Progress in Mathematics and Logic — IV

paradoxes[for a brief explanation of this ongoing series, as well as a full table of contents, go here]

A panoply of logics

The striking thing about contemporary logic is that it is plural. Indeed, Logics (Nolt 1996) was the title of the book I used as a graduate student at the University of Tennessee, and that in itself was a surprise for me, since I had naively always thought of logic as a single, monolithic discipline. (But why, really? We have different ways of doing geometry and mathematics, and certainly a plethora of natural sciences!). The following brief look at modern logic should be enough to convince readers that the field is both vibrant and progressive, in the sense discussed above.

Consider, for instance, modal logic (Garson 2009), which deals with the behavior of sentences that include modal qualifiers, such as “necessarily,” “possibly,” and so on. It is actually a huge field within logic, as it includes deontic (“obligatory,” “permitted,” etc.: Hilpinen 1971), temporal (“always,” “never”), and doxastic (“believes that”) logics. Arguably the most familiar type of modal logic is the so-called K-logic (named after influential 20th century philosopher Saul Kripke), which is a compound logical system made of propositional logic, a necessitation rule (using the operator “it is necessary that”) and a distribution axiom. A stronger system, called M, is built by adding the axiom that whatever is necessary is the case, and this in turn yields an entire family of modal logics with different characteristics. Starting again with K-logic, one can also begin to build a deontic logic by adding an axiom that states that if x is obligatory, then x is permissible. Similarly, one can build temporal logics (with the details depending on one’s assumptions about the structure of time) and other types of modal logics. Indeed, Garson (2009) presents an elegant “map” of the relationships among a number of modal logics, demonstrating how they can all be built from K by adding different axioms. Furthermore, Lemmon and Scott (1977) have shown that there is a general parameter (G) from the specific values of which one can derive many (though not all) the axioms of modal logic. Garson’s connectivity map  and Lemmon and Scott’s G parameter are both, well, highly logical, and aesthetically very pleasing, at the least if you happen to have a developed aesthetic sensibility about logical matters. (Notice, once again, that these are all nice examples of non-teleonomic progress propelled by internally generated problems and consisting in exploring additional possibilities in a broad conceptual space that is evoked once one adds axioms or assumptions.)

A major issue with modal logic is that — unlike classical logic (Benthem 1983) — it is not possible to use truth tables to check the validity of an argument, for the simple reason that nobody has been able to come up with truth tables for expressions of the type “it is necessary that” and the like. The accepted solution to this problem (Garson 2009) is the use of possible worlds semantics (Copeland 2002), where truth values are assigned for each possible world in a given set W. Which implies that the same proposition may be true in world W1, say, but false in world W2. Of course one then has to specify whether W2, in this example, is correctly related to W1 and why. This is the sort of problem that has kept modal logicians occupied for some time, as you might imagine. Modal logic has a number of direct philosophical applications, as in the case of deontic logic (McNamara 2010), which deals with crucial notions in moral reasoning, such as permissible / impermissible, obligatory / optional, and so forth. Deontic logic has roots that go all the way back to the 14th century, although it became a formal branch of symbolic logic in the 20th century. As mentioned, deontic logic can be described in terms of Kripke-style possible worlds semantics, which allows formalized reasoning in metaethics (Fisher 2011).

Of particular interest, but for different reasons, are also the next two entries in our little catalog: many-valued and “fuzzy” logics. The term many-valued logic actually refers to a group of non-classical logics that does not restrict truth values to two possibilities (true or false; see Gottwald 2009). There are several types of many-valued logics, including perhaps most famously Łukasiewicz’s and Gödel’s. Some of these admit of a finite number of truth values, others of an infinite one. The Dunn/Belnap’s 4-valued system, for instance, has applications in both computer science and relevance logic. Multi-valued logic also presents aspects that reflect back on philosophical problems, as in the area of concepts of truth (Blackburn and Simmons 1999), or in the treatment of certain paradoxes (Beall 2003), like the heap and bald man ones. More practical applications are found in areas such as linguistics, hardware design and artificial intelligence (e.g., for the development of expert systems), as well as in mathematics. Fuzzy logic is nested within many-valued logics (Zadeh 1988; Hajek 2010), consisting of an approach that makes possible to analyze vagueness in both natural language (about degrees of beauty, age, etc.) and mathematics. The basic idea is that acceptable truth values range across the real interval [0,1], rather than lying only at the extremes (0 or 1) of that interval, as in classical logic. Fuzzy logic deals better than two-valued logic with the sort of problems raised by Sorites paradox, since these problems are generated in situations in which small/large, or many/few quantifiers are used, rather than simple binary choices. Therefore, fuzzy logic admits of things being almost true, rather than true, and it is for this reason that some authors have proposed that fuzzy logic can be thought of as a logic of vague notions.

A whole different way of thinking is afforded by so-called intuitionistic logic (Moschovakis 2010), which treats logic as a part of mathematics (as opposed to being foundational to it, as in the old Russell-Whitehead approach that we have discussed above), and — unlike mathematical Platonism (Linnebo 2011) — sees mathematical objects as mind-dependent constructs. Important steps in the development of intuitionistic logic were Gödel’s (who, ironically, was a mathematical Platonist!) proof (in 1933) that it is as consistent as classical logic, and Kripke’s formulation (in 1965) of a version of possible-worlds semantics that makes intuitionistic logic both complete and correct. Essentially, though, intuitionistic logic is Aristotelian logic without the (much contested) law of the excluded middle, which was developed for finite sets but was then extended without argument to the case of infinities.

Finally, a couple of words on what some consider the cutting edge, and some a wrong turn, in contemporary logic scholarship: paraconsistent and relevance logics. Paraconsistent logic is designed to deal with what in the context of classical logic are regarded as paradoxes (B. Brown 2002; Priest 2009). A paraconsistent logic is defined as one whose logical relations are not “explosive,” [12] with the classical candidate for treatment being the liar paradox: “This sentence is not true.” The paraconsistent approach is tightly connected to a general view known as dialethism (Priest et al. 2004), which is the idea that — contra popular wisdom — there are true contradictions, as oxymoronic as the phrase may sound. Paraconsistent logic, perhaps surprisingly, is not just of theoretical interest, as it turns out to have applications in automated reasoning: since computer databases will inevitably include inconsistent information (for instance because of error inputs), paraconsistent logic can be deployed to avoid wrong answers based on hidden contradictions. Similarly, paraconsistent logic can be deployed in the (not infrequent) cases in which people hold to inconsistent sets of beliefs, sometimes even rationally so (in the sense of instrumental rationality). More controversially, proponents of paraconsistent logic argue that it may allow us to bypass the constraints on arithmetic imposed by Gödel’s theorems. How does this work? One approach is known as “adaptive logic,” which begins with the idea that consistency is the norm, unless proven otherwise, or alternatively that consistency should be the first approach to a given sentence, with the alternative (inconsistency) being left as a last resort. That is to say, classical logic should be respected whenever possible. Paraconsistent logics can be generated using many-valued logic, as shown by Asenjo (1966), and the simplest way to do this is to allow a third truth value (besides true and false), referred to as “indeterminate” (i.e., neither true nor false).

Yet another approach within the increasingly large family of paraconsistent logics it to adopt a form of relevance logic (Mares 2012), whereby one stipulates that the conclusion of a given instance of reasoning must be relevant to the premises, which is one way to block possible logical explosions. According to relevance logicians what generates apparent paradoxes is that the antecedent is irrelevant to the consequent, as in: “The moon is made of green cheese. Therefore, either it is raining in Ecuador now or it is not,” which is a valid inference in classical logic (I know, it takes a minute to get used to this). The typical objection to relevance logic is that logic is supposed to be about the form, not the content, of reasoning — as we have seen when briefly examining the history of both Western and Eastern logic — and that by invoking the notion of “relevance” (which is surprisingly hard to cash out, incidentally) one is shifting the focus at least in part to content. Mares (1997), however, suggests that a better way to think about relevance logic comes with the realization that a given world X (within the context of Kripe-style many worlds) contains informational links, such as laws of nature, causal principles, etc. It is these causal links, then, that are deployed by relevance logicians in order to flesh out the notion of relevance (in a given world or set of possible worlds) — perhaps reminiscent of Dharmakīrti’s invoking of causal relations to assure the truth of a first premiss, as we have discussed. Interestingly, some approaches to relevance logic (e.g., Priest 2008) can be deployed to describe the difference between a logic that applies to our world vs a logic that applies to a science fictional world (where, for instance, the laws of nature might be different), but relevance logic has a number of more practical applications too, including in mathematics, where it is used in attempts at developing mathematical approaches that are not set theoretical, as well as in the derivation of deontic logics, and in computer science (development of linear logic).

So, what do we get from the above historical and contemporary overviews of logic, with respect to how the field makes progress? The answer is, I maintain, significantly different from what we saw for the natural sciences in Chapter 4, but not too dissimilar from the one that emerged in the first part of this chapter in the case of mathematics. Logicians explore more and more areas of the conceptual space of their own discipline. Beginning, for instance, with classical two-valued logic it was only a matter of time before people started to consider three-valued and then multi-valued, and finally infinitely-valued (such as fuzzy) types of logical systems. Naturally enough, this progress was far from linear, with some historians of logic identifying three moments of vigorous activity during the history of Western logic, with the much maligned Middle Ages not devoid of interesting developments in the field. Other signs of progress can readily be seen in the expansion of the concerns of logicians, beginning with Aristotelian syllogisms or similar constructs (as in the parallel developments of the Stoics) and eventually exploding in the variety of contemporary approaches, including deontic, temporal, doxastic logics and the like. Even dialethism and the accompanying paraconsistent and relevance logics can be taken as further explorations of a broad territory that began to be mapped by the ancient Greeks: once you chew for a while (in this case, a very long while!) on the fact that classical logic can yield explosions and paradoxes, you might try somewhat radical alternatives, like biting the bullet and treating some paradoxes as “true,” or pushing for the need for a three-valued approach when considering paradoxes. As in the case of mathematics, there have been plenty of practical (i.e., empirical) applications of logic, which in themselves would justify the notion that the field has progressed. But in both mathematics and logic I don’t think the empirical aspect is quite as crucial as in the natural sciences. In science there is a good argument to be made that if theory loses contact with the empirical world (Baggott 2013) then it is essentially not science any longer. But in mathematics and logic that contact is entirely optional as far as any assessment of whether those fields have been making progress by the light of their own internal standards and how well they have tackled the problems that their own practitioners set out to resolve.

What about philosophy, then? It is finally to that field that I turn next, examining a number of examples of what I think clearly constitutes progress in philosophical inquiry. As we shall see, however, the terrain is more complex and perilous. More complex because while philosophy is very much a type of conceptual activity, sharing in this with mathematics and logic, it also depends on input from the empirical world, both in terms of commonsense and of scientific knowledge. More perilous because a relatively easy case could be made that a significant portion of philosophical meanderings aren’t really progressive, and some even smack of mystical nonsense. Unfortunately, this sort of pseudo-philosophy does appear in the philosophical literature, side by side with the serious stuff, and occasionally is even the result of the writings of the same authors! Nothing like that appears to be happening either in science or in mathematics and logic, which I believe is a major reason why philosophy keeps struggling to be taken seriously in the modern academic world.


[12] A logical explosion is a situation where everything follows from a contradiction, which is possible within the standard setup of classical logic.


Asenjo, F.G. (1966) A Calculus of Antinomies. Notre Dame Journal of Formal Logic 7:103-105.

Baggott, J. (2013) Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth. Pegasus.

Beall, J.C. (ed.) (2003) Liars and Heaps. Clarendon Press.

Benthem, J.F. van (1983) Modal Logic and Classical Logic Bibliopolis.

Blackburn, S. and Simmons, K. (eds.) (1999) Truth. Oxford University Press.

Brown, B. (2002) On Paraconsistency. In: D. Jacquette (ed.), A Companion to Philosophical Logic, Blackwell, pp. 628-650.

Copeland, B.J. (2002) The genesis of possible worlds semantics. Journal of Philosophical Logic 31:99-137.

Fisher, A. (2011) Metaethics: An Introduction. Acumen Publishing.

Garson, J. (2009) Modal Logic. Stanford Encyclopedia of Philosophy (accessed on 31 May 2013).

Gottwald, S. (2009) Many-valued logic. Stanford Encyclopedia of Philosophy (accessed on 22 August 2013).

Hajek, P. (2010) Fuzzy logic. Stanford Encyclopedia of Philosophy (accessed on 30 March 2011).

Hilpinen, R. (1971) Deontic Logic: Introductory and Systematic Readings D. Reidel.

Lemmon, E. and Scott, D. (1977) An Introduction to Modal Logic. Blackwell.

Linnebo, Ø. (2011) Platonism in the philosophy of mathematics. Stanford Encyclopedia of Philosophy  (accessed on 11 October 2012).

Mares, E.D. (1997) Relevant Logic and the Theory of Information. Synthese 109:345–360.

Mares, E. (2012) Relevance logic. Stanford Encyclopedia of Philosophy (accessed on 28 August 2013).

McNamara, P. (2010) Deontic logic. Stanford Encyclopedia of Philosophy (accessed on 22 August 2013).

Moschovakis, J. (2010) Intuitionistic logic. Stanford Encyclopedia of Philosophy (accessed on 22 August 2013).

Nolt, J. (1996) Logics. Cengage Learning.

Priest, G. (2008) An Introduction to Non-Classical Logic: From If to Is. University of Cambridge Press.

Priest, G. (2009) Paraconsistent logic. Stanford Encyclopedia of Philosophy (accessed on 14 September 2012).

Priest, G., Beall, J.C. and Armour-Garb, B. (eds.) (2004) The Law of Non-Contradiction. Oxford University Press.

Zadeh, L.A. (1988) Fuzzy logic. Computer 21:83-93.

135 thoughts on “Progress in Mathematics and Logic — IV

  1. Alan White

    I have to sign on with Kaufman (Dan, if I may?) about the 1st CI and the GR. Willing that a maxim elevate to logically consistent universal law is far different from doing to others what you would have done to you. The first depends only on an appreciation of the logical quality of universalization of the concepts involved in the maxim. The second depends upon the particular desires or ideology of the individual. Kant would no doubt say libertarian-type selfishness could not be consistently universalized. But I can imagine someone accepting that watching out for oneself is prescriptively wise even if others doing so might hurt you in some instances.

    Liked by 2 people

  2. garthdaisy


    “The second depends upon the particular desires or ideology of the individual.”

    So does the first. The desire to be logically consistent. This is the point Kant was missing. Everything he said about morality was a consequence of his desire to live in a moral world. And contrary to Daniel Kaufman’s assertion, what we know today about human nature is very much relevant and helpful to figuring all of this out.


  3. garthdaisy


    “They do not come from the same intuition, nor do they say the same thing. Not even close. The appearance of similarity is entirely superficial.”

    “Also, “our current scientific knowledge of human nature” has nothing to do with it.”

    You keep making these statements of certainty without offering any data or arguments. I have noticed in the past that just because a philosophy professor says something about philosophy, it doesn’t mean they are correct. It would be helpful to the discussion if you could muster up more than just to quote someone and state that their comment is categorically false, “fundamentally flawed,” or “entirely irrelevant.”

    Why and how is it fundamentally flawed, categorically false, or entirely irrelevant?

    Liked by 1 person

  4. synred

    I’m sorry I chose Kant and his ‘categorical imperative’ as an example of something that might not exist w/o the particular philosopher to be contracted with Newton’s work on color recombination which somebody was bound to figure out sooner or later.

    I did not intend to start a discussion of Kant, but to address one of the possible differences between progress in philosophy and science, i.e., the topic of Massimo’s book.

    Kant was just the name of a philosopher that sprang to mind, that I can spell :_).

    Liked by 2 people

  5. Daniel Kaufman


    Alan is absolutely correct in hist account of the difference between the CI and the GR. And no, Kant’s CI is not motivated by “the desire to be logically consistent.” Nor is empirical knowledge of “human nature” (if there is such a thing, which I doubt) relevant to Kant’s conception of duty. Indeed, the entire opening of the Groundwork is devoted to a discussion of why moral obligation cannot be grounded in contingent, a posteriori knowledge.

    Your surrounding comments about what you’ve “noticed in the past” is a good part of the reason why I am not engaging more in the discussion, as it is reflective of the attitude of many here. At this point, I only weigh in when I see real howlers and am worried that others may be mis-educated on an important philosophical subject, but I do not stick around and debate the issues back and forth. People are free to make of it what they will or ignore it. And for some, at least, the fact that I have been teaching these subjects at the university for over twenty years does provide a reason to perk their ears up and check out what I’ve “asserted” for themselves.


  6. Daniel Kaufman

    Massimo, I disagree with you, entirely, about CI and the Golden Rule. The wide difference between the two is stated very nicely, here, by Stephen Daniel, from Texas A&M:

    “Note how Kant’s Categorical Imperative is different from the Golden Rule (“Do unto others as you would have them to unto you”): it is not based on what you want but on what is necessary for any being to act rationally (that is, universally, without consideration of his/her own self-interest)”

    The categorical imperative — indeed, moral duty in general — describe the basic conditions of rational personhood. It has nothing to do with reciprocity or charity or anything else that might tie it to the GR. Indeed, it is precisely that sort of misreading of the CR that I was first warned against, when taught the Groundwork as an undergraduate, at Michigan. (I actually think it was Steven Darwall who said it, but I can’t remember for sure.)

    Liked by 1 person

  7. garthdaisy


    As I said I think the Kant example is no different than any other philosophy in this regard. I think all philosophy past was inevitable, and all philosophy future is inevitable. It all comes from the human brain and human curiosity and human desires, and we humans are embarrassingly almost exactly like each other. 99.9% identical. And that tiny differential is mostly in personality differences not our base intuitions, desires, and cognitive abilities. Yes some people are smarter, and some are more compassionate, and some are more strict but to very small degrees. I don’t think there are people so special out there who are coming up with philosophical ideas that no one else would or ever could come up with. The homo sapiens brain was eventually going to come up with all of this stuff.

    Art is different however. I think because it’s intention is not towards consensus forming.


  8. Daniel Kaufman

    One last thing:

    I am speaking entirely about how best to understand the CI in the context of Kant’s moral philosophy. I am *not* making any claims about the historical Kant, his personal motivations, or what he personally thought about the GR. Kant, of course, was from a Pietist family and there are any number of Christian influences that affected him and his work. (I want to say that somewhere in the Critique of Practical Reason, he says that the CI is consistent with the GR).

    So, I am doing moral philosophy, when I speak here of the CI and it’s interpretation, not Kant biography. And one of the first things you learn as an undergraduate, when you study the Groundwork, is how the superficial similarities of the CI and GR can be dangerously misleading in understanding the former.


  9. garthdaisy


    “The categorical imperative — indeed, moral duty in general — describe the basic conditions of rational personhood.”

    To achieve “rational personhood” is a desire. Otherwise why bother? The theory could only be conceived to satisfy that desire. But I can understand why someone who believes that natural selection, modern psychology, and neuroscience, reveal nothing about human nature that is relevant to moral philosophy would not be swayed by such arguments.


  10. garthdaisy


    “is how the superficial similarities of the CI and GR can be dangerously misleading in understanding the former.”

    “Dangerously?” Misleading maybe, but if the professors who taught you were using the hyperbole “dangerously misleading” I would be suspicious of their motives.


  11. synred

    Well that’s the issue. I’m not trying to answer it, just ask (in perhaps my overly concrete style).

    Philosopher’s might come up with every possible idea sooner or later, but how do we tell who’s right?

    Nobody agrees even with each other!


  12. brodix

    Doesn’t the categorical imperative presume the ideal as absolute?

    One would be the epitome and the other would be the essence.

    If the ideal were absolute, wouldn’t we already be living in a perfect world?


  13. Alan White

    Free will for Kant only had two masters–reason or desire, and he regarded them as exclusive. Thus the absolutism that submerges individual desires to moral oblivion, If one is a reasoning being, then one subscribes to the logical rigors of reason or one elects to follow desires–there’s the foundation of ultimate responsibility given that one knows the difference. And one should know the difference once one understands the CI. There is no desire to reason for Kant–being subject to reason is the very rejection of desire.

    Liked by 2 people

  14. synred

    So is use of analogy and metaphor something philosophy can sort out for us definitively?


    This kind of conflict—where opposing armies mass on either side of a seemingly clear and intractable boundary—can be resolved by philosophy, whose role is to detect and expose the confusions and ambiguities that make such boundaries seem intractable in the first place. In the case of metaphors in science, a philosopher would instinctively point out that not all metaphors work in the same way, or for the same reason. Metaphors in science, in fact, work in at least three different ways.

    Crease, Robert. The Prism and the Pendulum: The Ten Most Beautiful Experiments in Science (p. 117). Random House Publishing Group. Kindle Edition.

    This discussion is about Young’s discovery of the wave nature of light which he is said to have done using ‘analogy’ to water-sound waves. It’s not clear that Young thought of it as analogy; he was a very laconic sort of guy.

    I don’t think anybody would call water vs. sound waves an analogy, so I don’t see why we’d call electromagnetic waves as anything but waves in different stuff (electromagnetic-field).

    Yet people, even scientist, seem to argue about this too.

    Philosophers might object to the very narrow role assigned to them by Crease, but still it’s a role and may be one where progress could (has) occurred.


  15. Daniel Kaufman

    garth: I’m simply telling you what Kant’s view actually is. You can think whatever you like about the relevance of desire, natural selection, so-called “human nature”, etc. I am simply talking about what *Kant’s* views are.


  16. brodix


    It seems an elemental form of dualism; Mind=reason, versus body=desire.

    In other threads, I’ve argued reality is also a basic dualism, between energy and form and one of the arguments I put forward for this, is that over billions of years of evolution, we evolved a central nervous system to process form/information and the digestive, respiratory and circulatory systems to process the energy. Mind/body=information/energy

    The essential difference is that as energy is conserved and constantly changing form, the arrow of time for energy is past to future form, while the arrow of time for form is future to past, as it comes into being and dissolves. So our body moves from prior to succeeding events, while our mind is recording and analyzing these events, as they either coalesce into stable memory, or disperse.

    So is reason inherently moral and desire inherently amoral? I don’t see it.

    Conscious reason is to distill form, structure, patterns, efficiencies, etc. from the world around us, in order to survive. There is an inherent and overwhelming tendency to view that which is beneficial to our sense of identity, be it of the individual, the group, the profession, the nation, the ideology, the religion, etc. as a moral good and that which is negative, as bad. Meanwhile the desires; for sustenance, procreation, security, contentment, etc, are not really distinct from our rational motivations, just more intuitional.

    The problem is that while the mind tends to be quite cognizant of the body’s limits, it is often in denial of its own. For one thing, the mind naturally considers itself as broadly dispersed over a wide area of knowledge, while it perceives the body as a small, finite, mortal and fairly utilitarian hunk of protoplasm, whose seeming function is to carry the mind. Yet it could legitimately be argued the opposite is true. The body exists as a product of a long and diverse process that is integrated into and an expression of a much larger culture and environment, much of it at a subconscious level. While the mind has a fairly limited function as executive decision making process and has to frequently ignore that much broader range of input, in order not to be too distracted from the subject matter at hand.

    While Kant may seek to avoid being specifically theistic, his premises seem to be based on the assumption of a societal ideal as a moral absolute, to be discovered through reason, rather than a theological absolute, to be experienced and/or deified.

    Yet an ideal would be a goal to be sought, irrespective of the context, while an absolute would be an elemental state, with no delineation, thus good or bad.


  17. Alan White


    Forgive me for further taking this thread off-topic. Let me say again that your OP was a wonderful overview of the evolution of logic.

    As to Kant and the CI. Perhaps most strongly in reaction to Hume, Kant clearly wishes to logicize morality. (Not unlike Bentham motivationally. Except Kant wished to go a priori, and Bentham more empirically and scientifically.) That clearly stands behind the 1st CI, though I think the 2nd CI is not in fact logically equivalent to the 1st. But clearly Kant wants to make morality merely a function of pure reason in the 1st CI, and reason allied with free will (incompatibilist) makes the ultimate choice between following reason or contrary desire–good versus evil. Thus absolutism.

    Liked by 1 person

  18. garthdaisy


    “I’m simply telling you what Kant’s view actually is.”

    I know what Kant’s view actually is. When I said it was a rip-off of the golden rule, obviously I don’t think that’s what Kant’s view is. I know Kant didn’t think he was ripping off the GR. It’s my view that the instinct that inspired the GR is part of human nature, and unbeknownst to Kant, influenced his CI. But he thought it came from his pure reason. He thought he had found a way to outthink his desire. But we know better today. At least those of us who don’t put a “so called” in front of human nature. That certainly says everything about why we disagree, and I can tell I’m not going to convince you that human nature exists here so we’ll have to agree to disagree I think.

    Liked by 1 person

  19. Massimo Post author


    Yes, I know you are right in terms of strict philosophy to differentiate the CI from the GR, exactly along the lines you do.

    But as you point out, there are other aspects to the question, such as the biographical one of what Kant was trying to do. Seen from that perspective, the genealogical connection between the GR and the CI is obvious.


    That said, I would agree with Dan that knowledge of human nature doesn’t enter into Kant’s picture of the CI, for precisely the reasons he stated.

    Liked by 1 person

  20. garthdaisy

    Alan White

    ” If one is a reasoning being, then one subscribes to the logical rigors of reason or one elects to follow desires–there’s the foundation of ultimate responsibility given that one knows the difference.”

    But we know better than that now. Mountains of evidence show that our reasoning is almost always acting as a shifty lawyer for our emotions and desires. Even Kant would have changed his mind after seeing these compelling studies and with the benefit of knowing about evolution by natural selection.

    Liked by 1 person

  21. Robin Herbert

    Hi garthdaisy,

    But we know better than that now. Mountains of evidence show that our reasoning is almost always acting as a shifty lawyer for our emotions and desires.

    I am not sure who didn’t know that or when at what time in history that would have been a surprise. It seems to be a main theme in works by people like Shakespeare, Chaucer etc.I guess if I was more familiar with classical literature I would probably find that theme even farther back.

    But I think that the fond hope of philosophy is that we can sometimes transcend that.

    Liked by 1 person

  22. brodix


    Not that they are not worthy areas of study, but occasionally what is necessarily lost in studying the details, is a sense of the broader context, that might well be shaping those details. Just as with a view of the bigger picture, much of the detail is lost. There is no objective point of view.


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