What is the meaning of "epistemic", "epistemological" and "ontological" in this context?

Question

I was reading The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us by Noson S. Yanofsky and in some paragraphs of this books, The writer uses the words "epistemic", "ontological" and "epistemological" and first I thought that the word "epistemic" too refers to "relating to the study or theory of various aspects of knowledge" but apparently philosophers differentiate the meanings of “epistemic” and “epistemological”. In this link, it says: "Philosophers differentiate the meanings of “epistemic” and “epistemological” where, broadly, epistemic means "relating to knowledge (itself)" and epistemological means "relating to the study or theory of various aspects of knowledge" but in these contexts, because it comes with the words "ontological" and "epistemological", I am confused and wanted to ask if you can tell me that in each of these sentences, What is the meaning of "epistemic", "epistemological" and "ontological? in this context, does the word "epistemic" refer to the former definition or latter definition? and if it does refer to the latter definition, does "ontological", that is in the same paragraph, refer to "relating to nature of being (itself)"? In other words, I wanna know each of the bold words in the contexts below refers to the former definition or the latter definition? except for the word "ontological" that I said earlier what I want to know.

Here are the sentences from the book:

1. on page 55:

From the view afforded by extreme nominalism, it becomes apparent that the reason we cannot answer questions about the ship of Theseus or changes to human beings has nothing to do with linguistic limitations. It is not that we lack the right words or definitions of these concepts. There is also no epistemological problem— that is, it is not a lack of knowledge of the exact definition of the real ship of Theseus. Nor is it a problem of having some type of deeper knowledge of the ship of Theseus beyond its physical stimuli. Rather, we are dealing with a question of existence. In philosophical parlance this is an ontological problem. A real ship of Theseus need not exist.

1. on page 67:

Philosophers are usually split as to why there is vagueness. Some philosophers promote ontological vagueness—that is, the reason some terms do not have an exact meaning is that an exact meaning of these terms really does not exist. While there is an exact definition of “above six feet,” there is no exact definition of “tall.” In contrast, other philosophers promote epistemic vagueness. They believe there is an exact definition of vague terms but we simply do not know what it is.

3. on page 70:

How is one to understand such paradoxes? Some philosophers say that the sorites paradoxes show us that there is something wrong with the logical rule of modus ponens. By following modus ponens we came to a false conclusion, so modus ponens cannot be trusted. This seems a little too harsh. The modus ponens rule works so perfectly in most logic, math, and reasoning. Why should we abandon it? Other philosophers (who believe that all vagueness is epistemic—i.e., they believe exact boundaries exist that we are not aware of) assume that the rule If n grains are not a heap, then n + 1 grains are also not a heap. is simply false. For them, there is some n for which n grains do not form a heap but n+1 grains do form a heap. We mortals are not aware of which n this is but it nevertheless exists. For such philosophers modus ponens is true, but this implication is simply not valid and so cannot be used in a modus ponens argument. As noted above, to us it seems that vagueness is not an epistemic but an ontological problem. There are no exact boundaries and the implication from n to n + 1 grains is, in fact, always true.

Answer 1

Others have provided holistic responses, hopefully this serves to more "directly" answer your question.

Despite the distinction, the use of "epistemic" and "epistemological" in philosophy is mostly interchangeable and occasionally simply a matter of convention. Grammatically, these look very much like noun adjuncts that often have a few versions that are used interchangeably.

My interpretation of the particulars of how these words are used based on the definitions you provided are as follows:

1. Page 55

There is also no epistemological problem... this is an ontological problem.

• epistemological problem(A): as in problem of knowledge itself"
• ontological problem(B): as in problem in the study...

Note that (A) refers to "a lack of knowledge", which supports the "knowledge (itself)" meaning. Whereas (B) refers to the challenging question that the thought experiment poses, which supports the "study of" meaning.

Epistemic would probably have been more idiomatic in this passage, but I get the impression that the author chose epistemological to emphasize the distinction they are making between what is within the scope of epistemology vs ontology.

2. Page 67

Some philosophers promote ontological vagueness... other philosophers promote epistemic vagueness.

Interchangeable. Both "vagueness in ___ itself" and "vagueness as it relates to the study of ____" are equally valid. These are just terms to refer to the respective positions.

3. Page 70

Other philosophers (who believe that all vagueness is epistemic—... ... As noted above, to us it seems that vagueness is not an epistemic but an ontological problem.

• epistemic: interchangeable, but closer to "problem intrinsic to knowledge itself"
• ontological: interchangeable, but closer to "problem intrinsic to reality itself"

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As a final note, there is a certain danger in trying to deduce meaning from individual words in this way.

Some good reading on the topic of word meaning can be found here.

Answer 2

Any time we use a noun — and in particular a proper noun — we ought to recognize that we are using an incomplete reference to a putatively exact object. The incompleteness of that reference is not usually obvious to us, because we naturally fill in the blanks. If I say to you "Give Bob this chart, please", it won't occur to you that there are in actuality millions of Bobs in the world, any one of which could be the referent of that statement. You'll know through context which Bob I mean, and if there's any confusion, it will be between maybe two or three people, and you'll ask for clarification. Analytically it looks like you should be confronted with millions of options, pragmatically you'll have one or two likely options; but philosophy doesn't really think about things in pragmatic terms.

The philosophical problem is that if I say "Give Bob this chart, please", I can't really be sure that the term 'Bob' correctly specifies the object that I want the chart to go to. On the most ridiculous level, 'Bob' is a living, breathing creature, so between the beginning and the end of my sentence he has undergone metabolic processes that make him physically different, so that the 'Bob' I referred to is measurably different than the 'Bob' who receives the chart. Of course, we all want to say those changes are trivial, and that the 'Bob' referred to at the beginning is essentially the same as the 'Bob' who receives the chart. But that notion of essential qualities — things that are fixed, definitive qualities of 'Bob', as opposed to things that are ephemeral — creates headaches as we try to bind the referent term to the reference object. We can break those headaches down as follows:

• There are fixed, definitive qualities inherent to Bob as a reference object, so that Bob is ontologically (in the real world) identifiable, we just don't know what those qualities are. The term 'Bob' is a 'strong' reference, even though we cannot precisely measure the thing being referred to. This is an epistemic problem: we have correctly associated a term with an object, we just cannot put our finger on what makes that association correct.
• There are no fixed, definitive qualities inherent to Bob as a reference object; Bob is a constantly changing object whose boundaries are intrinsically vague in the real world (ontologically). The term 'Bob' is a 'loose' reference, pointing at an object that has consistent interrelationships or patterns, but which is constantly under transformation. Think about an eddy in a stream, which is a consistent feature that has no consistent substance. This is an epistemological problem: every time we are confronted with a 'new' appearance of Bob, we have to evaluate it in terms of the 'old' appearances and seek out continuity.
• There is nothing ontological (in the real world) at all being referenced. 'Bob' is a use-label that we apply to different things in different contexts as we see fit, and any mapping between language and reality is purely conventional. This is a purely linguistic problem: are we using the term 'Bob' in a way that is consonant with other uses of the term, by ourselves and others?

Yanofsky seems to be coming down on the side of ontological ambiguity, arguing that vague referent terms point at reference objects that are themselves vague (meaning that terms like 'Bob', 'a heap' or 'the Ship of Theseus' have no explicit and exact reference object); thus he rejects the epistemic approach. It's not clear to me from these quotes whether he wants to retain an epistemological attitude — holding loose references between terms and objects, which must be discovered — or shift to a purely conventional, linguistic model. The former would imply seeking out ontological regularities which we aggregate user the label 'Bob'; the latter would rely on linguistic usage, such that 'Bob' is defined by the consistent application of the term 'Bob'.

Answer 3

Your definitions of “epistemic” and “epistemological” seems to adjust to the standard (AFAIK). Ontological is not precisely related to knowledge.

Knowledge is a model that the mind creates in order to interact with the world, kind of a map that allows moving through the terrain. The previous terms are related to the subject of knowledge, the map that each subject creates of reality. Ontology would be related to the objects that exist in reality (considering that knowledge is the map, not the terrain). The elements on the terrain, that is, to the object of knowledge, the things existing in the map. More precisely, how do they exist.

Knowing a thing implies interacting with the thing in some way (a subject interacts with an object, and such interaction produces knowledge). Given that:

• Approaching phenomena from an epistemological perspective means observing how does the subject know objects. That is, observing the interaction subject-object, in what is concerned to knowledge.
• The epistemic perspective is related to the observation of knowledge itself. That is, observing an attribute of the subject.
• The ontological perspective is mostly related to the observation of the object itself, how does it exist, what do the features that the subject can know could be, if we would be able to exclude the subject from the interaction (which is impossible; that's why being objective implies getting better knowledge that if we bias it by being subjective). Objectivity implies the attempt to exclude subjective biases from knowledge, ontology would be the study of the object upon such assumption.

Not precisely related:

As noted above, to us it seems that vagueness is not an epistemic but an ontological problem [...]

This is quite interesting. If we know only the map and want to understand the objects in the map, how do we know that the terrain has the same boundaries that are represented in the map and that define objects? For one side, yes, it is an ontological problem. But I prefer considering the Kantian approach, that would suggest that objects don't exist per se. That it is the subject that defines the objects.

That, because absolute objectivity (pure ontology) would imply the absolute denial of the subject, which is impossible (just logic, then no references are provided). Rainbow objects exist because of where and when subjects exist. If the subject moves, the rainbow changes. Rainbows cannot exist outside of a mind. Rainbows, smells, sounds of trees falling down in a solitary forest, heat or rocks do not exist per se, but as subjective productions.

That's why the ontological perspective cannot be addressed without addressing the epistemic and epistemological perspectives. Kant's position against ontology is more radical [1].

[1] https://plato.stanford.edu/entries/kant-metaphysics/#PreRemRejOntGenMetTraAna