I think that one of most important goals of philosophy is the idea of understanding (of the world, our being in the world, or in general relations between things of which we are aware). To be an understanding it needs to carry necessity – to remove a “why?” questions. The knowledge alone doesn’t produce understanding, and while one can learn things from experience about some relation, the question of “why this state of affairs is true in reality and not some other?” is left unanswered.
However, I want to point to two interesting situations that arise:
- We can check experience in order to confirm our understanding, and
- We may in some cases come to understand something after we have learned it from experience.
But isn’t there something wrong with (1) and (2)?
While we might feel that there is something strange, I think if we think of some examples they appear very normal…
A mathematician can check his theorem by checking if it works on concrete examples.
Or she might first learn about some regularity by just playing with some mathematical entities, and only then understand the nature of that regularity (why the given relation holds).
Programmers (hopefully) understand how the code they write will implement the intended behavior. But they test those programs. And really often find bugs. So, the bugs are the sign that there was something wrong with their understanding. They maybe overlooked something, or had wrong assumptions somewhere. And (hopefully) they will understand why the bug appeared, and with this new (richer) understanding, they can fix the code.
Also often in understanding the bug, programmer will try a bunch of concrete cases, in order to shrink the number of the possible causes of the bug, and only after that get to reading the relevant parts of the code.
So, while I think that those relations between understanding and learning from experience as in (1) and (2) are normal, we need a way to resolve two problems here:
a) the apparent contradiction between the understanding carrying necessity and yet also there being possibility to turn out wrong.
b) the value of understanding once we already have knowledge from experience.
UPDATE:Changed the title, because it was kind of silly. (It was ‘Can A Priori Knowledge be False’)
Swiss invented time so as to sell more clocks.
Philosophers’ Carnival #53 (in a form that I like the best) is over at UNF Philosophy Blog.
Vallicella at Maverick Philosopher has little discussion of sqrt(2) [square root of 2] in this post. It is related to his previous posts on the issue of actual vs. potential infinites. In the post Vallicella says:
Suppose you have a right triangle. If two of the sides are one unit in length, then, by the theorem of Pythagoras, the length of the hypotenuse is the sqr rt of 2 = 1.14159. . . . And yet the length of the hypotenuse is perfectly definite, perfectly determinate. If the points in the line segment that constitutes the hypotenuse did not form an infinite set, then how could the length of the hypotenuse be perfectly definite?
What I want to point is that the hypotenuse doesn’t have any particular number related to it. It is square root of 2, only in relation with the sides which *are taken to be* 1. The nature of the number to be a ratio is shown here… the number which we assign to the hypotenuse is about the ratio between it and the other sides. However, we could instead take the hypotenuse to be 1, and the sides would be then sqrt(1/2). Or we could take the sides to be 3, and the hypotenuse would be then 3sqrt(2), etc… We see that what doesn’t change is the ratio, and what is perfectly definite here is the ratio.
Now, is there anything infinite here? I don’t think so… the hypotenuse and the other sides of the right triangle have a certain and limited length. Also, such as they are, we can speak of the ratio they form, and hence speak of numbers in relation to them. But numbers are not merely sums – we might *try* to express the ratio of the hypotenuse and the side of the right triangle through a sum, but in the given case we will fail. And this failing, this impossibility to finish with the “translation” of this ratio from its “definiteness” into our numerical notation, IS what we have as infinity here. We just can’t succeed into finishing this translation *because it can’t be done*! Some things can’t be translated into aggregates or sums. That is because there is more to this world than aggregates (or sums).
This ratio also has relations to other ratios which can be expressed as ratio of whole numbers. It can be bigger than some of those ratios and smaller than others. And just because of it, there is possibility of getting as close as needed to this ratio by using ratios of whole numbers. (Of course the ratio of rational numbers also falls under ratio of whole numbers as a/b:c/d is nothing other but the a*d/b*c ratio of whole numbers).
Of course, we can continue this translation as much as we can, and only because it will never succeed, we might be inclined to say that the product of this translation is infinite. But if we search for an ‘actual infinity’, it will not show itself in the results of some repeating iteration, but what is just “imperfectly” expressed by this sum, is as actual, definite and finished in the form of the term sqrt(2) (*and all of different cases which share the ratio with the ratio between the hypotenuse of the right triangle, and it’s side*, or which can be showed as identical).
Seems to me, that if we want to talk about actual infinity, we can just talk about being infinite in relation to something else – i.e. that that former can’t be reduced to the later.
Can you recognize the following scheme?
1.Have a bad metaphysics
2.Interpret the scientific results through the prism of this metaphysics
3.Deny that you have metaphysics, but think of the interpretation as the result of the science itself.
4.When the resulting metaphysical picture doesn’t make sense, blame the reason itself!
By bad metaphysics I think here of the metaphysics where what is taken as ground of all phenomena is little self-subsistent particles, with their self-subsistent properties existing in the self-subsisting space-time container, and where some self-subsistent physical laws (which are seen as more or less arbitrary, so that it is just matter of some incident that they are such as they are) control what happens with the former.
The combination of this metaphysics with the empirical results has given us all kind of strange results in Relativity and Quantum Mechanics, which are said to be “unintuitive”.
And instead of being critical of this “invisible” metaphysics, what is done?
It is said that evolution tends to select useful traits. Our faculty of reason is nothing more than such a trait. It is selected for reasons which are connected to our staying alive and reproducing in particular environments, so we are not to expect that it is infallible and if something doesn’t make sense to us (even under our ideal reasoning), doesn’t mean that it is impossible in reality. We are not to wonder why we get weird results “from science”.
So, instead blaming bad thinking, we are to blame the thinking in general!
I’ve quoted Hegel on this once, by I think it is worth repeating:
At present, students of nature who are anxious to avoid metaphysics turn a favorable ear to Atomism. But it is not possible to escape metaphysics and cease to trace nature back to terms of thought, by throwing ourselves into the arms of Atomism. The atom, in fact, is itself a thought; and hence the theory which holds matter to consist of atoms is a metaphysical theory.[…] The real question is not whether we shall apply metaphysics, but whether our metaphysics are of the right kind.
I had a discussion with a friend few days ago about non-intentional mental phenomena. Here is what I ended up defending…
In our lives we are sometimes nervous, sometimes uneasy, sometimes sad, and sometimes happy and eclectic.
But we are not nervous, uneasy, sad, and happy towards something. We are nervous, uneasy, etc… because of something. Sometimes it is a reason that we are aware of, but other times it might be result just of chemical imbalance in our body. But in both cases, even if the reason is something that we are aware of, the nervousness, happiness, or sadness are not connected to just that particular content, but are present through (or within) the other mental acts that we do. So even I’m nervous because my work wasn’t appreciated enough, the nervousness won’t be limited only to the thoughts of the boss not appreciating my work.
Here we can point that often we do use “sad about X”, or “nervous about X”. For example “She is sad about John’s leaving the city”, or “He is nervous about the meeting”, and so on… Also we ask “What is he/she nervous about?” or “What is he/she happy about?”
Of course in those cases, while the “about” points to the reason why somebody is sad, nervous, happy, and so on, we don’t think that the nervousness is special mental act oriented towards the intentional content in question. In fact we can probably say, that whenever the person thinks *about*…, or remembers *that*…, he gets sad, nervous, happy, and so on. And while there are verbs (or if there aren’t we can invent ones) which relate to those nouns, I don’t think that the verbs will point to genuinely simple intentional acts, but to thinking about/remembering of etc… something combined with how we are affected by it (i.e. how it makes us sad, happy, and so on…)
For those reasons it seems to me unproblematic to say that there are non-intentional mental phenomena (for which we have names, e.g. ‘sadness’, ‘happiness’, ‘nervousness’, etc…).
But to accept that there are non-intentional mental phenomena is not to say that those phenomena can be self-subsistent, i.e. that there can be some part of our life where we can be merely sad, happy, nervous, and so on without in same time performing any intentional act. In other words even if we accept that there are non-intentional mental phenomena, it doesn’t follow that any actual part of our conscious life can
be without intentionality.
I will try to give analogy with objects, their form and their color. We can say that there is a phenomenon of colors which doesn’t fall under phenomenon of form, but that still color can be present only if there are objects, and all objects have form. So while we can talk about non-form phenomena in case of objects (i.e. colors), there can’t be merely colored object without that object having form. Or… that color will always show itself in the actual cases as related to some form. In this analogy ‘object’ stands for part of our conscious life, ‘color’ for non-intentional mental phenomena, and ‘form’ for intentional mental phenomena.
I was trying to systematize my views a little, so I ended up with this rough Wittgenstein-like outline…
1 We become aware of things
1.1 We become aware of objects
1.2 We become aware of objects’ properties
1.2.1 Awareness of objects’ properties include awareness of the object
1.3 We become aware of events.
1.3.1 Awareness of events includes awareness of objects involved in those events
1.4 We become aware of relations
1.4.1 Awareness of relations includes awareness of relata
1.4.2 We become aware of multitudes and their similarity
1.5 We are aware of the things we imagine, and things we assume.
2 Things of which we are aware are in relation of context and aspect
2.1 Aspects don’t exist as self-subsistent, but exist only because the context exists.
2.1.1 Properties exist only as properties of the objects.
2.2 Aspects can have further aspects, and contexts further contexts
2.2.1 An object has color. Color has hue and brightness as aspects
2.3 Different aspects of the same thing are related because of sharing common ground (the context on which they are dependent)
2.3.1 One is always affecting the context. The affecting of the aspect is only secondary (abstract), even we might not be aware of it
18.104.22.168 One can’t merely change the position of an object. What one does is changing the context of bodies, so that the distance between different bodies will be different.
2.4 Sometimes we are aware of the aspects but not of the context
2.4.1 In such cases we tend to think of the aspects as self-subsistent
2.4.2 When we think about those things we encounter contradictions because of their assumed self-subsistence
22.214.171.124 Zeno’s paradoxes appear because of imagined self-subsistence of space and time
2.4.3 The way out of this is becoming aware of the context, and becoming aware of how those assumed self-subsistent things are actually aspects of the context (one might already be aware of context, but not aware of the context-aspect relation)
2.4.4 Bachelorhood is aspect of certain kind of social relations
2.4.5 Phenomenon of chairs is aspect of our society, needs, etc..
3 We perceive some things
3.1 Our perception is limited, and picks-out certain aspects of the world
3.1.1 The color we see is an aspect of objects.
3.2 There is no experience which represents things, and which has what-it-is-like aspect
3.2.1 We have experience in the sense that we participate in the events of which we are aware (and we learn something from them, or we are affected some way from them)
3.2.2 The what-it-is-like is wrongly assumed because the physical is not taken to be aspect
3.2.3 The representational faculty is assumed to explain the illusions, hallucination and dreams
126.96.36.199 About general way to address those without accepting experience as representing things see (6.1)
4 We become aware of other people
4.1 We become aware of other people being aware of the things
5 We give names to what we are aware of
5.1 When the intentional content is an individual thing, we speak of proper names
5.2 We give names to the multitude sharing certain aspect – those are the common nouns.
5.3 Individual events and relations, and also multitudes of events and relations sharing certain aspect can be given proper names, or common names too.
5.4 We can name imagined or assumed content
6 We are not aware of everything about the context
6.1 We might mistake one context for another, because the former shares some aspect with the later.
6.1.1 We might mistake virtual thing for a real thing if we are unaware that we wear virtual reality glasses
6.2 Of course we can become aware of the things we weren’t aware of.
7 Using language is acting
7.1 One of the use of language is making someone aware of something through sentences
7.2 The sentences describe the relations (of which the other is not aware) through words for things (of which the other is aware)
7.3 The sentences might introduce new words (of which the listener becomes aware while listening the sentence)
8 Some things have a physical aspect
8.1 Physical aspect is not self-subsistent
8.1.1 World is not reducible to physical
8.2 The physical aspect is the measurable aspect
8.2.1 Measurement is comparing – it is making a ratio between two magnitudes
8.2.2 There are truths about numbers as ratios
8.2.3 Those are truths of the physical aspect
8.2.4 The number aspect is not self-subsistent, but dependent on the context. The number-truths are true of the number aspect just as long this aspect exists as part of the context.
8.3 Our awareness of things has physical aspect
8.3.1 Our awareness of things is not reducible to the physical aspect
8.3.2 The physical aspect of our awareness of things includes the physical aspects of our bodies, the physical aspect of the things of which we are aware, and the physical aspect of the acts of perception (including the physical aspect of the history)
8.3.3 When our awareness changes, the physical aspect will probably (but not necessarily) change too.
8.4 We are affecting physical aspect through affecting the context (see 2.3) even if we are not aware of that
8.4.1 When affecting certain brain parts, we are really affecting our awareness of things