What is Certain Knowledge?

Relentless · 2016-01-02 02:49:53

What kinds of truths, in all seriousness, do you think are absolutely impervious to doubt? Suppose that you are the kind of person who does not believe anything you can find the smallest amount of uncertainty in. You will, of course, reject authority, religion, the methods of most fields of knowledge; in fact virtually anything that is merely said or written down. You will only trust things you see for yourself, for a while.

But then it gets more interesting, if you are a ruthless doubter. You will start to question everything outside yourself; you will lose your belief that certain historical events actually occurred, that there is a Great Wall of China, that the earth is spherical or not the centre or even the entirety of the universe. For that matter, why even believe there is an earth, except for what you are currently looking at; perhaps most of it disappears when you turn your back to it. One day, if you persist, you will even doubt that other people have minds like you do, and you will stop believing that they are alive.

Continue in this manner, and one day the following question will occur to you: How do I know I am not dreaming? How do I know I am not in a simulation or a hallucinatory or drug-induced trance? At which point, your doubting mind will systematically assume that everything you experience is totally unreliable.

The question is, what is left? When Descartes tried this thought experiment in the 17th century, he concluded that he knows only that he is having experiences, and therefore that he exists. He did not even believe that mathematical knowledge (1+1=2) or tautological knowledge (all bachelors are unmarried) were absolutely reliable, since he thought we may just be perpetually confused.

For my part, I think certainty is in all of those or nothing. If we can't even lay down definitions with a certain meaning, i.e. we can't ensure that our language correlates at all to our thoughts, then how can anyone say they know for sure that they exist, given that they may not even know what, if anything, the word "exist" refers to? It seems more likely to me that the logical consequences of our definitions in maths, logic and linguistics provide certainty; namely, it is certain that those definitions imply those consequences.

Nehushtan · 2016-01-02 05:20:31

There are two types of knowledge: a priori and a posteriori. A priori knowledge is deductive knowledge such as mathematical axioms and linguistic tautology; as such it is certain knowledge. I don’t know why Descartes thought such knowledge should be unrealiable, really. On the other hand a posteriori knowledge on the other hand is inductive knowledge such as Newton’s laws of motion or the laws of thermodynamics; this is the sort of knowledge that cannot be 100% certain, based as it is on probability.

Calligar · 2016-01-02 09:24:51

To answer the first question (

What kinds of truths, in all seriousness, do you think are absolutely impervious to doubt?

), I'll put a very simple answer, rather than the lengthy one I was going to put. What if I believed 1 + 1 = 4 instead of 2? This knowledge is wrong, though perhaps it is because I'm misunderstanding something, or maybe I'm right in a different sense where I count using numbers differently. However, to make this simple, let's just assume I'm wrong and it is just 1 + 1 = 2. One can still be certain he is right, even though he is wrong. He may actually believe that, and he himself may have no doubts, no matter how many people say he is wrong. Therefore, to answer the question at the beginning, I can argue that 1 + 1 = 4 is a truth absolutely impervious to doubt, and continue to do so with lots of other examples.

Now for the second question (

The question is, what is left?

), which is very dependent on these events. An answer I can also give for this, your own ability to think.

Interesting thing to answer, I'm curious what other people's responses are.

Agnishom · 2016-01-02 13:37:58

I am so glad that you're back

Relentless · 2016-01-02 15:58:08

Hi everyone

I personally agree with Nehushtan that a priori knowledge is certain - this is actually what I meant to say, but without the terminology (it is not a philosophy forum, after all ). But I think there has to be an important qualification to this: We know that particular theorems follow from particular axioms, and particular implications follow from particular definitions. But we don't know for sure in what sense those axioms or definitions are necessarily true.

It's related to what Calligar is getting at. My response to the argument that 1 + 1 = 4 is that if you don't agree that 1 + 1 = 2, then we aren't talking about the same thing; it is true by definition. But that is almost like saying it is true because we said it must be; in what sense is it certain that 2*1 equals 2, or x * 1 equals x, before we have defined those expressions to have that meaning?

It seems to me that all we know for sure is that, for example, GIVEN that x*1 = x, then 1+1=2. Which is quite restricted. Our certain knowledge is entirely conditional.

Last edited by Relentless (2016-01-02 16:09:59)

Agnishom · 2016-01-02 19:58:04

Are we discussing the geitter problem?

Relentless · 2016-01-02 20:32:00

Not really. Although I can see why you'd link it, since the Gettier problem is about how difficult it is to specify the "justified" criterion of knowledge. But it's not the same because most people do not want to define knowledge as certainty; most people are fallibilist. So we aren't specifically discussing the general definition of knowledge at all; unless you want to make knowledge and absolute certainty synonymous.

Last edited by Relentless (2016-01-02 20:34:25)

Relentless · 2016-01-08 05:02:52

What do you think of the Gettier problem, Agnishom? I have not thought about it for a while, but I remember finding it very difficult; and the more you think you have a resolution, the more it slips out of reach.

Agnishom · 2016-01-08 16:34:35

I do not have strong opinions, to be honest

Relentless · 2016-01-08 17:01:06

How do you define knowledge? P:

Math Is Fun Forum

#1 2016-01-02 02:49:53

What is Certain Knowledge?

#2 2016-01-02 05:20:31

Re: What is Certain Knowledge?

#3 2016-01-02 09:24:51

Re: What is Certain Knowledge?

#4 2016-01-02 13:37:58

Re: What is Certain Knowledge?

#5 2016-01-02 15:58:08

Re: What is Certain Knowledge?

#6 2016-01-02 19:58:04

Re: What is Certain Knowledge?

#7 2016-01-02 20:32:00

Re: What is Certain Knowledge?

#8 2016-01-08 05:02:52

Re: What is Certain Knowledge?

#9 2016-01-08 16:34:35

Re: What is Certain Knowledge?

#10 2016-01-08 17:01:06

Re: What is Certain Knowledge?

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