Over at Heideggarian Denken Kevin is having a discussion about whether logic is fundamental. (Primarily in the comments) I confess to having a very difficult time wrapping my mind around this question. It seems somewhat a category mistake. It is one thing to say that logic is accurate in the sense of providing true results. It's quite an other to make it the basis of a metaphysics. But I'm sure this is just me missing what folks are trying to say. However I did think it would be useful to provide this quote by Peirce on logic.
Philosophers have always been very loose and inaccurate thinkers; and since Fechner's immortal publication of 1860 their minds have been so turned in the direction of psychology that when they have once found how any given element of thought affects the human consciousness, they feel as if they had touched bedrock and had got to the bottom of that element. But psychology is as special a science as physics is. It is the glory of the post-Fechnerian psychologists that they have made it so. Now to found the science of the general upon the science of the mind is absurd.
Logic is no doubt a science of "thought"; but "thought," in that sense, is no more internal than it is external. Logic is the science of truth and falsity. But truth and falsity belong as much to propositions printed in books as to propositions in the human consciousness. The fact that a proposition is conscious or unconscious does not affect its truth or falsity.
But it may be said that logic is the theory of reasoning, and that reasoning can only be performed by a mind. That is certainly true, and must be true; for if anything could independently reason, it would be what we understand by a mind. But it does not follow that the phenomena that psychologists discover have any bearing upon the theory of reasoning. (EP 2:385)
Logic, says Herbart, psychologist though he was, is a science of concepts; but a concept is that which is conceived; so that logic is a science of the result of conceiving and has nothing to do with the means whereby the conceiving is performed. In these remarks of Herbart's, thought and thinking might be substituted for concept and conceiving. A concept is a symbol present to the imagination, - that is, more correctly speaking, of which a particular instance might be present to the imagination. But the imaginary character of the instance of the symbol has no importance for logic. Its rules hold equally for the symbol embodied in real existents. For it is with the symbol in its general mode of being and not with the individual embodiment of it with which logic has to do. The writer, in 1867, defined logic as the science of the formal lows of the relation of symbols to their objects. But a more mature consideration of the nature of the limits between the different branches of science has convinced him that it is better to regard logic as the entire cenoscopic study of symbols, and not only of symbols but all kinds of signs. It will be felt as a great objection to this view that a sign is not such unless it be interpreted and that it can only be interpreted by the human mind. The reply is that just as physiology explains all the operations of the animal organism purely and exclusively by the principles of general physics . . . so all the operations of reason can receive perfect logical explanation by principles which apply as much to real signs as to the imaginary signs called concepts. . . (EP 2:386)
I rather liked those quotes when I happened upon them. They're from Peirce's The Basis of Pragmaticism in the Normative Sciences. Note how Peirce presupposes an externalist view of mind rather than an internalist one (with its particular view of correspondence and representation) Also note how Peirce extends logic into general semiotics: the science of signs. One should finally note Peirce's anti-pschologizing, a concern that also inspired Husserl's phenomenology.
One bit of explanation is in order. The word cenoscopic is from Jeremy Bentham and is generally an opposition between it and idioscopy. The issue is the divisions of philosophy. This is roughly akin to the notion in Kant we discussed last week. Since it is relevant to what we're discussing and also related to that notion of "two philosophies" I'll quote a section of Peirce on it. This is from earlier in the same paper quoted above.
Two meanings of the term "philosophy" call for our particular notice. The two meanings agree in making philosophical knowledge positive, that is in making it a knowledge of things real, in opposition to mathematical knowledge, which is a knowledge of the consequences of arbitrary hypotheses; and they further agree in making philosophical truth extremely general. But in other respects they differ as widely as they well could. For one of them, which is better entitled (except by usage) to being distinguished as philosophia prima than is ontology, embraces all that positive science which rests upon familiar experience and does not search out occult or rare phenomena; while the other, which has been called philosophia ultima, embraces all that truth which is derivable by collating the results of the different special sciences, but which is too broad to be perfectly established by any one of them. The former is well named by Jeremy Bentham's term cenoscopy (κοινοσκοπια, the lookout upon the common), the latter goes by the name of synthetic philosophy. Widely different as the two science are, they are frequently confounded and intertangled; and when they are distinguished the question is often asked, "Which of these is the true philosophy?" as if an appreciation of one necessarily involved a depreciation of the other. In the writer's opinion each is an important study. Cenoscopy should be that department of heuretic science which stands next after Mathematics, and before Idioscopy, or special science; while Sythentic Philosophy, the subject upon which Francis Bacon, Auguste Comte, William Whewell, and Herbert Spencer have left us admirable works in their several ways, stands at teh head of the Retrospective Sciences. (EP 2:372-3)
It would be interesting to write a feminist analysis of logic as the science of what is 'conceived' independently of the act of 'conception'.
Alex,
is that a joke or are you serious?
I think C.S. Peirce is using a pre-modern sense of logic in those quotes. Logic in the modern sense has little or nothing to do per se with semiology or ontology. It is all about consistency. Now semantic problems can level an argument, but that has nothing to do with logic as such, it has to do with metaphysics.
I agree with Clark that to place logic in metaphysics is to make a category mistake. The metaphysics of reality do constrain the applicability of various modes of argumentation. Logic is useless in our world, if "our world" is a misnomer. That has nothing to do with the validity of logic in and of itself, however, just the reality of the world we find ourselves in, however particular or universal.
If logic is invalid, then perception, language, and thought are equally suspect. It would be more accurate to say we do not exist.
It seems rather difficult to talk about whether or not logic is invalid, because in order to do so, you have to make an argument that logic is invalid -- but if logic is invalid, then the argument that logic is invalid is also invalid.
The argument isn't whether logic is invalid but whether it is fundamental. It seems to me the real argument is over the nature of logic. I think to characterize it otherwise (as is unfortunately often done) can be misleading.
Put an other way, what is the relationship between metaphysics and logic. And what (if anything) grounds logic. For Peirce as I recall logic is grounded on ethics. That's because clearly logic is a kind of analysis of what should happen. i.e. what is just reasoning. That in turn is grounded on aesthetics.
For Heidegger (and I suspect Derrida) things are a tad more complex. But the clearest explanation there is Heidegger's "deconstruction" of Leibniz in The Metaphysical Foundations of Logic. Since debates about logic almost always hinge upon the law of the excluded middle it is an interesting text. I should note that I think the ultimate issue is vagueness (in the Peircean sense).
I wanted to add, on the 'feminism' comment, that I was, a la Kraus, half-serious or serious and a half: take a philosophical work, a major term in that work, and a contemporary synonym for that term that has certain interesting implications. Now systematically substitute the one meaning for the other in all interpretation of the work and see what emerges. It is a bit of a trick but I think it can still be carried out rigorously and with interesting effects.
To add to the original point. If we make a Nietzschean move and discuss issues of power-relations (which I suspect is what you mean by a "feminist" critique unless you simply mean the metaphor of womb and phallus) then we are likewise tied up in the question of ethics and aesthetics.
The all too common error I see people who make appeal to power making is that they assume power is something they control. That is in purporting to critique power they really just adopt a rhetoric wherein they think they can master power. This is very much opposed to Derrida's project and it almost always silly and naive. You can't control Being and that theory of technological mastery is underlying a lot of writings that purport to be in the line of Heidegger or Derrida.
Put more clearly, most phenomena we deal with are open to logical analysis and people critiquing this (as many feminists have done) simply come off looking like sollipsists or relativists or just plain ignorant. This is unfortunately why Derrida gets brushed so unfairly since his name gets associated with those doing this far more than is deserved.
One last point. I think Derrida, especially after his Levinasian turn, also ties logic (or logocentrism) with both aesthetics and ethics (justice). The reasons for this are pretty clear when one reads Heidegger. As I've said I'm not at all convinced Derrida is that original. But it is much more explicit in Derrida and he often brings to focus things that are minor or easily overlooked in a general "thought" of Heidegger.
So in all this justice is at play.
Well I don't have much to add myself in response, but I would like to mention someone recently wrote a book called "Before Logic" that seemed to me like it must tackle quite a few of these issues (I was browsing it at Powell's).
I think logic and ontology are much further separated than logic and ontology. Ethics is all about what should be, Logic is all about what cannot be otherwise. So unless you adopt a determinism that equivocates between Goodness and Necessity in one way or another they are at opposite ends of the spectrum.
"I think logic and ontology are much further separated than logic and ontology."
Huh? Did you mean one of those uses of ontology to be ethics?
Just to add, I think the point all the figures we're discussing would make is that logic presupposes what is and what is isn't necessarily necessary. So I don't think your critique regarding ethics and openness is correct. Further when one is engaging in logical reasoning one can make mistakes. So the ethics is at play there.
That is you are conflating the process of logic with the aim of logic.
Yes. My apologies -"logic and ethics". The idea that logic has an aim is subjectivist in the extreme. We can use logic, synthesize representations of logic, but logic in and of itself doesn't have a purpose, any more than 1+1=2 has a purpose. The only purpose logic has is what we can successfully impose upon it, and I do not see ethics so much as a consequence of logic, as a consequence of metaphysics of personal Being.
Logic is beyond fundamental - nothing can properly be said to be a consequence of logic because a world without logic cannot be conceived. But an a-moral world, without good nor evil, is trivial to be thought of. Many of the luminaries in the modern era consider morality to be an accident, from Nietzche to Singer.
The question for Singer and other evolutionary psychologists is why should a tiny assembly of prebiotic particles "care" whether it lives or dies? If Singer is right, we should fear for our computers, as surely the tipping point into consciousness is right around the corner. Second rate science fiction, worse science.
You might say I am a meta-Platonist with regard to logic and mathematics. Analytic truth doesn't have an aim, its applicability to the real world is a function of mapping of axioms to metaphysical realities. I don't think anything absolute has an aim. Only wills (intelligences) have aims.
And logic, properly speaking, is that which is independent of both will and metaphysics. Neither man nor God can make 1+1=3, in the proper sense of those terms. Once we have identified a proper set of axioms, we can explore the vast world of theorems to our hearts delight, but not change them one iota.
Neither will changing our set of axioms have any affect on the real world - all axioms are either valid or invalid in the context of any real world application. A wrong identification of the applicable axioms will be born out by self or world contradiction.
I'm not a logicist in the sense that I think mathematics can be reduced to logic. As to my view of logic these quotes of Peirce on Logic are probably apt.
Please excuse me gentlemen. IÕve never participated in a discussion of this sort (primarily because my knowledge of philosophy is so shallow). However, it seems to me that logic (reason) cannot be foundational because it is a process. Biologically speaking, logic is a problem solving process that the mind/brain uses primarily for survival. And what is true for the great processor, the computer, holds true for logic: garbage in garbage out. The problem logic or reason starts with is always affective in nature. If you begin with the problem: Jews are sucking the life blood out of German society. Logic will lead you to the ovens in Auschwitz. Greater intelligence will only create more effective ovens. Under these circumstances, affect is foundational not logic or reason. Given this, I suppose affect would be similar to PierceÕs ethics.
I agree that there is a sense that logic is a process. However logic as process only satisifies its own claims if its conclusions are unavoidable given the premises. Any conclusion of logic that is not an inevitable, determinate function of its premises, is not logic in the modern sense.
And indeed if a conclusion is arguably faulty, it is much more likely to be a problem with the premises or the metaphysics of terms, not the logic per se. Logical errors as such are much rarer than metaphysical errors. That is why philosophy is important - to identify errors and inconsistencies in metaphysics. The logicians can do logic just fine, once the metaphysics are in place - indeed the main disputes in logic are about metaphysics - meaning and applicability, not procedure. The "Law" of the Excluded Middle (LEM) is not a procedural dispute, it is a metaphysical dispute.
By the way, the argument you (Rich) describe, is faulty in its premises, and in its application. Neither is rational by any means or axioms acceptable to civilized peoples. There are some seriously noxious unspoken assumptions in there. Logic is hardly to blame - the contemporary cult of irrationality is a much more likely culprit than careful analysis.
I wouldn't say mathematics can be reduced to classical logic either. However I would say that for all intents and purposes, mathematics is a kind of logic, i.e. in its application it maps to metaphysics, truth, and reality in the same way conventional logic does, we just call the mapping "science" instead of "applied logic".
By the way, I do not think the rejection of the LEM entails mathematical anti-realism as so many intuitionists (notably Dummett) seem to imply, just a different sort of realism, a non-Aristotelian semantics of being. I see this error repeated in other contexts all the time.
A couple of brief thoughts. I had a great Peirce quote but I left it at home by accident. So you'll have to await on that.
Second we should perhaps clarify that we aren't just talking about logic broadly but what one perhaps ought call deductive logic. Peirce would argue there are two other logics: inductive and abductive Second we aren't talking about logic with vague entities (which can't have the law of excluded middle).
Finally while logic (and math) are human processes the question is the laws that guarantee truth. That is logic is a science that studies the laws regarding signs to their objects. So to a degree I agree with Mark in that we have to have that guarantee of truth. (At least in deductive logic)
The reason ethics come in is because there is no reason when we engage in thinking logically that we'll follow these laws. Thus, as Peirce says, we have to engage in careful and intense self-control so as to voluntarily follow these laws in our thought for our thinking process to be logical. But that's basically just a subset of ethical behavior. (That is conducting oneself voluntarily to a law)
I don't know how I feel about calling logic "ethical". If you read Fraenkel's "On Bullshit" for instance, he certainly comes across as recommending those discourses that produce claims that are true or false and hence a method of discourse (I assume logical) that would preserve truth or falsity. But I think that there's a very different sense in saying to someone, "You are wrong" regarding a problem of mathematics vs. an action. It might be a difference in the justification of the statement -- what is peculiar regarding ethical errors is the demonstration required to show that a decision was in error.
Alex
The axioms and theorems of deductive logic can easily be conceived to have mind independent existence, like mathematics. Abduction is more a matter of intuition / inspiration. Induction is pretty pointless separated from mind as well.
Also, while surely ethics requires one to be logical, it is hard so see why logic per se requires one to be ethical. Ethics is founded in metaphysical principles beyond the dictates of logic. Logic is all about relational constraints on what must be, where ethics is about what should be. If ethics were determinist we would have little reason to concern ourselves with the subject at all. The same might be said of science.
"If ethics were determinist we would have little reason to concern ourselves with the subject at all..."
But isn't ethics determinist in that it determines what we ought to do? Assuming an ethics based on some notion of free will, we have the freedom to choose between right and wrong, but we are constrained by that very freedom to choose what's right (it's the Kantian dilemma...I'm not sure if I'm getting it quite right. I'm thinking of Sedgewick, though...)
Alex
I mean determinist as in our actions could not have been otherwise. As far as the other sense of determinist (absolute), I do not think ethics are that much more absolute than say the golden rule, that the more highly prescriptive senses of morality are indeed a superstructure creatively established on baseline principles, like a symphony from a few basic themes. In other words something of a middle position between moral relativism and moral absolutism.
Clark: ŅFinally while logic (and math) are human processes the question is the laws that guarantee truth. That is logic is a science that studies the laws regarding signs to their objects. So to a degree I agree with Mark in that we have to have that guarantee of truth. (At least in deductive logic):
You guys have studied formal logic and I havenÕt. So please forgive my dumb remarks but I do not see how deductive logic can guarantee truth. At best logic tries to insure that the laws governing the process are correct. For the conclusions to be true, however, the premises must also be true. Therefore to wind up with truth you must begin with truth. So some truths would seem to be independent of logic.
Let me use a simple case of deductive logic in operation. Hercule Piroit (thatÕs right, while you guys were diligently studying logic I was watching old British mystery programs) has a subject who claims to be Mr. Able. Now Mr. Able has an alibi for the night of the murder. Hercule knows that the real Mr. Able is left-handed. He notices that the person claiming to be Mr. Able is right-handed. Using deductive logic (and his little grey cells), Hercule comes to the ŌtruthÕ, the man claiming to be Mr. Able is an imposter. And is lying. The reason Hecule discovered the ŌtruthÕ is grounded in the fact that the premises were true. Had either of the premises not been truth, his conclusion would have been false. Now the truth of the two premises rested not on logic but on experience. Therefore, these ŌtruthsÕ are true independent of logic.
If, for logic to derive truth it must begin with truth, and if these truths are independent of logic, how can logic guarantee truth? It seems to me that the best deductive logic can say is, Ņgiven the premises are true, this is the correct process for discovering additional truths.Ó This seems to me to be a long way from being able to say that it can guarantee truth.
Sorry to be so dense but what does Ņlaws regarding signs to their objectsÓ mean. IÕm familiar with SausuerÕs discussion of signs but this doesnÕt seem to be relevant. By the way, donÕt be shy, if I donÕt have the background and understanding to participate in these discussions please let me know and let me know where I can go to get better prepared. I donÕt want to turn this into a remedial course on logic (deductive or otherwise).
Deductive logic is only reliable if the given information is perfect, and the metaphysics of terms are as well. It most often fails due to bad assumptions, particularly bad metaphysical assumptions about conceptual simplicity.
However, under proper conditions it works like clockwork or arithmetic - susceptible to no error whatsoever. I typically model deductive logic with regions in a multi-dimensional possibility (phase) space, and there each logical operation looks like "constructive" solid geometry - a sort of multi-dimensional Venn diagram - clip, merge, test and so on - no ambiguity at all (assuming the terms are all appropriate black and white (bivalent)).
In this model, reality is a point or sometimes a path in possibility space and statements are volumes. An empty statement covers all space, and further assertions whittle down that space to some sort of theory about the real world. The difference between a true statement and a false statement is that reality is a proper subset of a true statement, and not a proper subset of a false one.
A completely false statement (one that is not ever true) is a statement where reality lies outside the statement volume. Most statements, of course, have some correspondence to reality but often contain subtle flaws where reality escapes the asserted constraints.
Detection of a contradiction is trivial, by the way, because it is the intersection (logical conjunction) of two or more non-overlapping volumes, i.e. the empty set in possibility space. And of course no real set is the subset of the empty set. Reality exists - of that we can be quite sure.
The question is what kinds of things are allowed mind-independent existence and what does it mean to be mind-independent? Does it mean independent of all minds or simply what any particular mind might think about it? A subtle but important distinction.
Peirce allows for real universals of a sort thus the laws of logic and mathematics can be real, although with regards to mathematics there is an element of possibility and imagination in them. But since he's a scholastic realist he thinks there are real universals.
I believe both Heidegger and Derrida end up doing this as well. Indeed I think that in a sense Heidegger's ontic/ontological distinction leads to this. (And of course Heidegger was influenced by Scholastic philosophy as well)
The issue then becomes the metaphysics of these universals.
I don't really think the 'reality' of logic is something we can talk about at all.
It all depends upon what one means by "real."
There are lots of common semantic gradiations of the term real. The tightest consensus definition is self-existent, unitary, and irreducible. Next layer is a neutral concept of something that is self-existent and irreducible. Next layer is something that closely corresponds to properties, attributes, relations, histories, etc of such things. Next layer is a composite object - the referent of neutral composite concepts of such things, and the concepts themselves.
So yes unicorn is a real concept, but not a real object, at least not yet, and even then it wouldn't be a "thing".
However, we cannot conceive of the universe operating without something like differential equations, so the mathematics of PDEs seems to be either a sine qua non for the universe or to closely correspond to some such essential property thereof.
On the other hand, Beethoven's Fifth Symphony or anything closely related does not seem to need to exist for electrons to keep going around in their orbits.
I was thinking of Wittgenstein -- that perhaps the priority or necessity of logic is a metaphysical question that we can't answer within language.
Mark -- I'd be interested in your definition of 'self-existent' -- by irreducible I suppose you mean something that can't be explained in terms of a more fundamental system, such as (one might entertain the idea just for the sake of the example) consciousness vis a vis neurobiology?
Alex
I think he simply means the "ontic" to use Heidegger's terminology. Existent is notoriously hard to define and often depends upon ones other metaphysical commitments. Real is a little easier since most uses simply mean that which is there independent of our thinking of it. One can find subtle variations of that definition but that's usually what they end up entailing. Of course one can then add in other notions. But that often then conflates issues. Dummett did that unfortunately in his famous paper "Realism."
Most analytic philosophers take the real to be coextensive with existents. However as I mentioned many philosophers, especially the scholastic realists, reject that presumption.
But that's just what I think is impossible to decide -- whether 'logic' "really" exists. Just as, in order to know what appears, we would have to see "behind" appearances, in order to state whether logic is real, we'd have to be able to speak beyond our speech.
I wouldn't necessarily *define* self-existence that way, but the test you outline is one of the best. The problem is that with low level abstractions there is considerable ambiguity as to which abstraction is fundamental - like with the E/M field some people might say that the (A,phi) vector potential is more fundamental than (E,M), which option is doubly confusing because one can perform what are called "gauge transformations" on the vector potential without changing its real world semantics.
And indeed in QM (E,M) does not look primary either, and it is hard to say when the descent of explanation will stop. And indeed the EM field appears to both to be contingent on charges and to have an actual energy density in space, to be created as virtual photons in some sort of odd way, even when charges are not accelerating.
So all I can say is that I consider self-existent to be whatever corresponds to the most accurate description of ultimate reality, the things in themselves, and not the referent of our imperfect conceptions of such things, although they are and should be very closely related. I think any conception of science that has no things-in-themselves, but just mystical non-determinate fuzz, like Bohr's conception of QM, to be incoherent.
So can say that I am a pragmatic instrumentalist, not a
doctrinare anti-realist instrumentalist - I believe there really are things down there, foundational, clearly describable things. Many instrumentalists don't believe that - and I tend to agree with Lee Smolin that such metaphysical indifference has stalled the modern scientific project - with regard to physics, at least.
I think Alex that's true in certain ways. That is there are essential limits on what we can signify. Both Wittgenstein and Derrida get at this. As I think mentioned I believe Peirce does as well in a way. But since Peirce adopts a thorough-going fallibilism I don't think this ends up being a problem the way I think Derrida establishes that it is for Frege or Husserl. (This is also getting at the point of Davidson's critique of the Fregeans I discussed last month and need to get back to)
Since this is the main theme of Speech and Phenomena and I just found my copy finally today I might write something up tomorrow (I'd misplaced it for a few months) The introduction to my copy has a great Wittgenstein quote from the Tractus that is pretty relevant.
I don't think it matters whether logic exists. The question is - does it work, how well, and under what conditions? The answer is a function of fundamental metaphysics. If the law of non-contradiction does not apply to fundamental being, then logic is useless. If there is no temporal regularity, then most of science is out the door. If there are no things-in-themselves, then it is hard to imagine that any of our abstractions approximate them.
Ultimately it is the same as always - we test and refine logic, language, and metaphysics by trial and error, taking confidence in our successes that we are converging on better and truer things. Most scientists and engineers have that feeling in spades, it is the humanities that are the current headquarters of doubt and despair. Hopefully that will change one day.
"If the law of non-contradiction does not apply to fundamental being, then logic is useless." -- Somehow I can just never make the leap from logic to reality. To me, logic is a property of a system, not of the isomorphism between that system and the real world. I really like the intro. to the logic book when it defines logic as a method of "preserving truth". I see logic as being comparable to the rules of chess -- it doesn't matter whether or not it really exists but (to distinguish my position from yours, Mark) it isn't really important to ask that question or to discover the limits of those rules -- if one wants to play chess, one simply assents to the rules of chess, because that's what it is to play chess. This is a bit muddled, but I'm in a rush.
Alex
Alex: ŅI see logic as being comparable to the rules of chess.Ó
IÕm not sure Pierce would agree. He seems to make a distinction between science (logic) and the thing science investigates (the rules of reason - the rules of the game). Pierce seems to state that the relationship of signs and their objects are established by laws, rational laws. It is these laws which are investigated through the use of logic. If the relationship was irrationally based, logic would be of no use. Thus Pierce makes the distinction between the 'laws of reason' and 'logic'. Reason then becomes foundational. Logic is a means of uncovering the rules of the foundation. Logic has a more limited role than reason. Logic becomes a tool, a method, of solving problems. The problem in this case is discovering the rules of (pure) reason, or semantically the rules by which signs and objects are established. I think this is what Pierce seems to be saying when he calls logic a science that studies the laws regarding signs to their objects. It is a tool not a foundation.
Of course this comes out of the Kantian tradition of pure (a priori) reason. A priori reason is the mechanism by which phenomenon exposed to the mind are organized. We donÕt see the thing-in-itself but rather we see what reason has categorized for us. This is the idea that Pierce seems to be using. Pure reason is foundational. This is for all phenomenon including language. This, of course, relates to what you (Clark) had mentioned before about KantÕs view of Schulbegriff and Weltbegriff. The fact that the one can contribute to the other is do to manÕs foundation: a priori reason. Logic, as a creation of pure reason, is posteriori and thus cannot be foundational, cannot be the rules of the game. Of course this leaves open the question is a prior reason the true organizing instrument by which phenomenon are understood by the mind?
Hopefully my two posts today threw a bit of light into this topic.
I think you're right Rich that the Kantian distinction is important. This brings together Peirce and Heidgger I might add. We always have what one might call projective metaphysics. That is hypothesis with which we make our guess concerning reality and thereby structure our experience. Deductive logic like mathematic is purely in terms of possibility. That is what would be the case if our hypothesis were true. That is it is an imaginative projection. However it depends essentially on abduction or pragmatism. We are forever cut off from the full presence of the objects we encounter. Our thinking is in terms of signs and signs have but a hint at their object. We can but say that if abductive reasoning were carried on indefinitely that we'd eventually reach the Truth. But one could easily argue that as finite human beings any individual can't do this.
Regarding the laws of deductive logic, I think you are completely right in that Peirce would say that they are found through abduction.
Regarding grounding logic on metaphysics, psychology, or even linguistics (as conceived in the late 19th century) Peirce has a rather interesting quote.
There are several sciences to which logicians often make appeal by arguments which would be circular if they rose to the degree of correctness necessary to that kind of fallacy. They are Metaphysical Philosophy, Psychology, Linguistics (of which they barely know that of the Aryan languages. . .), History, etc. (CP 8.242)
I think he is right in this that it is hard to ground logic the way some do without becoming circular. Perhaps some, such as Derrida, provide their aporias because of this recognition. The claim to escape the vicious circle when ones "logic" demands it thus forms the aporia.
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