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Lately, I have come to the sad realisation that I know virtually nothing. This understanding was only fully realised for me when I looked back on my own education thus far; in spite of having just completed an undergraduate degree in Mathematics for instance, I feel I have only just scraped the surface of mathematical knowledge.

I have realised too, though, that (perhaps due to the nature of the archetypal mathematician, perhaps not) I know of hardly anything outside of mathematics. When I engage in political debates with my friends, I often become stuck in a specific strand of the subject in which I am not well versed. I am always left wondering, why do I lack such knowledge? I read books every now and then but it seems like, though some of those books are fantastic resources for some of the aforementioned instances in which I find myself in, I simply haven't learnt properly from them.

The question is, is this due to my cognitive abilities or is this something more universal? And how can I make sure that I do know what I have learnt properly? Because there is nothing more frustrating than wanting to know about things and talk about them with other people, yet knowing that you are still an amateur in the subject; but then should we refrain from speaking about something which we don't have a high knowledge of?

  • Why the close vote? It looks like a perfectly decent question and strangely enough follows the pattern, in rough terms, of the platonic dialogue Theatatus. – Mozibur Ullah Jun 11 '15 at 22:54
  • It's very common for competent people to doubt their own abilities, because they're good enough to see their shortcomings. This is known as the impostor syndrome. And I guess you're suffering from it. On the other end of the scale, really incompetent people are often extremely confident, because they lack the competence to see their shortcomings. This is known as the Dunning-Kruger effect. So, cheer up, while you do know next to nothing (as I) you're able to see that; most don't. – Cheers and hth. - Alf Jun 12 '15 at 22:02
  • It is quickly becoming virtually impossible to "know anything". Looking at the speed at which knowledge changes, Ray Kurzweil has determined it will be impossible for anyone to keep a positive balance on the percentage of their own field they know quite shortly. Within the next forty years, the percentage of a field one can confidently discuss will be constantly shrinking even as you initially learn it. He calls this the "singularity" and thinks this has huge implications for education and economics. So no, you are not alone. – jobermark Jun 13 '15 at 0:37
  • @MoziburUllah I would counsel against the 'Have you noticed... Am I normal?' framing as having mostly psychological and relatively few philosophical answers in general, whatever the underlying question. I do think we should close, if the question cannot be edited to appear less neurotic. – jobermark Jun 13 '15 at 0:46
  • @jobermark: I don't follow you; where am I saying 'have you noticed...am I normal'? – Mozibur Ullah Jun 13 '15 at 13:22
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Mathematics, at least when I was at school, would be notionally attached to the famous (or infamous) Platonic dicta 'let no-one ignorant of geometry enter here' which turns out, to stretch a term, an urban myth; and possibly more due to the nature and vagaries of the English pedagogical tradition.

There is, in fact a Platonic Dialogue, Theatatus where Socrates asks Theodorus, a mathematician that hailed from Cyrene, a colony in North Africa, to recommend any students of his that would make promising philosophers; he does - the eponymous Theatetus.

Given his description:

Snub-nosed with protruding eyes

Which is not far off descriptions of Socrates himself; it's hard not to think that it's Socrates counselling his younger self. The subject of the dialogue, surprisingly, is the nature of knowledge - Socrates asks Theaetatus is there a simple formula for it.

This, in essence, is the gist of your own question - to establish a simple formula for knowledge; such formulas have been established already - the Descartian axiom, the Turing Test and Wittgensteins Logic - but of course these are at best partial answers; it's also in the context of this dialogue that Godels incompleteness theorem displays it's special interest, at least philosophically.

I read books every now and again ... [but] I haven't simply learnt from them.

Reading helps, but did only reading help with mathematics? Perhaps it did, particularly early on, but to enter into the spirit of mathematics today, especially as it is today, takes a certain serious devotion: Questions must be posed, and answered; the real structure of a proof understood, as well as variants and all this must come, somehow naturally - this is the process of subjective dialectic as dramatised in the dialogue above.

It's no different to any other field that has rigour - political philosophy included; this is if real knowledge is sought (and I mean real in the sense of your own questions); however it is true that strong opinions strongly and articulately held often count as knowledge - it's this that Socrates skewers in the Sophist (which doesn't mean that the skill of polemic and rhetoric if done rightly is not a virtue - this is in part, the nature of good journalism).

Should we refrain from speaking about something about we have no high knowledge of

In the particular instance that one is called upon to be an expert, then no, of course not; but then again you will not be called to be an expert witness (this being no disparagement of you abilities) so this situation is nothing to fear.

In the general situation this will depend on the company - people are various; as you've noticed it's often worth asking questions - and besides philosophy on SE, there is history and politics; quite often I have seen good questions and answers get low votes and views and quite commonly too; this given the nature of the site should be taken as a given - so one needs to learn to recognise what counts as a good question and answer; yours, by the way, was a good question.

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I call into question the premise that you "know virtually nothing". We can assume that you don't know everything, or half of everything. Indeed, if you sum up everything that every human knows or knew for all times, that wouldn't sum up to half of everything, or a tenth of everything, at least everything that can be known. In fact, omniscience is impossible. Rather than being concerned comparatively with how much you know compared to others, it would be more productive to consider what you know, and whether it is appropriate to your purpose in life. Suppose for example you had only taken one term of calculus -- would you then know "enough" mathematics for your life goals? Presumably not.

Rather than refraining from speaking in an area where you are not the wisest person, you can refrain from making indefensible assertions. If there is some debate over "climate change" and you don't feel that your grasp of the underlying physical science is impeccable, it is perfectly correct to not make a bold assertion. That should not stop you from asking a bold question.

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In my humble opinion, understanding something is compounded by how we understand the meaning and essence of the subject. For example, differential equations are not too hard to understand. If we compound that understanding with a essential value fundamental to its meaning, I believe the understanding has reached a higher dimensional quality. As an analogy, water is quite basic, yet water was believed by the ancient philosophers like Thales to be the most essential and most basic element to all life.

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