Browsing on the Internet, it seems to me that knowledge (viz. the ability to know that) is invariably linked to propositional modal logic.

Why is that? Could we not say, for instance, that knowledge lies with what we can prove, having hence an intuitionistic approach to knowledge. Or, even simpler, that the ability to know is simply implied by the theorems of the classical propositional calculus?

If so, this means that there are several approaches to knowledge. But, then, what is knowledge in itself? Do philosophers really know what knowledge is (apart from defining it through properties knowledge is supposed to have)?

  • What are the sources of the statement : "knowledge is invariably linked to propositional modal logic" ? It seems clear (to me) that "that there are several approaches to knowledge" : see the history of philosophy, form Plato and Aristotle, to rationalism and empiricism and Kant and ... – Mauro ALLEGRANZA May 29 '14 at 19:24
  • (1) Like Mauro and Dan, I found the claim about the connection to modal logic a bit too strong. (Our epistemic/modal-logical explication of knowledge (going back to, at least, Hintikka) is something like half a century old. Non-modal approaches to knowledge reach all the way back to the ancients. (2) Perplex's point is that there are various approaches to knowledge, but those approaches don't seem to him/her to answer the fundamental question: what is knowledge? (I think this is a pseudo-question, but good discussion might come out of answering it nevertheless). – Hunan Rostomyan May 30 '14 at 3:45

I don't know exactly where you came across the idea that 'knowledge (viz. the ability to know that) is invariably linked to propositional modal logic', but there are a couple of things, both of which are worth giving a brief overview of. These are epistemic logic -- the logic governing statements of ascriptions of knowledge -- which is a form of modal logic, and knowability -- questions about when it is possible to know something. This is naturally formalised in a propositional modal logic (perhaps a modal epistemic logic).

Epistemic logic.

We might ask -- what is the appropriate logic for reasoning about knowledge? If I make the following argument:

  1. I know that it is sunny outside
  2. I know that if it is sunny outside then there is less than 100% cloud cover
  3. Therefore: I know that there is less than 100% cloud cover.

Is this argument valid? If so, why? What are the principles that govern knowledge ascriptions.

Here's how we might start: Suppose that we start with propositional logic -- the logic of 'and', 'or', 'if-then', 'not' and so on. How do we add knowledge statements? It is natural to think that knowledge is knowledge of a proposition. So, we add a symbol 'K', so that for any sentence φ, 'Kφ' is well-formed, intuitively read as 'It is known that p'. (We might subscript K with a letter denoting who knows that p'.

What principles should we expect. Here are a couple:

(Nec) If you can derive φ without assumptions, then derive .

(K) Kφ & K(φ→ψ) → K(ψ)

The first of these says that, if we've proved that φ, then φ is known. This is a bit controversial, since it seems to suggest that all logical truths are known. But perhaps we can brush this aside and assume we are dealing with some kind of idealised perfectly rational being.

The second says that knowledge is preserved under known entailment. Seems pretty plausible to me.

Anyway, if K satisfies these principles, it means that the logic is what is called a normal modal logic. So that's one way to think that modal logic might be important for epistemology.

You can read more about it at the Stanford Encyclopedia of Philosophy here


I won't say much about this. But there's been a lot of discussion about knowability. So, for example, we might as whether every truth is knowable, in principle. Although this seems quite plausible, it turns out that, with some plausible assumptions, it entails that every truth is known. This is known as the knowability paradox.

This topic is linked to modal logic since it's about the possibility of knowledge. And lots of writers on the issue make use of modal logic when discussing it.

You can read more about this, again at the SEP, here

(You mention intuitionistic attitudes to knowledge. This topic is very closely related to that, in that people have tried to use the knowability principle -- that every truth is knowable -- to argue for intuitionistic logic. So it might be something you'd be interested in reading up on.)

Does this matter?

I'm conscious that I've not really answered your question. I've instead just tried to give a few details about some of the topics where issues to do with knowledge are tied up with issues to do with modal logic.

But must it be tied up in this way? No, absolutely not. There's plenty of discussion in epistemology which has nothing to do with modal logic. Again, SEP is a good guide to some of the issues that are popularly discussed: Epistemology at SEP. Many of these discussions are explicitly concerned with your last question: 'do philosophers really know what knowledge is?'. The answer: no, but they're working on it!

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IMHO epistemology to logic is what music is to acoustics. Although it seems that music "is invariably linked" to acoustics the viewpoint on what amounts to audible wave propagation is completely different: semantic (for the lack of better word) in epistemology & music versus mechanical in logic & acoustics.

The apparent self-reference in the question "do philosophers know what knowledge is" hints to a possible answer: the concept of knowledge is so basic that it should be defined by the totality of the corresponding axioms. A nice example is Euclidean Geometry: although the basic concept such as "point" and "line" are not explicitly defined, one can consider the totality of Euclidean axioms to be the definition of what "points" and "lines" are.

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I don't have much time, so I must be brief and I'm afraid this will be a gross over-simplification, but...

Measurements of the enviornment procured by the sens(or)es can be considered data. When this data is analyzed and woven together to fit in the size of an instant, it is the experience of consciousness at which point the data can be considered information, as it is data which directly describes something. There is consciousness and also self-consciousness... cogitol ergo sum, I think therefore I am, is referring to the I which is able to be conscious of being conscious. It is the self-consciousness we usually think of as being us and when data becomes information via consciousness, self-consciousness is yet another level of analysis of the original data, but on the higher level of information. We run analysis after analysis of the information and the result is new information related to the old. We pick and choose what information we commit to memory based upon its usefulness to us. Therefore, knowledge is simply data in the form of information which has some sort of usefulness for us. Simply put, to looking at a well pump, one is aware of all the info the senses deliver about it- what it looks like, etc. Perhaps we move the handle and now we have more information- the thing has a moving handle. Pumping the handle causes water to come out and now we now have the knowledge that pumping the handle will produce water, as we consider getting water from the well to be a useful thing. As I said, oversimplified but I'm out of time right now. Hope this helps

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Why do you think modal logic is necessary for true understanding? The mathematical basis of science is based entirely on ordinary 2-value logic (true and false). And who these days can argue with obvious success of modern science in advancing our understanding and knowledge of the universe?

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