Well, for starters, I think that you vastly overestimate philosophy's impact on the world. The revolutions you cite were definitely not the "direct consequence" of philosophers, but rather the consequence of a complex web of social, economic, and political factors, factos that were in a complex feedback relation with philosophy. To credit the history of the entire 20th century to "Continental Philosophy", whatever that means (is Carnap a continental philosopher? Schlick? Cassirer? Hermann Cohen? What about figures such as Max Weber or Simmel?), seems to me not only absurd, but incredibly naive and borderline idealistic (in the sense of believing that history is solely shaped by ideas---note that I'm not denying that ideas are a factor, rather, I'm denying that they are the sole factor).

But leaving to the side your faulty characterization of history and of continental philosophy, I'm also concerned about your characterization of analytic philosophy as somehow technocrat. It is true that logic, and the sciences more generally, inform much of analytic philosophy, but that does not mean that analytic philosophy is reducible to a bunch of techniques. Consider, by way of example, Hartry Field's extremely technical account of truth. The details are rather unimportant, but Field defends a non-classical reading of truth (he denies universal validity to the excluded middle) and also an extreme nominalist position in the philosophy of mathematics (for the former, cf. his very demanding Saving Truth from Paradox and for the latter the essays in Realism, Mathematics, and Modality). These may seem as purely technical exercises that are entertained as answers to purely technical problems (e.g. formal versions of the liar), but I think this would be a mistake. Field adopts both views in part because he thinks those are the only views that cohere with a certain outlook of human's situatedness in nature, a certain view of the human capacities for knowledge. That is, the ultimate aim of his philosophy is to try and make sense of our place in the world, even if this worry is not always in the foreground. In other words, technique is not here an end in itself, but is at the service of a broader project, which Sellars once characterized, in a phrase that is almost a cliche now, as "to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term".

True, it is sometimes easy to forget this ultimate aim and simply concentrate on the latest trendy logical puzzle (this is the inevitable consequence of professionalization, I think, which might be one of the factors which explain why analytic philosophy became dominant in the academic world today). And if you read just journal articles, which are perforce just one piece of a giant jigsaw puzzle, you may leave with the impression that's all professional philosophers do. It would, however, be a rather myopic impression, I think.

Finally, I don't see what's so absurd with the comparison with the sciences. I do think philosophy is increasingly becoming more science-like, and this reflects the degree to which the many sciences have become more mature and autonomous. For example, in the beginning of the twentieth century, philosophers could more or less ignore the contributions from linguistics (at their own peril!), since it was still a fledgling science. Not so today, when even semantics and pragmatics are rather advanced (in part thanks to philosophers such as Carnap, Montague, and Lewis, not to mention philosophy-inclined linguists such as Barbara Partee, Angelika Kratzer, and Irene Heim). Similarly with cognitive psychology. And as philosophy enters with diverse partnerships with the sciences, it is not surprising that it becomes science-like.

Well, I thought that you wanted your principle as a solution to a problem described in the OP. If the relation between them is irrelevant to you, ok, I'm happy to leave matters as they are.

Yes, we use folk psychology all the time in interacting with other people (interestingly, this is now studied under the heading of "theory of mind" and may have connections with autism, a finding that is surely noy obvious). But that does not mean that psychology is reducible to folk psychology, in particular, developmental psychology that studies core cognition is not so reducible.

I'm aware of the so-called replication crisis, but I haven't found any study questioning the specific findings that I mentioned (I would actually be surprised if that were the case, since they have been replicated in dozens of studies by different laboratories, but these things are subtle and I may have missed something). If you are aware of studies questioning, e.g., habituation methodology, I would be interested in hearing about it.

As for your point about prejudices, yes, some people some times approach infants with prejudice. So what? How is this related to the conclusions that I mentioned?

Finally, any existence claim is non-falsifiable in principle (short of a contradiction), so I suppose you also consider particle physics (which, e.g., postulate the existence of certain particles to explain a given phenomenon) to be non-scientific?

But then, how can he justify that what is beyond the physical cannot be perceived? Surely this a metaphysical claim about the nature of whatever it is beyond the physical? Anyway, I would like to be clearer about what exactly is the position you're attributing to Hume before considering whether what you are proposing is or is not an answer to it.

Well, according to you, he is saying that what is not perceivable is not physical, which seems a pretty strong connection between perception and reality...

Sure, but Hume is not denying that some things can be perceived, nor he is denying that there is a connection between perception and reality. So, again, your principle seems to be irrelevant to his worries, at least in the way you formulated them in the OP.

I strongly recommend reading Kenneth Mander's papers in The Philosophy of Mathematical Practice, edited by Paolo Mancosu (you can easily find the volume for download at the usual sites). They are among the best accounts of diagrammatic proofs that I know of (oddly, from a quick glance, I don't see them mentioned in Giaquinto's entry linked in the OP---it's especially odd because Gianquinto also has two contributions to that volume).

Anyway, some of Mander's claims may help to distinguish the algebraic proof of left-cancellation from diagrammatic proofs (incidentally, I found Giaquinto's discussion of the algebraic proof baffling). In particular, he distinguishes exact from co-exact figures of the Euclidean diagrams. Exact features are things like equalities and proportionalities, which "fail immediately upon almost any diagram variation", whereas co-exact features are things like "part-whole relations of regions, segments bounding regions, and lower-dimensional counterparts", that is, properties of the diagram that are "insensitive to the effects of a range of variation in diagram entries". (All quotations from p. 69)

Mander's point is that the diagrams enter in the proof only in order to verify the co-exact features, and never the exact features. I think this is important, because it points to a difference between Euclidean diagrams and the proof of left-cancellation. In the latter case, we are not using any "co-exact" properties of the array of equations to justify the proof, but rather just quantifier rules and substitution, which are logical rules.

You asked about whether we can scientifically study people's minds, with the specific challenge that we somehow do not have access to the inside of people's heads. I pointed out that we do have access to the inside of people's heads, and have used this access to collect impressive amounts of data about the mind's architecture and content: that we have innate systems that analyze spatio-temporal trajectories for information about objects and goal-directed actions, that we have innate concepts of objects and actions, that we have innate systems for parallel tracking of objects and for analog magnitude representations that inform our cardinality judgments, etc., etc. We have detailed (though, obviously, far from complete!) knowledge about the format and development of these systems and representations.

In answer to this, you claimed, first, that such results are easily derivable from common experience, and, second, that psychology's "shallow or negative assumptions about people" somehow invalidate this mass of data. Well, with regards to the first, I don't know how to reply except with an incredulous stare---if such data were derivable from common experience, then we would expect it to be common knowledge, yet it is not common knowledge, being, in fact, very surprising (in the very representative sample of two, namely me and my wife, we surely found it surprising, and my wife works with children, if that's relevant).With regards to the second objection, leaving to the side the bizarre implication that a discipline approaches people with certain assumptions (as opposed to its practitioners), I don't see how that is remotely relevant here. Either the results are true or not. If they are true, then the assumptions of "psychology" (?) are not relevant; if they are not true, then you should be able to point out where are the relevant mistakes, instead of merely handwaving about supposed assumptions.

I don't see the relevance of the principle to the problem. If something can't be perceived, then no one can perceive it, so, ipso facto, there will be no "majority" who perceives it.

Some of these ideas are captured by modal logic, especially counterfactual logics (cf. Lewis's theory of causation, for instance). But I'm not sure why logic should study the nature of causation, which seems to me much more amenable to a physical treatment (perhaps along the lines of Bayesian theory).

We're not just studying behavior, we're studying the content and structure of people's mental architecture. For example, current psychologists think that there are differences between central processes (which are available to consciousness and can use information from many different sources) and specialized modules (such as depth perception, which is largely unconscious and informational encapsulated). This is a structural claim. On the content side, most of them think that we are endowed with innate principles of object permanence and numerical cognition (parallel processing and analog magnitude representation), which have the status of proto-concepts.

Well, perhaps you and I have had different experiences and, as a result, different expectations. I certainly didn't learn, before reading the relevant studies, that children a few months old had a complex physics and knew about object permanence principles; nor did I infer that we work with two systems of numerical representation, parallel object files and analog magnitude representations, with the latter obeying Weber's law!

Notice that there are other ways of measuring things than just by directly observing them. For example, we do not directly observe forces, but we can measure them by indirect observations. Similarly, we cannot directly observe "the mind", but we can understand it by indirectly observing people's reactions.

Here's an example of what I have in mind. Until the 80's, it was widely believed that infants operated under "dumb association mechanisms", i.e. they had no conceptual apparatus and whatever discrimination they made was based on an innate similarity space that measured how much similar one perceptual stimulation was to another (in philosophy, this paradigm was famously defended by Quine: cf. Word and Object and The Roots of Reference). Starting in the 80's, however, a group of researchers, especially Elizabeth Spelke and her collaborators, devised new methods to investigate how infants organize their world. The idea was simple enough: you habituate the infant to a certain stimulus, and then present a new stimulus differing from the new one over a controlled dimension. If the infant's reaction was different (especially if the infant displayed surprise, as measured by looking times), then we know that he or she can discriminate the controlled dimension.

This idea is simple enough, but it showed that infants as young as two months already have an implicit physics and the concept of object, so that objects are thought of by the infant as cohesive wholes (i.e. wholes that maintains their parts connected and boundary integrity) that only move together as they touch and which are tracked through a continuous space-time trajectory. Further studies also showed that infants have integrated senses (so they can use information from touch to discriminate by vision an object) and use analog magnitude representations in order to calculate with numbers. Notice that most subjects studied are pre-verbal! So we can acquire a lot of information about their minds without needing to literally observe it.

Incidentally, I think this is congenial to a point John McDowell repeats over and over again. We tend to think of minds as organs, as if they were "located" in some sort of para-space, which we cannot access and hence must somewhat guess its contents. McDowell urges us to drop this talk and instead recognize that to talk about minds is to talk subjects of a mental life, i.e. to talk about people. So in some sense we can in a sense see the person's mental states because they show us (unwittingly, in some cases, such as the infant's) their mental states.

Currently, aside from math/logic textbooks, I'm reading a lot of cognitive psychology, especially the Oxford Series in Cognitive Development. I've just finished Jean Mandler's The Foundations of Mind: Origins of Conceptual Thought and Susan Gelman's The Essential Child: Origins of Essentialism in Everyday Thought, and am currently reading Susan Carey's The Origin of Concepts. Great stuff! These books demolish the idea, dear to Quine and others (including Piaget and Vigotsky), that children are, in the words of a theoretician, "dumb associatinist mechanisms", easily impressed with outward, perceptual appearances; instead, they are more like, in Gopnik's turn of phrase, little scientists, probing the world to find hidden causes and stable properties. Such books also have the added advantage of containing many anecdotes about the researchers' interaction with children, which are always funny or endearing.

I don't mind discussing Kant's theory of intuition or his conception of things in themselves, but I don't want to hijack this thread (specially since I want to go back to some of the things in the OP). Isn't it better to start a new thread?

I'm not following (perhaps you're already regretting your statement?). Let us suppose, with Kant, that space and time are the form of our intuition, and are therefore the result of our productive imagination, i.e. ens imaginaria, as he puts it. Let us also grant that this means that things, as considered in themselves, are not represented as in space and time. How does this impact the abstract/concrete division? One can still hold that concrete refers to things in space-time, and that abstract, if it refers at all, refers to things not in space-time. To be sure, this would make things, as considered in themselves, to be an abstraction, but I don't think that is very far from what Kant was thinking.

Nonlinear reasoning does not avoid circular reasoning; it argues that, in some cases, it is both unavoidable and not vicious (or, perhaps, more positively, indeed virtuous). That is Quine's stance: we always start in the middle of things, so to speak, and there is no problem in using our background knowledge to understand how we came to have that knowledge in the first place. The point is that, once we realize that our knowledge is not linearly arranged, but rather forms an intricate web, we give up the search for foundations (so that the aim of epistemology is not to secure knowledge---i.e. it is precisely not to argue against the skeptic), and rather try simply to further the knowledge we already have.

Thanks for the compliment (I think it was a compliment?)!

As for Kant, I'm not sure I understand your point. Yes, for Kant, space and time are imposed by our productive imagination onto the phenomena. But I don't see how this relates to the concrete/abstract distinction---unless you're saying that things, as considered in themselves, are neither concrete nor abstract? Is this your suggestion?

If your beef is exclusively with modus ponens, then rest assured that it is dispensable (well, sort of, for some systems).

But that does not seem to be your problem with modus ponens; rather, you seem to be wary of using any rule of inference at all (incidentally, note that this is not my reading of Carroll's story at all---I think he is pressing the need for distinguishing axioms from rules of inference). Behind this wariness there seems to be some kind of linear propositional support requirement, namely that "a proposition or theory must be supported by inference from accepted premises to a conclusion, and that the conclusion not appear among the premises, premises of the premises, etc." (Paul Gregory, Quine's Naturalism, Chapter 1) The name derives from the fact that this requirement imposes a linear structure on our knowledge, i.e. P < Q iff P supports Q. It is well known that this requirement leads to skeptical conclusions, in the form of the Agrippan trilemma. Ironically, you seem to apply modus ponens to this argument (If there is a requirement for linear propositional support, then we must embrace skepticism; there is such a requirement; therefore, we must embrace skepticism), whereas it seems to me that it would be better to apply modus tollens and reject the linear propositional support requirement. (For what is worth, that is precisely Quine's strategy in "Epistemology Naturalized".)

If that is your definition of justified, then modus ponens is entirely justified, since it always takes us from true beliefs to true beliefs. For suppose toward a contradiction that P and if P, then Q are both true, but Q false. Since P is true and Q is false, it follows that if P then Q is false, contrary to what we have assumed. Therefore, if we believe in P and we believe in if P then Q, we are rationally justified in believing that Q.

Expanding a bit, it is always possible to justify our rules of deduction by soundness proofs, which are typical in mathematical logic.

In that case, I don't have much more to add.

Here is why I think the analogy is poor: for Lewis, "actual" is an indexical, because it is short for "in this space-time continuum". So, from the point of view of this space-time continuum, we're actual; from the point of view of another space-time continuum, they're actual and we're possible. So whether or not something is actual or possible depends on which space-time continuum you're in. With abstract and concrete, however, there is no such relativity: either you are in a space-time continuum, or not. If yes, then you're concrete; otherwise, you're abstract.

So, in your proposal, it's not like I'm abstract from one point of view and concrete from another. Rather, everything is abstract (everything is in Plato's heaven, to use your terminology), and we simulate concreteness by appealing to certain properties of abstracta. As I said, this is very similar to what (I remember) Quine proposed: take the pure sets, find the reals inside them, form $\mathbb{R}^4$, and identify the concrete objects with sets of points in this space-time surrogate. Of course, you can also go on and say that this simulation is what people have "meant" all along by concreteness, or perhaps simply follow Quine and say that, if this is not what they meant, so much the worse for them ("explication is elimination"). I don't personally find this Quinean route very appealing, but it not all that implausible...

I don't think the positions are analogous at all. Lewis can say that other worlds are real because he is assuming that to be a real world is to be a concrete entity (say, the mereological sum of all spatio-temporally connected parts of its domain). In your case, you're saying that abstract entities are real because... what? They are concrete? But then they are not abstract. That is, either there is a space-time in which a thing inhabits or there is not. If there is, then the thing is concrete, if there isn't, it is abstract. I don't see any way to relativize this distinction further.

As I said in my reply above, I don't think platonists need to be saddled with such Cartesianism. There would be such a need if they thought there is any interaction between concrete and abstract objects, and wondered about the (per force, mysterious) character of such interaction. But, as I said, I don't think platonists are committed to there being any such interaction, and in fact I would argue that most (all?) deny that there is such an interaction.

I don't think most platonists would recognize the need for any relationship between actual, concrete objects and abstract objects, at least not in this direct way. It is useful, however, to distinguish between two types of platonists here (I take this classification from Sam Cowling's Abstract Entities, a very useful---and opinionated---survey of the terrain). Expansive platonists include among the existing abstract objects not only numbers, pure sets, and propositions, but also what has commonly been called abstract types, such as, perhaps, musical works, poems, recipes, letters (in the sense of "a", "b", etc.), etc. Austere platonists countenance only numbers, pure sets, and, perhaps, propositions and properties. So expansive platonists may want a relation like "partake" between types and tokens, perhaps in the form of instantiation. But austere platonists will not need any such a relation. If there is any relation between concrete "triangles" (I use scare quotes to indicate that I'm not taking such "triangles" to be literally triangles, i.e. instances of an abstract type) and abstract ones, it will probably be one of approximation (say, we can map an abstract triangle up to a margin of error to the space-time points occupied by the concrete triangle), where this relation is itself an abstract set.

As for your proposal, I think there are a couple of separate issues here. First, there is the question of whether there is a conceptual distinction to be made between abstract and concrete objects. Notice that this is a conceptual question: perhaps there is such a distinction, but all objects fall only on one side of the divide (that is, e.g., the nominalist position), or perhaps the distinction is not exclusive, i.e. there are hybrids (which is what I mentioned with the problem of classifying {Nagase}). Still, it must be possible to make such a distinction independently of any ontological questions.

Second, there is the question of whether the ultimate constituents of reality fall on one side or the other of the division. Some people believe that reality is hierarchically structured, with metaphysical atoms at the bottom and every other object constructed out of such atoms (and constructs of such atoms) by way of metaphysical operations (perhaps "building" operations in the sense of Karen Bennett)---one model for this is a cumulative set-theoretical hierarchy with (or without) ur-elements, with the ur-elements (or the empty set) being the atoms and the "set-builder" operation being used to construct the other sets. Given this, it's possible to ask what reality is really like, that is, how to characterize the objects at the bottom (the fundamental objects, those that really, really exist): is it abstract or concrete?

Third, supposing the hierarchical structure picture is true, there is the question of the character of the constructed entities. Are they abstract, concrete, or hybrids? Notice that, if supposing there are hybrids, depending on the character of the building operations that you use in "constructing the universe", there may be a way to reduce everything to abstract entities. One influential program tried to do precisely this, supposing that everything could be constructed out of time-slices of atoms and sets of such time-slices (I think Quine held something like this). Here's the idea: pick any set of ur-elements; presumably, they are countable (if not, you'll need some choice to make the idea work). So map the ur-elements into the natural numbers and use this map to construct a set that is the extended image of the original set (more formally: if f is the original map, build f* recursively by setting f*(x)=f(x) if x is an ur-element, otherwise set f*(x)={f*(y) : y in x}). This will build an abstract replica of the original universe, preserving its structure. So everything you wanted to do with the original universe, you can do with the new universe. Simplicity considerations then may dictate that the new universe is the real universe. (I don't endorse this line of thinking, but it may be of interest to your program.)

Finally, about Shelah, my point is this: (A) some people define logic as xyz; (B) but xyz doesn't contemplate what logicians such as Shelah are doing; (C) therefore, xyz is not a good definition. I think this is true when you take "xyz" to be "the study of logical consequence relations", and doubly true when you take "xyz" to be "the study of relations between ideas". Personally, I'm attracted to a definition of logic as being the study of local invariant relations, but there is much here to work out...

Incidentally, for what is worth, I would highly object to treating logic as dealing with relations between "ideas" or laws of thought, or whatever. This is completely misses the point of what logicians such as Saharon Shelah are doing (I'm thinking of his classification theory). Of course, some people are happy to bite the bullet and simply classify his work as some kind of more abstract algebra, but I personally think that there is some philosophical payoff to treat his program as being engaged with logic.

A couple of quick comments:

(1) Your theory of mood is very similar to the way most formal semanticists treat mood. Already Lewis in his "General Semantics" (cf. pp. 220ff of his Philosophical Papers) he proposed to analyze sentences as containing a sentence radical and a mood operator. That is, however, the easy part of the analysis. The difficult part is to specify a formal semantics for these syntactic operators. One idea, close to possible world semantics, would be to treat proposition radicals as sets of possible worlds and then treat the declarative as assigning the same function as the propositional radical (thought of as its characteristic function), the interrogative as assigning partitions of possible worlds to the proposition radical, and similar to the other moods. An up-to-date treatment of moods along these lines is given by Paul Portner's Mood (Oxford University Press, 2018), which I highly recommend.

(2) On Platonism, I don't know any current platonists (with lower case "p") who defend that concrete objects "partake" in abstract objects. Most platonists, in fact, think that there is no interaction whatsoever between abstract and concrete objects, since any such interaction would have to take place at least in time, and abstract objects are (generally, though not always) thought to be outside space-time. There are a host of problems here with "mixed" objects (e.g. {Nagase}, the singleton whose only member is me: is that abstract? concrete? partially abstract and partially concrete? is it abstract with concrete parts?), but ignoring those, I think most platonists would be happy to think that there is a complete separation between the two types of objects. Their commitment to abstract objects is wholly theoretical: our best theories need abstract objects in order to be true, hence, those objects exist.

(3) Finally, it is not clear to me how your proposed solution works. You're proposing that mathematical objects are actually concrete? So they inhabit space-time (such that I could kick the number 2, for instance)? Or are you proposing that nothing is concrete?

When faced with canonical works such as Aristotle's Metaphysics, I generally turn to the secondary literature for help. Fortunately, in this day and age, it is easy to find most of this literature for download on the internet if you know where to look...

Now, generally the secondary literature itself may be a mess, so how to navigate it? If you're completely new to the subject and would just like an entry point, one good beginning is to look at SEP and IEP, already linked by . Another is to search for guidebooks and authoritative translations. In the case of the Metaphysics, for example, there is a guidebook by Vasilis Politis in the Routledge Guidebook series that seems fair enough for a beginner, and there is also a recent translation of the book (with many, many notes; in fact, there are more pages of notes than of the text itself!) by C. D. C. Reeve (you can read a friendly review here).

After this, well, it depends on your interests. If you are puzzled by specific books, you may either consult the translation of those books in Clarendon's Aristotle series, which tend to be excellent; and, if you are lucky, there may also be volumes of the Symposium Aristotelicum dedicated to it (I know for certain that there are volumes dedicated to Alpha, Beta, and Lambda, which are all excellent). From there, you may try reading the more specialized literature, which has mostly concentrated on Zeta. Classics here are G. E. L. Owen's articles "Logic and Metaphysics in Some Earlier Works of Aristotle" and "The Platonism of Aristotle" (Owen was a detestable man, but those articles are indeed important...), Michael Wedin's Aristotle's Theory of Substance, and, more broadly, David Charles's Aristotle on Meaning and Essence.

In my own case, I'm particularly interested in the relation of the Metaphysics to Aristotle's biological works, such as the History of Animals, the Parts of Animals, and the Generation of Animals, in the tradition of David Balme and his students. So I particularly like Montgomery Furth's Substance, Form, and Psyche, which approaches Aristotle's works through that lens.

But positing a "hidden hand" is just another way of saying that you believe that there is a structural feature of chess which explains the correlation. And this is exactly what requires proof, so that you can screen off the other explanations. Note also that causality is not merely statistical correlation; if you're saying that something has a cause, you're effectively saying that there is an underlying mechanism that explains how this something is produced. So this mechanism should be explanatory; a "hidden hand" falls short of this explanation, unless it is merely a placeholder for a structural feature, in which case we're back to the need for a proof.

Well, statistics is a branch of mathematics, so...

Nevertheless, here is another way of formulating my worry. The statistics you provided show a correlation between a player choosing white and the player winning. As anyone knows, however, correlation is not necessarily causation, i.e. just because two factors are correlated does not mean one causes the other. In order for the correlation to be a reliable indicator of causation, you need at least to screen off other potential causes, be it potential causes of white winning or potential joint causes of a player choosing white and winning. For example, perhaps there is a bias in strong players to choose white, not because white has an advantage, but because they like shiny white pieces. Or perhaps there is an odd psychological quirk that gives advantages to chess players when they go first. How do we eliminate such possibilities?

One way is to run experiments to rule out such odd explanations. But how can we rule out every other explanation? Here, experiments will be of no help. Fortunately, in the case of chess, there is another route available: we prove from a mathematical description of the game that white has a winning strategy. This way, we can show that the statistics are not merely reflecting an accidental correlation, but are actually a symptom of an underlying structural fact about chess.

A proof is a sequence of statements each of which is justified by appeal to an axiom or to some previously justified (i.e. proved) statement. Statistics are not proof; they are at best heuristics. Otherwise, the Riemann Hypothesis and the Goldbach Conjecture would be considered proved by now. The problem is obvious: even if all the even integers greater than 2 tested so far have been found to be the sum of two primes, that is no guarantee that tomorrow we will not find one that is not a sum of two primes. Similarly, even if statistics show that there is a bias towards white winning, this is very far from a proof that white has a winning strategy. Perhaps this bias is explained by some quirk in human psychology, or perhaps in the next couple of years we will see a reversal towards black winning.

Again, statistics are irrelevant for a mathematical proof that white has a winning strategy! I don't know what else to say in this regard.

First, the psychological conditions of the players are irrelevant. Either there is, or there isn't a winning strategy. This can be determined entirely by analyzing the space of the play, and is independent of such extrinsic factors.

Second, your claim that the first player will "dominate" the game is, again, pure speculation. We don't know that! If you do, I suggest that you write your proof and send it to a reputable journal on Game Theory.

But it is not a matter of statistics, it is a matter of whether there is a winning strategy or not. For all we know about chess, maybe white has a winning strategy, maybe black, maybe neither (that is, maybe the best strategy leads to draw).

But we don't know whether it is white that has the winning strategy. It may be black (or neither).

I've already replied to this in my second post in this thread: one of the players may be able to force the other to perform certain moves, or perhaps the other player's moves are somehow irrelevant (think of forced checkmates). That is, it may be that there are no advantageous situations in the decision tree of one of the players to be known.

I really don't understand what you're getting at. What exactly is your point?

Reject the pact or reject the applicability of game theory?

In any case, as with any mathematical formalism, game theory provides an ideal model of certain situations which involve strategic behavior. It is a model, in that it serves to highlight certain causal or structural dependencies of a given phenomenon (in this case, strategic behavior); it is ideal, because it involves a deliberate falsification of reality for simplification purposes (cf., among many others, the work of Nancy Cartwright and of Angela Potochnik for more on this). So I don't think applying game theory to reality is anymore nonsense than applying the Lotka-Volterra equations to study population equilibrium or the use of infinite populations in certain models to screen off genetic drift considerations, or even the application of ideal gas laws to explain the behavior of gases.

No, it does not help at all. I'm beginning to lose track of what is your point. At first, I thought you were (erroneously) claiming that there can be no winning strategies for any games, since, supposedly, players could readily adapt to any such strategy through rote training or whatever. Now you seem to be claiming that a game with a winning strategy for one of the players would be pointless to play, to which I replied that (i) the existence of a winning strategy does not imply that a particular play is determined, since, for a variety of reasons, it could be that the player with the winning strategy has no access to it and (ii) in any case people could want to play the game for a variety of reasons other than winning. Finally, you seem to claim in your last post that there is some kind of problem with applied game theory, but you don't indicate what the problem is or how it is remotely related to the fact that some games (like Hex) have a winning strategy for one of the players. So I'm kind of lost...

I suppose there could be other motives, such as boredom, incredulity, or simply to better understand why you can't win. Incidentally, note that the existence of a winning strategy for one of the players does not mean that in an actual, particular play, one of the players is guaranteed to win. Maybe he doesn't know the strategy, maybe nobody knows the strategy, maybe he knows the strategy but has forgotten it, maybe there is a strategy but nobody can follow it because it is too complicated, etc.

As for chess, I don't think everyone wants to start out as white. For some time I personally was more comfortable playing black, and I think many players don't mind playing either way. And in any case, it's not clear that there is a winning strategy for white. Either black or white has a strategy for not losing (i.e. at worst to force a draw), but nobody knows which. It could be black's.