughgoing than just admitting the autonomy of inertial motion. People have come to realize that we don't need to appeal to external agent causation in every instance. The world can go about its business absent any will to push it around.
  • Can the existence of God be proved?
    Because I think change or alteration implies a kind of dependence on another.NotAristotle

    Conceptually, change only depends on time. And time depends on change - it's a mutual dependence. What neither concept requires is a magic man pulling the strings from behind a curtain.

    A (pure state) quantum system evolves without an external cause. It's in the intrinsic nature of the quantum system.Relativist

    You don't have to go as far as quantum mechanics to illustrate the idea. Galilean physics will do just as well.
  • The 'Hotel Manager' Indictment
    That's a really good question. The only answer I can offer to support a claim that such demonstration has not only been impossible in the past, just as it is now, but that it inevitably will be so in the future, would be that when it comes to introspected intuitions we always will be working with the same data, that is the human mind, that we have always been working with.

    In science we may be working with previously unknown data, newly discovered phenomena, and I think this has clearly happened in the history of science. But when it comes to the purely speculative metaphysical ideas, unless we admit science into the equation and don't rely solely on intuitions (which has certainly happened in some metaphysical quarters) there would seem to be no new data to work with.
    Janus

    Our intuitions are not universal and unchanging. They are influenced by experience, exposure to ideas (from science, but also from history, philosophy, religion), socioeconomic conditions, moral attitudes... That's not to say that there is some fixed asymptote towards which our collective metaphysical intuitions are inevitably converging. They may well diverge, swing and meander this way and that forevermore.
  • The proof that there is no magic
    How high must the described order be in order to be an explanation rather than just a description?Quk

    Well, that's a far broader question than the original topic. You won't make much headway on the question of magic if, in order to answer it, you first have to settle the question of what constitutes an explanation.

    I think we can all agree that as a general requirement, an explanation should improve our understanding. A description does not satisfy that requirement, since a description is needed before we can even ask for an explanation (else, what are we even trying to explain?)
  • The proof that there is no magic
    Your idea of an explanation as nothing more than giving a name for what you want to explain is not even deflationary - it is patently silly. To wit:

    Why does the apple fall to the ground? Because of gravity. That explains it.Quk

    This is just the sort of pretension that Moliere lampooned in one of his plays (The Imaginary Invalid): When a supposedly learned doctor is asked to explain the action of opium, he attributed it (speaking, suitably, in dog-Latin) to opium's "dormitive property whose nature is to lull the senses to sleep." Virtus dormitiva has since become a byword for just that sort of pseudo-explanation that merely names or rephrases the issue without providing any insight.
  • Phaenomenological or fundamental?
    I think that most physical theories are phenomenological and very few fundamental.
    Galileo and Newton only give descriptions of what actually happens without a fundamental explanation. It was also Leibniz's criticism that Newton could not explain how the interaction of gravity actually comes about.
    I think there are but a few fundamental theories, for example:
    - the general theory of relativity which indicates that the emergent phenomenon of gravity arises from the curvature of 4-dimensional space
    - quantum mechanics which considers physical quantities at the atomic level as merely random results of measurements
    Ypan1944

    From what you have written, I cannot tell what distinction you make between a phenomenological and a fundamental theory.

    The contraposition of "descriptions of what actually happens" vs. "a fundamental explanation" offers no clarification. All theories seek to describe what actually happens, and all theories seek to explain - that's just what the word "theory" means. But what is it that makes a theory fundamental, as opposed to merely phenomenological?
  • Bannings
    And the people in power are the ones who decideT Clark

    You could leave the rest of the sentence as a wildcard, since what you wrote up to that point is a truism (or at least that is what it is meant to be). This "universal acid" style of rhetoric can be applied to anything, but that is what makes it unconvincing.
  • I found an article that neatly describes my problem with libertarian free will
    Others characterize libertarianism by what it means more generally, — SophistiCat

    What does it mean more generally?
    flannel jesus

    Libertarian free will requires agency, causal control, and most importantly, "genuine" alternative possibilities. The devil, as always, is in exactly how these requirements are cached out. My own view is that a lot of seemingly oppositional views on free will aren't as far from each other as they might present themselves.
  • I found an article that neatly describes my problem with libertarian free will
    Why do you think libertarianism isn't a subcategory of incompatibilism?flannel jesus

    I am going to take back what I said. While not everyone frames libertarianism as a species of incompatibilism, some do, and that includes some prominent proponents of libertarianism, such as Robert Kane:

    Those who are convinced that there is a conflict between free will and determinism, for these and other reasons, are called incompatibilists about free will. They believe free will and determinism are incompatible. If incompatibilists also believe that an incompatibilist free will exists, so that determinism is false, they are called libertarians about free will. — Robert Kane

    Others characterize libertarianism by what it means more generally, rather than by what it implies for determinism specifically. On that account, libertarianism and incompatibilism simply answer different questions.
  • I found an article that neatly describes my problem with libertarian free will
    He does? I missed this. I don't think he said incompatibilism at all in his article. Libertarianism is a subcategory of incompatibilism, and that's what he's talking about.flannel jesus

    Well, it's not. Libertarianism and incompatibilism often go together, but they are neither identical nor subcategories of one another.
  • I found an article that neatly describes my problem with libertarian free will
    https://www.georgewrisley.com/blog/?p=47

    This has been my issue with libertarian free will for maybe decades. I've worded it in various ways myself, but I think this guy puts it pretty well.

    In short, if you maintain that if you were to set the entire world state back to what it was before a decision (including every aspect of your mental being, your will, your agency), and then something different might happen... well, maybe something different might happen, but you can't attribute that difference to your will.
    flannel jesus

    This is a well-known objection to libertarian free will. It even has a name in the literature - the Luck Objection. Naturally, libertarians are well aware of it and try to address it in various ways.

    The author of the blog post articulates the argument pretty clearly, but he is misrepresenting some key terms. For example, he conflates libertarianism with incompatibilism, and he presents compatibilism as a variety of determinism.

    I would suggest reading an introductory article on the subject, such as Randolph Clarke's SEP article Incompatibilist (Nondeterministic) Theories of Free Will
  • Bidzina Ivanishvili
    Oh, I am not being pessimistic, just saying that the situation there is a lot more complicated and uncertain than the domino metaphor would suggest. Even Georgia insiders don't offer any confident predictions on how the events will unfold.
  • Hinton (father of AI) explains why AI is sentient
    This is going in circles, and I am not keen on repeating myself.
  • Hinton (father of AI) explains why AI is sentient
    How is it empty if it justifies the second premise of the argument that you ignored?Leontiskos

    Your argument is not a truism, but its crucial premise stands without support.

    I don't know why it is so controversial to insist that in order to make a substantive argument, you need to say something substantive about its subject (and not just things like "AI cannot transcend its limitations"), and for that you have to have some knowledge of it.
  • Bidzina Ivanishvili
    It's all too tempting to reach for a recent precedent, but Georgia is nothing like Syria. Without an understanding of its specifics, it is useless to speculate about whether "Ivanishvili might be the next domino tile falling," and even then prediction is a risky game.

    Authoritarian regimes are often said to be brittle. But brittle doesn't mean short-lived: there have been (and still are) authoritarian regimes that went on for many years and decades even (and some, like Russia, emerged briefly from authoritarianism, only to slip right back into it). They mostly appear to be brittle because when they finally fall, few can see it coming. But that's partly because they are also opaque.
  • Bidzina Ivanishvili
    I thought there was some major development in Georgia in the past few days that I hadn't heard about. But no, the ruling party is still in control and Ivanishvili is still its de facto leader. What's this all about then? Just a speculation about what might happen? (And shouldn't this be in Current Affairs?)
  • Hinton (father of AI) explains why AI is sentient
    I think you just haven't understood the argument, and thus are engaged in a "lazy dismissal." You could disagree with the claim that humans are able to "set their own norms," but you wouldn't be on very solid ground.Leontiskos

    I was addressing the argument - not the thesis about what is sine qua non for intelligence, but that it is out of reach for AI by its "very nature." No argument has been given for that, other than truisms, such as that AI cannot do what is outside its limits (no kidding!) But what are those limits? That seems like the crucial question to answer, but personal prejudices are all we get.

    dismissive truismsSophistiCat

    What exactly is your complaint, here? That it is true?Leontiskos

    That it is empty.
  • Hinton (father of AI) explains why AI is sentient
    This doesn't help with the logical fallacy of equivocation, for "the essential and enduring structure" of humans and computers are very far apart, both actually and epistemologically.Leontiskos

    No one said they were, so I am not sure whose fallacy you are attacking. I was just pointing out the emptiness of critique that, when stripped of its irrelevant elements, consists of nothing but truisms. I am skeptical of a so-called artificial general intelligence (AGI) arising in our time and along the existing lines of development, but my doubts arise from considerations of specific facts about AI (even if my knowledge is very limited in this area), not on dismissive truisms like this:

    Computer programs don't transcend their code.Leontiskos

    Well, of course they don't. That's what they are - code. And humans don't transcend whatever they are (which, if you happen to be of a naturalist persuasion, as Josh likely is, could be dismissively caricatured as "meat" or "dumb matter" or some such). So what?

    That which is designed has a determinate end. It acts the way it was designed to act.Leontiskos

    Another truism (as far as it is true). So, a hypothetical AGI would be designed to replicate and even surpass human intelligence. But that's not the desired conclusion, so now what? What is needed is not lazy dismissals, but getting down and dirty with what the actual limitations of actual AI might be.
  • Hinton (father of AI) explains why AI is sentient
    I think the difficulty with your position here is that when one says, "AI is designed and humans are designed," or, "AI has an architecture and humans have an architecture," the words 'designed' and 'architecture' are being used equivocally. AI is literally a human artifact. It literally has a design and an architecture.Leontiskos

    Well, like I said, the fact that AI is designed by people has little bearing on the question of its potential capabilities - at least not without specific argumentation to that effect. We can talk about architecture in a loose sense, as an essential and enduring structure of a thing. Every thing has such a structure - that is what makes it identifiable as a "thing." But then, saying that a thing cannot transcend its architecture is a truism.
  • Hinton (father of AI) explains why AI is sentient
    Now let’s say that a year later engineers produce a new A.I. system based on a new and improved architecture. The same will be true of this new system as the old. It will never be or do anything that exceeds the conceptual limitations of its design.Joshs

    Let's examine your thesis. "Conceptual" and "design" do no work here - they just point to provenance. What it boils down to is, "[AI] will never be or do anything that exceeds the [...] limitations of its [architecture]." Is there anything towards which this statement would not apply? Can the human mind exceed the limitations of its architecture?

    I am not defending the idea that generative AIs of today are sentient, but such trivial prejudicial critiques are unhelpful.
  • When Protest Isn't Enough
    Where did I say that? I was just reacting to you using the example of a lone vigilante murdering an insurance exec as "the people" taking matters into their own hands.

    But yes, for "the people" to do something, it requires some kind of organization and at least an implicit consent on their part. That's just a straightforward implication of what the words mean.
  • When Protest Isn't Enough
    I don't remember "the people" delegating murdering company execs to Luigi, do you?
  • Consciousness, Time, and the Universe: An Interplay of Observation and Change
    Also, on the entropy piece. I think that entropy is more fundamental than time itself, which is the reason why I used entropy to define time.

    In a universe where nothing ever changes, time has no meaning. Time emerges only when change or entropy is introduced.
    Ayush Jain

    Yes, you said this already in your opening post, and I explained why this is unworkable.
  • Consciousness, Time, and the Universe: An Interplay of Observation and Change
    These are kind of random musings. Discussion would be more productive if you took one of these theses, thought it through, and developed in a separate post.

    Here is one that you may not have thought through:

    Time is not an independent entity but a construct emerging from the increase in entropy. For the universe to exist beyond nothingness, time is essential to define and characterize change.Ayush Jain

    "[T]ime is essential to define and characterize change [over time]." That is a truism, of course, and it highlights the problem with trying to derive time as "emerging from the increase in entropy." Entropy increases - changes - over time. You need to have the concept of time before you can talk of an increase in entropy. Deriving time from entropy is circular, because the latter concept depends on the former.

    Entropy, arguably, can explain the arrow of time: the fact that past and future are asymmetric. It is by way of entropic processes that memories are inscribed in our brains, and thus we remember the lower-entropy past and not the higher-entropy future.
  • Mathematical platonism
    SophistiCat Could you explain the thing about the number 1/137 in physics?frank

    Not sure why the question is addressed to me - did I write something about this before? Anyway, this is more of a counterexample to the point being made (if we consider something like Fibonacci numbers as a paradigmatic supporting example). In the Standard Model of particle physics, there is a fundamental constant known as the fine structure constant. The interesting thing about it is that it is dimensionless, i.e., it is a number that does not depend on units of measurement - nor on anything else for that matter. (Avogadro number is also dimensionless, but unlike the fine structure constant, it depends on some arbitrarily chosen dimensional parameters, such as volume, temperature and pressure.) What was even more intriguing back when that constant was proposed was that, within the accuracy of early measurements, the number looked simple without being trivial: not 1 or 2 or some multiple of pi or e, but as close as permitted by early measurements to the ratio 1/137 (Avogadro number is ~6.023x1023). For that reason, physicists puzzled over the possible significance of that ratio. This led to some unfortunate numerology - long since abandoned - that grew ever more convoluted as later, more accurate measurements no longer quite fit that initial 1/137 estimate.

    Such speculation may look silly in retrospect, but it should be understood within its historical context. Physicists, probably more than anyone else in science, are obsessed with simplicity, unification and "naturalness," and not without reason, because this attitude has accompanied spectacular advances in physics over the past two centuries. But how philosophically justified is it? And how sustainable? I suppose that goes to the question of the proverbial "unreasonable effectiveness of mathematics."
  • In defence of the Principle of Sufficient Reason
    The context of the discussion is metaphysics- so the relevant modality is metaphysical possibility/necessity.Relativist

    Going from logic to metaphysics hardly clears things up.

    I've proposed that it is a metaphysical axiom that contingency needs to be accounted for: X is contingent iff whatever accounts for X could possibly account for ~X. In the absence of such an account, X is metaphyically necessary. A first cause is not accounted for by anything else, therefore it cannot be contingent. This conclusion follows from my axiomRelativist

    It does, if one accepts your idiosyncratic definitions of contingency and necessity (and accounting as well), but that makes the conclusion an inconsequential triviality. Physics has nothing to do with it - it is just an exercise in postulating what you want, which has the same advantages as the advantages of theft over honest toil, as Russell once said.

    You also alluded to an "absence of constraints" applying (I assume) to a first cause. It is contrained to being whatever it was, conceptual possibilities notwithstanding.Relativist

    Constrained by what? Your metaphysical axioms?
  • In defence of the Principle of Sufficient Reason
    That's not my reasoning.Relativist

    What follows doesn't resemble your reasoning above, either:

    if the foundation of existence didn't exist, there would be no existence at all; which is logically impossible because we obviously existRelativist

    In any case, your conclusion is incorrect:

    The first cause cannot have been contingent upon anything, because nothing is prior to it. So, whatever it actually was, it is metaphysically impossible for it to have been anything else.Relativist

    Contingency and necessity are context-dependent. In ordinary usage (let's leave logic out of it - as I already explained, it does not apply here), this contextual meaning is usually unproblematic. We can recast it in terms of constraints: contingent events or choices are those that are not fully constrained by facts and assumptions that go into our reasoning, necessary ones are constrained to a single outcome, and impossible ones are ruled out. However, what those constraints are taken to be can vary widely, depending on discourse.

    When it comes to the necessity or contingency of the world, the problem statement is so far outside ordinary usage of these words that it is not at all clear what is being asked. You interpret the question as being solely about event causation (without explaining your choice). Given such framing, a superficially plausible conclusion could be to say that the first cause must be contingent, since nothing constrains it - which is the opposite of what you concluded. But this too would be wrong.

    The presumed absence of constraints on the origin of the world does not imply a multiplicity of possible outcomes, because there is no space of outcomes given to us. Note that I said "no space" - not an empty space and not a singleton space [consisting of a single possibility]. The latter is what you would need to make your conclusion of necessity, but assuming such a singleton space would beg the question. Assuming any space of possibilities would take you outside your original formulation, and so, the right conclusion is simply that contingency/necessity does not apply in this degenerate scenario.
  • In defence of the Principle of Sufficient Reason
    There can be no explanation for the foundation of existence, and (as noted) it can't be contingent. Since it's not contingent, its existence is logically necessary: it can't not exist.. (i.e. if the foundation of existence didn't exist, there would be no existence at all; which is logically impossible because we obviously exist).Relativist

    Let's see... Me buying milk today was logically necessary, because I obviously did buy milk. That's not right, is it? Logic cannot imply existence or non-existence, necessity or contingency of anything outside its universe. The only way you can get the necessity of our existence as a logical conclusion is if you front-load it with postulated propositions, but that would be question-begging in the present context.

    I think you confused logical contradiction with performative contradiction of denying your own existence.
  • Can One Be a Christian if Jesus Didn't Rise
    The general consensus among Christians is that the resurrection is the good news. If that's not it, then most Christians are mistaken.Brendan Golledge

    Most Christians believe that most Christians are mistaken*. So what?

    * There are thousands of Christian denominations in the world. The largest of them - Catholic - accounts for less than half of the total number of members.
  • Visualization/Understanding or Obscurantist Elitism?
    Let me phrase it this way. If we are talking about things we regard as fictions and are only to be taken as fictions does it make intelligible sense to talk about a made up thing which is itself unimaginable?substantivalism

    I am not sure what you mean by fiction here. Scientific theories? Metaphysical interpretations? Illustrations, analogies, simplifications and other narratives used for pedagogical purposes?
  • Visualization/Understanding or Obscurantist Elitism?
    Thanks for providing some context and examples. I am not familiar with Philipp Frank's book, but I did read Trout's Scientific explanation and the sense of understanding paper. In it he critiques "the role of a subjective sense of understanding in explanation." In particular, he draws on a number of studies that reliably demonstrate psychological biases that result in unjustified confidence given to explanations. He does not develop an alternative, though he notes that on his part, he would defend an objectivist conception of good explanation: "What makes an explanation good concerns a property that it has independent of the psychology of the explainers..."

    I happened to find this further article which attempts to give a 'metaphysics' of neo-positivismsubstantivalism

    OK, that's interesting and I'll give it a read, but I am not sure how this relates to the topic.

    If someone tried to explain what the second law of thermodynamics is and how that connects to the problem of the arrow of time I think I'd be at rather a loss if observables weren't referenced. However, I could see how pointing to certain phenomena could obscure what it is exactly we are getting at and the mathematics are too abstract to assist us here.substantivalism

    I think your concerns are more pedagogical than epistemological. In the present context, the former is concerned with accessing, internalizing and operationalizing established science (such as the Second Law of thermodynamics). The latter is concerned with establishing criteria for what constitutes a good scientific explanation. Trout above is concerned with epistemology and has little to say about pedagogy, other than that the two should not be mixed up.
  • In Support of Western Supremacy, Nationalism, and Imperialism.
    Again, you seem to have missed the point. A meritocracy guided by secular values may be your preference but others may hold to religious values as superior, that it is religious values that have elevated us above the savagery, cruelty, and viciousness of secularism.Fooloso4

    Yeah, but others haven't got the Maxim gun. That's the unstated premise underlying Bob's fascist fantasy.
  • In praise of anarchy
    Right, ignore what everyone is telling you and repeat yourself - that will work.
  • Visualization/Understanding or Obscurantist Elitism?
    No one, I was making a caricature. Course, the founders of quantum mechanics were notorious for either abandoning any attempt at the intelligibility of the atomic or grew rather pessimistic at said notion.

    However, its the explicit dogma of neo-positivist to discount anything that isn't either descriptive/observable language or theoretical abstraction/modeling as mere window dressing to further observable/theoretical statements. That, or if its untranslatable to discount it as irrelevant to the sciences.
    substantivalism

    Who are these neo-positivist dogmatics? What are they actually saying?

    Further, anything more is either metaphysical nonsense or TOO VAGUE to be meaningful of anything. Right?substantivalism

    Well, I don't know what kind of understanding you are after. Do you have a clear idea of what would satisfy you that you understand something?
  • Visualization/Understanding or Obscurantist Elitism?
    Yeah, that is what the point and purpose of comparative thinking (metaphor/analogy) along with computational/concrete analogue models serve as their purpose. To bring understanding and serve as explanations.substantivalism

    Metaphors and analogies may help - or mislead - but I don't think they are necessary for understanding. We are capable of understanding scientific concepts on their own terms.

    However, this would then be at odds with neo-positivist inclinations which seem to paint themselves into a strange corner saying, "I can describe these things but despite that I don't understand anything here and cannot explain a single thing as well. Mostly, because I see any non-abstract or non-mathematical avenues of thought as mere pointless ventures leading us no where."substantivalism

    Who actually says that? Do you have examples (other than the overused Feynman quip)?
  • In praise of anarchy
    Yes, that's because you never bothered to understand Ourora's point about rights. You could disagree with her, or meet her halfway by accepting her framing of rights and falling back on justice or the good. But you don't seem to be capable of an actual debate.
  • In praise of anarchy
    As I wrote previously, if what you propose hasn't ever happened, won't ever happen, can't ever happen, then your idea is a fantasy. Meaningless. If you can't see that or show me how anarchy might work, then we'll never come to any resolution. That's my best shot.T Clark

    Ought implies can. The idea that all forms of government are unjust must be rejected until it can be shown (against all available evidence) that the alternative is possible in a society larger than a modern-day commune. Even then it would likely come down to choosing one injustice over another, because there is no rule that rejecting one form of injustice leaves you with a (more) just state of affairs.


    No, they did have rights and those rights were not respected. I am not sure I can argue with someone who thinks a person has a right if and only if the government of any community of which they are a member says they do. That view is so plainly false to me that I am at a loss to know how to argue with someone who is willing to embrace its implications.Clearbury

    I am not sure you can, either - at least you have not demonstrated such an ability. Saying that your opponent is obviously wrong and leaving it at that is a conversation-ender.
  • All Causation is Indirect
    Why should this be the case? I drop an object from a certain height and predict when it will hit the ground. How does this eliminate causality? There are a host of factors involved in this physical feat, and one can argue one's way through that jungle, rather than citing a principle cause, gravity.jgill

    That sort of cause fits with the conventional contemporary ideas of causation, what @Count Timothy von Icarus refers to as granular efficient causation: gravity is the cause of the object dropping to the ground, or, alternatively, your releasing it from your grasp is the cause. No argument from me here, other than what has already been noted about such causation being in part subjective.

    (I wrote a math note a year or so ago that partitioned a causal chain temporally so that each link was formed by a collection of contributory causal effects added together to produce one complex number associated with that link. Just a mathematical diversion, but a vacation from the plethora of philosophical commentaries about the subject.)jgill

    But here I would question whether the notion of cause adds anything that is not already given in the mechanistic description.
  • Visualization/Understanding or Obscurantist Elitism?
    I think you overstate the limitations of our conceptual grasp. We are not locked into a fixed Kantian conceptual universe. Our minds have some flexibility and room for development, enabling us to comprehend formerly incomprehensible (or at least convince ourselves that we do so comprehend). Galilean principles of motion were once unthinkable, as it seemed obvious to everyone that motion must be sustained by a motive force, and there had to be a categorical difference between motion and rest. But we have learned to get over this conceptual hurdle (even though our folk physics is still more Aristotelian than Galilean). Newton's spooky action at a distance (setting aside further developments in General Relativity) also doesn't seem to be causing as much consternation as it did in his day. In general, people working in their fields, be it fundamental physics, genetics or linguistics, develop conceptual tools that enable them to apprehend even complex and unintuitive ideas, at least to some degree.