## Describe Heideggerian ontology with predicate logic

• 10
I've always thought the cogito was a logically sound argument. Heidegger criticises Descartes for "subjectivity" and replaces Cartesian ontology ("noumenology?") with phenomenology. I struggle to see how phenomenology could be considered objective and noumenology could be considered subjective, as Heidegger claims.

If Cartesianism could be written logically as follows:

$Thinks(x)$ is defined as being in intimate contact with the source of thought noumenally (not phenomenally)

${E}$ is defined as the set of all existing things (not to be confused with $\exists$ which when talking about ontology can only refer to a specific subject of discussion rather than a thing which literally exists)

Cogito:
$\forall x (Thinks(x) \wedge (x=a) \implies a \in E)$

Weak Solipsism:
$\forall x \neg (\neg Thinks(x) \wedge (x=a) \implies a \in E)$

Then how would one describe Heideggerian ontology using predicate logic?

Note that the equations I wrote took less than 5 minutes to make so I'm likewise not asking for a rigorous proof, my goal is only to understand the logic of Heidegger.

Edited to use mathjax.
• 5k
Then how would one describe Heideggerian ontology using predicate logic?gurk
Why, exactly? Are you thinking it might fit? Or that your Procrustean bed will serve to lop off unsuitable appendages? And is it a "description" you're after? Or a reduction of some kind? Or just some royal road to a sense that is notoriously obscure?
• 10

Because if an opinion is logically unsound, then it is obviously inferior?

Hence why I am asking for help understanding why this would not be the case with Heidegger. Expression in predicate logic is an easy way to show the soundness of an argument.
• 5k
Because if an opinion is logically unsound, then it is obviously inferior?
Hence why I am asking for help understanding why this would not be the case with Heidegger. Expression in predicate logic is an easy way to show the soundness of an argument.
gurk

I'll tread water here - or stay in the shallow end - until a real swimmer jumps in. It appears you want to appeal an idea to rigorous test, "put it to the question," in a manner of speaking. Any road here, but it seems to me the most direct approach is to observe that before you can test, you have to establish in some significant and meaningful way exactly what you're testing. That is, you shall have to know your Heidegger before you can test, at least enough of it to make the test meaningful. And I suspect when that's done, you won't need any such test.

Corollary: tests seem to be static. I'm not sure Heidegger's thinking will be still long enough.
• 4k
Then how would one describe Heideggerian ontology using predicate logic?gurk

If you need citations for things I will find you them.

I think for him analysing something with predicate logic requires taking a theoretical stance towards what is analysed that reduces it to a present at hand entity if you treat logic as characterising the being of its entities when you use it. I'll spell out the reduction.

If you treat an entity as you do in predicate logic, it's an element of fixed domain of discourse to which predicative statements apply or fail to apply, like "If x satisfies P(x) and for all c such that P(c) - P(c) implies Q(c), then Q(x)" - the entitites x are connected to characteristics of their being (predicates) which can be turned on or off corresponding to whether the statement is true or false of the entities in question.

There's a lot of "given" that goes into formulating something in predicate logic; the symbols are interpreted in some way, the predicates are interpreted in some way, and if we wanted to apply it to something in real life we'd need to represent the aspect of real life in a manner that conformed with the standards of predicate logic. As an example on how artificial this can be, in predicate logic "X is red" and "X is coloured" have distinct predicate symbols, the implication that "X is red => X is coloured" then needs to be included as an argument premise to conclude from "X is red" that "X is coloured" validly. But in order to do that, we must have a skilful understanding of how the concepts are to be represented as statements of predicate logic. In that example, we leverage our understanding that if something is red that means that it is coloured to represent that extra-logical fact as an entailment. "If something is red, it is coloured" is not by itself a theorem of predicate logic. This comes down to leveraging a knowledge of how words are used to describe and relate the properties of entities - in Heidegger's terms, leveraging an understanding of the being of entities (for representational purposes in predicate logic).

Imagine if we assumed that the entities in question - red things like apples - were fully determined by how they were represented in predicate logic, this would equate every characteristic of a being with the being of its representation - and we would have the strict identity between the represented and the representation. That is the nature of the "reduction" I alluded to. The being of entities apprehended representationally is always present at hand - a know that - but the means of apprehension is different - a know how or a formation of it. This is not to say we can't have declarative knowledge regarding know how - but that strictly equating the represented with the representation is a metaphysical/ontological error.

Now, if we say that our knowledge of how red things are always coloured things is represented by the implication that red things are always coloured by including that as an argument premise, there is the question of the means of that representation and how it is is enabled through the "given" practical competences we leverage.

Heidegger situates his ontology in the "given" revealed by that gap between representations (outputs of representational behaviour) and the means of representation's leverage of know how. If you follow Dreyfus' take on Heidegger's Critique of Descartes, it isn't that present at hand is bad or wrong, it's that it's only part of the account of the being of entities which is over emphasised. One means of understanding them - as in there are others, and they are important. If you're familiar with Wittgenstein, it's a similar brand of error to using a word outside of its context without noticing the violence done to its meaning ("language running idle") - the error here being one of apprehension/theorising style, taking a present at hand mode of apprehension outside of its intended context and not noticing the violence done to its topics of concern (similar to hyper reflection in Merleau Ponty maybe).

Personally, I've been mostly separate from Heidegger study for a few years, and while I think the jargon can be stultifying the critique of Descartes he has is one of those ladders Wittgenstein spoke of. It should be climbed, but discarded after.

Edit: I should've mentioned, he has a book on logic, "Logic: The Question of Truth".
• 5k
is one of those ladders Wittgenstein spoke of. It should be climbed, but discarded after.
Or also said, perhaps not climbed at all.
• 10

That is a very thoughtful post. Some responses:

There's a lot of "given" that goes into formulating something in predicate logic

The critique of logic you mention-- that we have to explicitly state relationships such as that the set "red" is a subset of "colored"-- seems to ignore that this is exactly the same way that we as humans also learn that red is a subset of colored. I grew up speaking english, I live in a 4 dimensional universe with cartesian geometry and photons, I have light and sound sensing organs, and so after a few years of existence I learned that when I hear "red" it means a certain wavelength of light, and when I hear "colored" it means the set of all visible wavelengths of light. The problem of the "given" you mention in logic is just because we don't have the same patience when formulating logical statements as we do when raising children.

Imagine if we assumed that the entities in question - red things like apples - were fully determined by how they were represented in predicate logic

I agree that the noumenal apple is very different from the logical representation of it. The logical representation is only supposed to abstract the phenomenon.

Now, if we say that our knowledge of how red things are always coloured things is represented by the implication that red things are always coloured by including that as an argument premise, there is the question of the means of that representation and how it is is enabled through the "given" practical competences we leverage.

Not sure I follow... The means of that representation would just be something like

$\forall x (x \in R \implies x \in C)$

Heidegger situates his ontology in the "given" revealed by that gap between representations (outputs of representational behaviour) and the means of representation's leverage of know how.

I don't see room for Heidegger between two things that shouldn't be separated. It seems like you're saying he focuses on phenomenology, which is certainly true, but where are the noumena? This is my difficulty. You can't have a sound ontology without addressing noumena. Discussions on the limits of logic seem to me unrelated to this issue.

Edit:

If you're familiar with Wittgenstein, it's a similar brand of error to using a word outside of its context without noticing the violence done to its meaning ("language running idle") - the error here being one of apprehension/theorising style, taking a present at hand mode of apprehension outside of its intended context and not noticing the violence done to its topics of concern (similar to hyper reflection in Merleau Ponty maybe).

Do you have any examples of this Heideggerian violence? I'm generally familiar with Wittgenstein but his criticisms of language, ironically for this discussion, are easily solved by using logic instead.
• 4k
I don't see room for Heidegger between two things that shouldn't be separated. It seems like you're saying he focuses on phenomenology, which is certainly true, but where are the noumena? This is my difficulty. You can't have a sound ontology without addressing noumena.gurk

Whether Heidegger is ultimately an idealist or a realist of some flavour is debated. There's support for both:

In so far as Being constitutes what is asked about, and "Being" means the Being of entities, then entities themselves turn out to be what is inter-rogated. These are, so to speak, questioned as regards their Being.But if the characteristics of their Being can be yielded without falsification, then these entities must, on their part, have become accessible as they are in themselves. When we come to what is to be interrogated, the question of Being requires that the right way of access to entities shall have been obtained and secured in advance. — Being and Time, Macquarrie and Robinson translation

So there's strong support for the claim that entities themselves inform inquiry regarding them so long as the method of questioning is appropriate for the type of entity. That entities in fact do this is a very realist position. But as regards being itself, he makes remarks like this:

Entities are, quite independently of the experience by which they are disclosed, the acquaintance in which they are discovered, and the grasping in which their nature is ascertained. But Being 'is' only in the understanding of those entities to whose Being something like an understanding of Being belongs.

Things like that make Heidegger scholar William Blattner strongly believe Heidegger is ultimately an idealist of some sort. An idealist with regard to being, a realist with regard to entities. Which, I think, can be decently analogised to relativising the ontology of entities to a conceptual scheme (though I assume Heidegger would insist that conceptual schemes are representational devices of objects for subjects, a Cartesian "for-us").

These investigations, which take precedence over any possible ontological question about Reality, have been carried out in the foregoing existential analytic. According to this analytic, knowing is a founded mode of access to the Real. The Real is essentially accessible only as entities within-the-world.

That makes him pretty close to Kant (empirical realism (ontic realism) and transcendental idealism (ontological idealism)), so if you're meaning "noumenon" in the Kantian sense, there's some textual support for an analogue of it in Heidegger's thought. Though I think remarks like "(entities) become accessible as they are in themselves" (through their manifesting as phenomenon) would make Kant advocates very uncomfortable I imagine.

If you're using the world "noumenon" as a proxy for nature in its indifference to us, I agree with you that this is a weak point in his approach. If you're using it in the Kantian sense, there's a similar conception in Heidegger "the Real is essentially accessible only as entities within-the-world", and "the world" is more similar to "what is derived from and implicated in human activity" than indifferent nature.

Not sure I follow... The means of that representation would just be something likegurk

A formula like $\forall x: \hphantom{,} R(x) \rightarrow C(x)$ is a representation. The means of representation is the practical competence that maps the understanding that red things are coloured to the formula of predicate logic. The formula in predicate logic merely expresses the fact, which we learn elsewhere through the use of language. Think of how your formula and my formula are understandable as the same thing, but how we don't have to go through a proof that my functional notation is the same as your set membership notation (for finite domains anyway). I think Heidegger is very right in highlighting this flavour of equivocation; and I agree with (my understanding of him) that we often don't notice the equivocation because of the unexamined trappings of theorizing as a practice.

Do you have any examples of this Heideggerian violence? I'm generally familiar with Wittgenstein but his criticisms of language, ironically for this discussion, are easily solved by using logic instead.gurk

Well, the above thing you did is a decent example of it I think! There's a generic sort of formula for it Heidegger reuses - when people are using representational devices (like a translation into predicate logic), the standard mode of apprehension for objects output from the representational device (the specific formula components and what they mean) does not resemble the mode of apprehension of the concerned objects in its usual function (the network of linguistic and theoretical competences that enable the translation). People do the same thing with truth apt sentences (here's looking at you @Banno), and all the world becomes equivalent to a function that maps a sentence to a truth value. Studying Heidegger attunes you to the sort of error that confuses the properties induced by the use of a representational device with the properties of the entities themselves. I think. At the very least, being able to suspend the philosophical impulse to treat everything as an object with associated predicates is valuable. A bad framing of an issue can induce us to see things in it which are not there; regurgitating the framing rather than analysing the issue. (Heidegger is pretty guilty of this too I think!)

Another thing I think is a good example is the idea of a "quale", which is allegedly an experiential property that we experience as a component part of an experience (like the red part of an apple's skin). It's a split done in retrospect (reflectively) and induced by the representational behaviour in reflection (which regards experience as an object of analysis) rather than being innate to the experience at the time. The use of qualia vocabulary often splits experience up in a manner unexamined in using the vocabulary. This is a me example, not one I immediately know of textual support for in Heidegger (though I recall Dreyfus talking about qualia like that in a lecture).
• 4k

Found this which might be of interest to you - it talks about Heidegger's conception of predication (in statements) as a kind of "seeing as" (seeing something as something), and how it derives from a more practically oriented "seeing how" - somewhat analogous to Wittgenstein's distinction between saying and showing but couched in terms of perception.
• 10
Thank you for the clarifications @fdrake

My understanding of Heidegger, and please correct me if I'm wrong, is as follows:

1. Cartesian ontology proved that Solipsism cannot be disproven logically. Heidegger does not dispute this conclusion.

2. Heidegger's novelty was not in addressing the problem of the un-knowability of the noumenon, but rather in ignoring the noumenon and using phenomenological experience instead of the cogito as the "axiom" for building his ontology. If he occasionally claims that the noumenon can be known, the claim does not have a logical basis.

3. Since his ontology is based on phenomena, he spends a lot more time investigating human psychology than other ontologists would. He claims that logic is not adequate to absolutely express phenomenological ontology, and that certain aspects of phenomena (and therefore, ontology) must necessarily lie outside the realm of logic for reasons such as the false equivocations that you pointed out. All logic is given meaning only through interpretation by a Dasein, and therefore all logic must necessarily fail to describe those axioms that the Dasein used in order to create it. It is (and always will be) impossible to prove the definitions of "and" or "implies" using logic, because these things are in some sense not logical, but phenomenological.

Is this a fair representation of his thought?

If so, then I fail to see the value in it. Perhaps Heidegger would be shocking to Descartes, but his ideas on the fallibility of logic and the central position of phenomena in human existence were already articulated several millenia ago by Laozi and Buddha respectively.

Would it be a valid criticism to state that his major achievement was in translating Eastern ontology into philosophical language for a Western audience? Or am I still missing something?
• 4k
1. Cartesian ontology proved that Solipsism cannot be disproven logically. Heidegger does not dispute this conclusion.gurk

I don't think he disputes it directly. His account does very much undermine the motivating framework that allows solipsism to get going, though. Human beings are "beings in the world", rather than minds in perceptual cages that have phenomenal content. He tries to use everyday life as a starting point, albeit a very quotidian stereotype of everyday life that excludes vital aspects (eg. human bodies, politics, personalities...). Rather than beginning in abstract space of reasons and searching for necessary structure.

2. Heidegger's novelty was not in addressing the problem of the un-knowability of the noumenon, but rather in ignoring the noumenon and using phenomenological experience instead of the cogito as the "axiom" for building his ontology. If he occasionally claims that the noumenon can be known, the claim does not have a logical basis.gurk

I don't know how you're using the word noumenon. Regardless, the relationship of a human to their environment is conceived by Heidegger as predominantly practical rather than epistemic; knowing (with its structures of concepts and judgements) being just one flavour of practical understanding. I imagine that when he's talking about hammering, he thinks that the "noumenal hammer" (yuck) is moved in the act and that this is essential for understanding how a hammer works. Its use really does help put nails into things.

3. Since his ontology is based on phenomena, he spends a lot more time investigating human psychology than other ontologists would.gurk

I think it intersects with psychology in some places - like his analysis of moods+dispositions and private experiences (erlebnis? It's been a while. Edit: Also note generic phenomena are not private!). But it's quite different in others - most of the phenomenal structures he analyses do not concern mental qualities or patterns of thought, or even the individual human beings that have them. But I think what you're saying is broadly true; he discusses psychological, sociological and linguistic themes and treats them as relevant to ontology. Since ontology for Heidegger begins in the analysis of human beings.

Would it be a valid criticism to state that his major achievement was in translating Eastern ontology into philosophical language for a Western audience? Or am I still missing something?gurk

I don't know much about Eastern philosophy or how Heidegger was influenced by it.
• 10

Sorry, I should have been more clear; I'm using "noumenon" in the Kantian sense.

Here's a brief mention of Buddhist influence on Heidegger in Wikipedia. I'm sure if you have access to scholarly publications you'll find much discussion on the topic.

Anyway, thank you for enlightening me on Heidegger. If I may, I would absolutely suggest reading more about Eastern philosophy. If you want primary sources, the Dao De Jing, Zhuangzi, Genjokoan, Heart Sutra and Mulamadhyamakakarika are very focused on ontology and epistemology. Buddhism especially has a very interesting ontology, which uses as its basis a synthesis of the Cartesian and phenomenological viewpoints, but instead develops it into a rigorous system of ethics. A good tertiary source is of course basically anything by D.T. Suzuki.
• 992
I struggle to see how phenomenology could be considered objective and noumenology could be considered subjective, as Heidegger claims.gurk

Heidegger never claims this.

Excellent response.
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal