Theories of the Ontology of Logic and Reason?
February 12, 2015 1:40 AM   Subscribe

I have recently become interested in the question of what sort of existence or "being" logical laws, reason, mathematical truths, rationality have. That is, what is the ontological basis of logic? Where does the a priori reside? Is it part of the universe or if it is somehow "absolute" then "where" do these truths reside? Who has theorised about this, can you give pointers of philosophers, and books that have tackled this issue? Did Russell or Frege talk about this? Plato's realm of Ideas seems one approach to the problem but what are contemporary theories?
posted by mary8nne to Education (14 answers total) 16 users marked this as a favorite
 
Well, it's a major theme in Heidegger, e.g. in "On the Essence of Ground," The Principle of Reason, "The Principle of Identity," and anywhere he talks about the "not"--specifically not the same as nothing--dividing beings from each other ("What is Metaphysics?" comes to mind, but I'm sure I'm not remembering the best example). In all those places and more, he's trying to work out some way of talking about the principle of sufficient reason, the law of identity, the law of non-contradiction, and transcendental arguments as (simplifying so greatly it's absurd) not just principles for reasoning about things or guidelines for representations of things but conditions under which stuff happens.

If you'll accept some evaluation of what he achieved with that, I think it was for him a wellspring of inspiration, giving him a way to dig into all kinds of topics and offer what was then a fresh take. Sometimes what comes out of it is interesting, so it's not the worst path you could go down. But honestly, I'd give it a miss and suggest trying to find someone attempting to say how key ontological categories actually even work at the Planck length and/or whether brains extrapolate or interpolate imaginary ontological conditions as messily as they do other information. It's not even slightly Heideggerian--pretty much the opposite--but things along those lines may offer some nice examples of how much we shouldn't assume when talking about ontology.
posted by Monsieur Caution at 3:01 AM on February 12, 2015


On the question of mathematical truths, you could start with Paul Benacerraf for an account of mathematical structuralism. That type of theory pretty much puts all the ontological work onto the underlying logic, but given the very close relationship between mathematical and logical truths, it's an important debate to understand because whether you come down more on a platonist or structuralist view about mathematical truths affects your ontological commitments to logic.
posted by crocomancer at 3:28 AM on February 12, 2015 [2 favorites]


A major motive for Russell was to avoid having to posit the existence of abstract entities like propositions, which he believed in when he was younger. The most important example of this (as far as I know) was his 'Theory Of Descriptions'.

Wittgenstein's Tracatus Logico-Philisophicus seems relevant to your interests.

In general, the questions you raise are, I think, usually discussed in the philosophy of mathematics.
posted by thelonius at 4:10 AM on February 12, 2015


For a starting point, try this section from the SEP entry on Platonism, describing the positions you could take on whether abstract entities like numbers exist.

See also: Nominalism, which means you'd think they are objects "in name only," or by convention, and then there are a few other alternatives too.

Mathematical objects are one type of abstract object, a bit more to chew on there.

But are you also asking about the epistemic status of the laws of logic (how do we know them?) and basic mathematical truths? That's a different question. One of the objections to Platonism about them is that it's not clear how we can learn about or know about something that's in the realm of the forms. Plato's answer was that we visit there before being reincarnated, but supppose you set aside that explanation; if these a priori things exist in a realm causally disconnected from our own, how do we learn about them in the first place?

The entry on logic and ontology might also be talking about some questions that would interest you.
posted by LobsterMitten at 4:43 AM on February 12, 2015 [3 favorites]


If you want to read more recent continental philosophers i.e. Heidegger you need to start with Kant's Critique of Pure Reason. It's split into 2 sections: Transcendental Aesthetic and Transcendental Logic. The 'Logic' speaks to some of your questions more directly but you need to read both.

Everything else is either an attempt to build on Kant or an effort to "categorically" reject Kant i.e. Russel and Frege.

Also, if you read the Socratic dialogues that most closely talk about 'ontology' i.e. theatetus or meno (i'm sure there's a list) you'll discover that Plato is less of a "Platonist" than he's made out to be.

honestly, there isn't a short answer to any of your questions. Plato should be somewhat easier to read than Kant, so starting with the Theatetus and Meno might work as a start.
posted by ennui.bz at 5:02 AM on February 12, 2015


also, one of the problems with heavy duty philosophy is the tendency (for even professional 'philosophers') to skip to the cliff notes version. So, a lot of what is attributed as the views of a given philsopher is really just referring to the accumulated conventional wisdom of various commentators who have various agendas. If you go into any used academic bookstore you'll find way more copies of commentaries on Hegel's Philosophy of Mind than copies of the original Hegel i.e. more people read the commentaries than the original source.

so, don't do that.
posted by ennui.bz at 5:08 AM on February 12, 2015


I should have mentioned that I'm actually currently doing a Philosophy MA and so yes I am quite familiar with Kant's CPR and have read a few Platonic dialogues in the past and parts of Heidegger's Being and Time.

Its been years since I read Wittgenstein's Tractatus - I feel it was more about the limits of language (no?) which although related is somewhat different.

I'm also not really interested in "What are numbers?" So much as what is the ontology of "logical reasoning" itself. Which Kant doesn't quite deal with directly. Does he?

In the CPR the categories include "relations" as a formal conditions (transcendental) of knowledge which thus are in the Subject in a similar way to Space and Time - So you could say that "reason" for Kant is possibly part of the human experience of the universe. That it would not extend beyond this universe. But in the sections on the Transcendental Idea it seems that there is a more fundamental notion of reason that Kant appeals to that would be outside the universe.

So I guess I"m wondering what other views are on this?

Thinking back - it was actually Kant that got me onto this question a few months ago - and this morning it was reading stuff about the "evidence" for the Anthropic Principle that set me off again. It seems that the Anthropic Principle in particular posits an ontology of "reason" that is external to the universe itself. As these questions of the values of constants of the universe rely on some notion of logic/reasoning that exists beyond the universe to make it sensible.
posted by mary8nne at 5:18 AM on February 12, 2015


A.J. Ayer deals with a lot of these ideas in Language, Truth, and Logic. Much of what he talks about there links directly into logical positivism and the output of the Vienna Circle (and especially Karl Popper).
posted by yellowcandy at 5:55 AM on February 12, 2015


I'm also not really interested in "What are numbers?" So much as what is the ontology of "logical reasoning" itself. Which Kant doesn't quite deal with directly. Does he?

iirc, Kant thinks that logic (which for him means Aristotlean, syllogistic logic) expresses the a priori "Categories" of thought, through which we must construct the world of experience. He devotes a lot of space (the 'transcendental deduction' and the 'metaphysical deduction') to trying to show that these a priori categories legitimately apply to experience. Of course, for Kant, they are invalid as soon as we attempt to apply them beyond the sphere of experience, i.e., to any kind of metaphysical object such as God or the soul.
posted by thelonius at 6:46 AM on February 12, 2015


Another place to look is at Dummett's theory of intuitionism (here, but you'll want to get it from the library unless you're rolling in dough). Basically, the idea is the rather pragmatist/pseudo-Kantian one that mathematical/logical objects are constructions of the individual minds of the thinker, where intuition is being used in the Kantian sense of formal intuition of space/time. Dummett is crazy good stuff.
posted by dis_integration at 7:15 AM on February 12, 2015 [1 favorite]


Also, to throw questions of the reality of logical principles into relief, I'd suggest reading some of Graham Priest's work on para and transconsistent logics, i.e., logics that reject or modify the principle of non-contradiction or the principle of the excluded middle. Aristotle famously lumped these together into the highest principle of all thinking in Metaphysics Gamma and wryly suggested that anyone who rejects them go jump off a cliff (because they'd be both jumping off a cliff, and not jumping off a cliff at the same time). Well, they were rejected in the 20th century (particularly by Ɓukasiewicz) and thinking went on. I don't think you can really get into the question of the ontology of logical principles without dealing with the fact that some of them seem, well, optional.
posted by dis_integration at 7:23 AM on February 12, 2015 [1 favorite]


Not sure if this is quite what you want, but if you're interested in a scientific perspective you might enjoy Eugene Wigner's The Unreasonable Effectiveness of Mathematics in the Natural Sciences and RW Hamming's The Unreasonable Effectiveness of Mathematics. Hamming might be more relevant than Wigner.
posted by pseudonick at 8:15 AM on February 12, 2015 [1 favorite]


Are you familiar with the work of Mark Lilla?

I like this blog a lot, and this is a review on this blog of Lilla's latest book
posted by 15L06 at 10:45 AM on February 12, 2015


The basic principle of constructor theory is that all fundamental laws of nature are expressible entirely in terms of statements of which tasks (i.e. classes of physical transformations) are possible and which are impossible, and why. This is a new mode of explanation, intended to supersede the prevailing conception of fundamental physics which seeks to explain the world in terms of its state (describing everything that is there) and laws of motion (describing how the everything changes with time). By regarding counter-factuals ('X is possible' or 'X is impossible') as first-class, exact statements, constructor theory brings all sorts of interesting fields, currently regarded as inherently approximative, potentially into fundamental physics. These include the theories of information, knowledge, thermodynamics, life, and of course the universal constructor.
posted by j03 at 7:17 PM on February 12, 2015


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