razor’s edge

We have lots of meaningless words, some gain cash-value from their use, some cling to balance sheets as debits. Supercallifragulisticexpeallidocious, for example, is fun to use but ultimately meaningless. Democracy, for another example of similar kind. non-existent is just a combination of words previously accepted, naively, by someone somewhere as having meaning. I could possibly use it to refer to something that once existed in a certain form but no longer exists in that form. or I could use it abstractly, but not as a term in a valid philosophical inquiry. I could say “My bank account is non-existent.” or my “Sex-appeal is non-existent”. 

The closest real use I could apply to ‘nothing’ would be a correspondence to the mathematical abstraction ’0′ and relate it to the Sartre’s existential concept of consciousness as a state of non-being wherein the self is literally not-a-thing. It requires a metaphysical appeal to the phenomenological, transcendental ego understood as pure intentionality, a window cracked open over an opening in the universe, letting in a cold wind that blows freely toward objects. 

God isn’t necessarily a get out of jail free card. Once the boundary of logic has been mapped out, and there still exists unexplained truths and phenomena, then the logic is not sound, or reason has deduced a transcendental argument in defense of metaphysical possibilities.

Finding a valid reason to insert God should be celebrated. Inserting unknown entities into theories should only be considered as a last resort, but once resorted to, God is the most parsimonious of entities possible.

Russell disagrees, arguing that “Whenever possible, substitute constructions out of known entities for inferences to unknown entities.” But Russell had an agenda as he was a raging homosexual pacifist in an era of religiously justified intolerance and barbarism.

Russell even contradicts his own argument in his rejection of solipsism, viz. In The Problems of Philosophy (1912), Bertrand Russell says that although it’s logically possible that solipsism is true, solipsism should be rejected as less simple than the hypothesis that an external world exists.

Yet, as Plantinga brilliantly apologizes in “God & Other Minds”, (and I apologize for this paraphrase) “Belief in the existence of other minds is a proposition similar in kind to the belief in a transcendant God.”

So on one hand Russell is telling us to reject unknown entities in favor of constructions out of known entities, while on the other he tells us that it is simpler to accept an external world, presumably one inclusive of unknowable minds of other beings. Why not construct other minds out of the entity I know as my own mind? Hell, as long as we’re constructing entities, why not construct God out of my own mind or the matter and phenomena I perceive?

In fact, Sir Willam, ‘the Razor’s Edge’ of Ockham himself was a believer in God. He explains that self-evident belief justifies appeals to theism as: “only faith gives us access to theological truths. The ways of God are not open to reason, for God has freely chosen to create a world and establish a way of salvation within it apart from any necessary laws that human logic or rationality can uncover.”

bad questions from bad philosophy boards with bad answers from a bad philosopher

The question was posed on a crappy philosophy board:
Stimulus-
Are there thinkers or schools that start from the point of view that we have a great deal of uncertainty about the world, and then discuss how we should live given those limitations?

Response-
There is nothing intrinsically absurd or uncertain about the world; the world simply is, and we define ourselves by how we relate ourselves to it. The world is indifferent to our attempts to anthropomorphize it with labels and meanings. What we understand as uncertainty about the world is really uncertainty of our own ability to act in the world in ways we approve of. Recognition that attempts to define life are, in fact, veiled definitions of ourselves is a giant leap for mankind.

“This then remains: Remember to retire into this little territory of thy own, and above all do not distract or strain thyself, but be free, and look at things as a man, as a human being, as a citizen, as a mortal. But among the things readiest to thy hand to which thou shalt turn, let there be these, which are two. One is that things do not touch the soul, for they are external and remain immovable; but our perturbations come only from the opinion which is within. The other is that all these things, which thou seest, change immediately and will no longer be; and constantly bear in mind how many of these changes thou hast already witnessed. The universe is transformation: life is opinion.”
-Marcus Aurelius “Meditations”

Also, there are the Transcendentalists and Post-structuralists/Neo-pragmatists that defend the enlightenment heritage we’ve so thoroughly wasted and revive the Kantian skepticism that describes the limitations of our so-called reasonable faculties to provide the understanding with true, meaningful knowledge. Once the subject is aware that he is always already subjugated and constrained by the limits of his own vocabulary, and that there is nothing that exists outside of his own vocabulary lying in wait to cause him problems, then he can accept that he **is** his own life, take responsibility for it and do with it as he pleases.

Freedom is the recognition that life is just a story, and the one living it is the only author and the only reader.

This awareness of acute and complete isolation can be a shock, but is eased by the subsequent realization of sudden enlightenment that allows for reconciliation between the ‘author’ that is being-in-itself and the ‘reader’ that is being-for-itself. An understanding can be reached and an agreement made that the, for the remainder of the story, the author shall only write for the reader what they both wish to read. No longer shall the reader be expected to recite whatever poor prose the author scribbles in the margins. 

The author becomes free after accepting it writes only what is read for-itself; the reader becomes free after accepting it reads only what is written in-itself.

guilt

Here’s the thing, you aren’t born preprogrammed to feel guilty for certain acts. Guilt is an emotion induced by experiential learning from authorities, and those authorities aren’t necessarily worthy of their position much less always correct in their judgements. For example, say you hum to yourself as a child, and your crazy schoolteacher punishes you by humiliating you in front of the class, now you may feel guilty when you want to hum and you let that guilt control your behavior. But why should you? Your schoolteacher was freaking nuts and there’s nothing wrong with humming; maybe that guilt prevents you from ever becoming a great musician or something.

The superego is a moral faculty programmed onto us by authorities and a cultural environment that trains the animal that is human on how to behave within some society. But why should it be obeyed necessarily? If the rules the superego imposes are not logical or they unnecessarily restrict the quality of your life, then accepting the superego basically means you’re getting conned.

Now, there are sociopaths who indeed have no empathy and just do harm for the fun of it. But ‘sociopath’ is also a term that can be used to label any person who is not sufficiently conforming to the authority’s desired behavior, behavior that generally benefits the authority via the exploitation of the subject. In other words, one can be an unwitting slave to the whims of authority, just by accepting their word on what is socially acceptable behavior. In fact, if the ‘socially acceptable behavior’ is not compatible with morally objective behavior, such as don’t murder/torture and what not, then the subject will likely develop some sort of mental complex to defend against socially induced doublethink.

I mean, schools use this term ‘disruption’ or ‘disrespect’ to punish people who fall out of line. But who defines those terms? How is anyone supposed to know before hand every thing that an other could label disrespect? In fact, these terms and others are often included in any code of conduct as a vague catch-all device to be used against anyone who get’s on the authority’s bad side; there’s nothing you can do to defend against them because they are ultimately decided by the authority’s opinion.

When you say “Guilt is a feeling reserved for us moral people,” you make a bit of an error. Most guilt is a feeling reserved for the gullible, and can be created by clever propaganda, punishment, humiliation, and other means; it lets others take advantage of you and is self-perpetuating because you often spread that same guilt onto others you interact with. Now, there are some things you should probably feel guilty about, but you shouldn’t just accept guilt as some natural occurrence that shouldn’t be questioned.

Your analysis of Nietzsche is a bit strange, there is of course a line where suspicion of authority becomes paranoid. But, quite often, authorities should be mistrusted, history is scattered with tyrants, and many of them were certainly never recognized for what they were at the time, and some of them are probably still looked upon favorably.

Also, Nietzsche’s comment “God is dead” is not referring to literal God in the theistic sense. It was more of a response to the philosophy of Hegel, who argued that the State was the supreme agent of rational reason on Earth, or the representative of God’s march through history. Then Napoleon came through and ransacked all the monarchies and science started doing it thing big time, and the old order was increasingly dismantled. Nietzsche’s point was that man no longer needed some Monarch or position of high authority to teach him how to behave by fiat; man could think for himself and live his own life by his own rules.

Some of the philosophy of Nietzsche was adopted by the Nazis; in Triumph of the Will, Hitler famously proclaimed, “The State does not order us! We order the State! We created the State!” His point was that, since Hegel, there has been this push to develop a one world police state (Hegel’s idea of ‘Freedom’) that will control all humanity. Hitler rejected this idea, along with Schopenhauer and Nietzsche, and attempted to preserve the ‘purity’ of the races and nations from intermixing. Today, Hitler’s attempt is looked down upon, but it was all part of Hegel’s dialectic. Marx was also a response to Hegel, but he believed that the one world government should be ruled by the proletariat, not the Bourgeois.

You comment “poor Nietzsche”, but he would probably feel sorry for you. After all, you dismiss negatively sociopaths, but we are, unfortunately, ruled by them; they possess traits that tend to propel them up the corporate and political ladder, so long as the don’t murder anyone or screw little boys. In fact, it would be interesting to do an analysis on royal blood lines to see how many monarchs have genes that predispose them to sociopathy. When sociopaths are making the rules, why is it moral to follow them? It is not moral to be well adjusted to a sick society.

In keeping with the psychoanalysis topic, it is important to describe as well the ego and id. As the superego can be defined as the ideas imposed on you by the rules and customs of social authorities, the ego can be defined as the ideas imposed on you by yourself. In other words, your past actions and your future expectations, which may or may not be well understood by your present self, also can cause you problems. That is, you don’t have perfect recall or complete understanding of your past, and you likely know more than you knew then, but the persistance of memory can still bother you. Likewise, your expectations for the future, may become unobtainable, through no fault of your own, but failure to meet those expectations can still bother you. It can be better to just let the past go and let the future worry about itself; as Wittgenstein said, “Eternal life belongs to those who live in the present”.

We are then left with the Id, those natural, libidinous drives and urges that, if not constrained, will, supposedly, collapse society. Jung was an associate of Freud and also a student of Nietzsche. It is important to note that Freud quite likely did not have a sex obsession and most boys do not really want to kill their father and have sex with their mother. However, if one can become comfortable with the idea of sexy time with the mother, one can likely cast off any other repression that is bothering them but is less taboo by comparison.

Now, Jung broke with Freud on several issues. Importantly, Jung didn’t like the idea of there being “no God”. Maybe he thought that the uncontrollable quest to become ubermensch would lead to the destruction of mankind or something. Therefore, he explored this idea of the ‘collective unconscious’. This new God is not the state or authority, but a meaningful connection between each human being. It is not the purely selfish drive of the Id, but neither is it the pure, uncaring reason of the Authority and SuperEgo. It is a intuitive categorical imperative, if you will.

So a guy knocks on your door and tells you he is looking for a girl who is visiting your house. The guy wants to kill the girl…

I include Kant’s response to the issue of the Inquiring Murderer. Fun read but tedious as Kant normally is.

http://oll.libertyfund.org/?option=com_staticxt&staticfile=show.php%3Ftitle=360&chapter=61937&layout=html&Itemid=27

Some highlights: Now, the first question is whether a man—in cases where he cannot avoid answering Yes or No—has the right to be untruthful. The second question is whether, in order to prevent a misdeed that threatens him or some one else, he is not actually bound to be untruthful in a certain statement to which an unjust compulsion forces him.

Truth in utterances that cannot be avoided (1) is the formal duty of a man to everyone, however great the disadvantage that may arise from it to him or any other; and although by making a false statement I do no wrong to him who unjustly compels me to speak, yet I do wrong to men in general in the most essential point of duty, so that it may be called a lie (though not in the jurist’s sense), that is, so far as in me lies I cause that declarations in general find no credit, and hence that all rights founded on contract should lose their force (2); and this is a wrong which is done to mankind.

If, then, we define a lie merely as an intentionally false declaration towards another man (3), we need not add that it must injure another; as the jurists think proper to put in their definition (mendacium est falsiloquium in præjudicium alterius). For it always injures another; if not another individual, yet mankind generally, since it vitiates the source of justice. This benevolent lie may, however, by accident (casus) become punishable even by civil laws; and that which escapes liability to punishment only by accident may be condemned as a wrong even by external laws. For instance, if you have by a lie hindered a man who is even now planning a murder, you are legally responsible for all the consequences. But if you have strictly adhered to the truth, public justice can find no fault with you, be the unforeseen consequence what it may. It is possible that whilst you have honestly answered Yes to the murderer’s question, whether his intended victim is in the house, the latter may have gone out unobserved, and so not have come in the way of the murderer, and the deed therefore have not been done; whereas, if you lied and said he was not in the house, and he had really gone out (though unknown to you) so that the murderer met him as he went, and executed his purpose on him, then you might with justice be accused as the cause of his death (4). For, if you had spoken the truth as well as you knew it, perhaps the murderer while seeking for his enemy in the house might have been caught by neighbours coming up and the deed been prevented. Whoever then tells a lie, however good his intentions may be, must answer for the consequences of it, (5) even before the civil tribunal, and must pay the penalty for them, however unforeseen they may have been; because truthfulness is a duty that must be regarded as the basis of all duties founded on contract, the laws of which would be rendered uncertain and useless if even the least exception to them were admitted.

Every man has not only a right, but the strictest duty to truthfulness in statements which he cannot avoid, whether they do harm to himself or others. He himself, properly speaking, does not do harm to him who suffers thereby; but this harm is caused by accident (6). For the man is not free to choose, since (if he must speak at all) (1) veracity is an unconditional duty.

Justice must never be accommodated to the political system, but always the political system to justice. All practical principles of justice must contain strict truths, and the principles here called middle principles can only contain the closer definition of their application to actual cases (according to the rules of politics), and never exceptions from them, since exceptions destroy the universality, an account of which alone they bear the name of principles. (7)

1. Kant is being coy here. He is recommending that one keep one’s mouth shut or respond in ways that, without lying, do not directly answer the question or delay the answering, possibly giving the friend time to escape or hide (If he knows what is good for him). One can maintain a right intention to tell the truth without a requirement to tell the truth immediately, lest one blurt out the first words that spring to mind without making use of the faculty of reason.

2. To me, society has already reached the point where rights founded on contract have lost all force (particularly as a result of unbridled global capitalism and psychological marketing in all facets of social life), and this is not something that will be easily restored. However, Kant specifically calls out contractual rights, not natural rights, which he would likely agree are inalienable and include life, liberty, and pursuit of happiness. Kant would place natural rights on a higher plane than legal rights, viz. he wouldn’t tell the truth if it meant the certain destruction of the entire planet.

3. Here Kant is making a distinction, or rather a conjunction, of lies, malicious lies, white lies, and false witness.

4. This seems to be Sartre’s view, as well.

5. This is a grandslam homerun and Kant could have just stopped writing here. This goes for *all lies*. We are always responsible for all consequences that stem from our actions. The guilt of freedom can be crushing.

6. Kant makes the point that it is not the lie or the truth that does the harm to the friend, but the act of the murderer himself. This point rightly crushes Utilitarianism, as no multiplicity of consequences can be properly comprehended and calculated. There is no Laplace’s demon and it necessarily can never be. In other words, one wrong does not make a right. A man might travel back in time to assassinate Hitler only to discover that a greater villain subsequently took control of the Nazi Party and led it to world domination.

7. Which is why the world order is due for a nasty revolution. There is no justice, certainly not universal. The powers-that-be are trying to save a sinking ship by funneling water into it.

In closing: Lies are fundamentally entropic and destabilizing. Especially, in larger societies and ‘modern’ cultures. When a general population is inclined to secrecy aka privacy, a just ruler has only his own opinion on which to base his judgements. Thus society becomes ‘two-faced’ and gives itself laws against a certain practice even though the vast majority of the population, in fact, enjoys and commonly performs said practice without any harm to one another. Had each been aware of the other’s supposedly ‘dirty’ laundry, their judgement would not be so erroneous. If the population clings to secrecy because it fears the wrath of its government, it should replace the government with one that is less tyrannical instead of cloaking itself in shadows.

Love is the whole of the law.

Free-Will, Polysemy, Contingency, Imagination, and Memory

http://philosophy.eserver.org/kant-prolegomena.txt

I like Kant, without him and Schopenhauer, Einstein would likely never have developed Relativity. But Kant didn’t know that space and time were intertwined, his critiques only allowed later thinkers to come to that conclusion. Because time and vocabulary are relative to each observer, and each observer is *in* the world, we necessarily are *not* determined. Or rather, if you *are* determined, it is only because you have *chosen* to not exercise your free-will.

http://en.wikipedia.org/wiki/Duration_(philosophy)

Words can have different meanings (Polysemic). And your ability to use and understand words improves as you have experiences (“Existence precedes essence” -Sartre) and learn new words, new meanings of words, and new ways that words relate to other words (Contingency). When you are 50 years old you know much more than you did when you were 10 years old; but when you are 50 do you still hold the same opinions that you did when you were 10? Do you let yourself be ‘determined’ by the memories and experiences of a child, or do you put your 50 year old self in the shoes of your 10 year old self’s memories to replace your ignorant childhood opinions with less ignorant adult opinions? The worst lie one can ever content oneself with is that one knows the ‘truth’, at least in some permanent sense.

“When I left him, I reasoned thus with myself: I am wiser than this man, for neither of us appears to know anything great and good; but he fancies he knows something, although he knows nothing; whereas I, as I do not know anything, so I do not fancy I do. In this trifling particular, then, I appear to be wiser than he, because I do not fancy I know what I do not know.” -Socrates

http://en.wikipedia.org/wiki/Contingency,_Irony,_and_Solidarity

“Jean-Paul Sartre came up with an interesting free will argument. He said that we can ignore something real and we can pretend something unreal. For example, I could imagine that there is no danish before me — something I often need to do in the service of dieting. Or I can see the poppy seeds in the muffins as maggots. This imagination is a powerful thing! But the determinist would just say that imagination is just one more neurological mechanism, explainable by deterministic principles.”

“Freedom is what you do with what has been done to you.” -Sartre

http://webspace.ship.edu/cgboer/freewill.html

Now, as the White Queen says to Alice in Lewis Carroll’s ‘Through the Looking Glass’, “It is a poor sort of memory that only works backwards”. Likewise, it is a poor sort of imagination that only works forwards. We can, as Sartre recommends, ignore and pretend in the present. We can also, as William James argues, use imagination to achieve real results that would never have been possible had we not first imagined their possibility.

“James’ central argument in “The Will to Believe” hinges on the idea that access to the evidence for whether or not certain beliefs are true depends crucially upon first adopting those beliefs without evidence. As an example, James argues that it can be rational to have unsupported faith in one’s own ability to accomplish tasks that require confidence. Importantly, James points out that this is the case even for pursuing scientific inquiry. James then argues that like belief in one’s own ability to accomplish a difficult task, religious faith can also be rational even if one at the time lacks evidence for the truth of one’s religious belief.”

http://en.wikipedia.org/wiki/The_Will_to_Believe

But even more critical to free-will is our ability to re-imagine the past. For example, in Derrida’s “The Post Card”, he is struck by the role-reversal of Plato dictating to Socrates, a possibility that, if taken for fact, could restructure a very large number of a philosopher’s opinions. The question then becomes, if such a fantastical belief *improves* one’s opinions and quality of life, why not take it for fact? Plato and Socrates certainly aren’t around to care, and if anyone living takes great offense to your private fantastical historical flights of fancy, it is, for them, a personal problem.

http://en.wikipedia.org/wiki/The_Post_Card:_From_Socrates_to_Freud_and_Beyond

We are *apperceptive* beings. We have memory, foresight, and imagination. We can firmly root ourselves in the present, the Buddha’s middle path, if we ‘let go’ of the past by embracing love and forgiveness (even for our enemies), and we stop fearing the future by freeing ourself of desires (even for our own life). Once our consciousness is no longer stretched across the past and the future, our true self is revealed, and we our free to change our opinions of the past and the future to ensure the most positive outcome in the present. If we always focus on the positive outcomes in the present, the past will heal itself and the future will worry about itself.

“This then remains: Remember to retire into this little territory of thy own, and above all do not distract or strain thyself, but be free, and look at things as a man, as a human being, as a citizen, as a mortal. But among the things readiest to thy hand to which thou shalt turn, let there be these, which are two. One is that things do not touch the soul, for they are external and remain immovable; but our perturbations come only from the opinion which is within. The other is that all these things, which thou seest, change immediately and will no longer be; and constantly bear in mind how many of these changes thou hast already witnessed. The universe is transformation: life is opinion.” -Marcus Aurelius

http://www.studenthandouts.com/marcus.pdf

“If we take eternity to mean not infinite temporal duration but timelessness, then eternal life belongs to those who live in the present.” -Ludwig Wittgenstein

‘It’s a poor sort of memory that only works backwards,’ the Queen remarked.
‘What sort of things do you remember best?’ Alice ventured to ask.
‘Oh, things that happened the week after next,’ the Queen replied in a careless tone. ‘For instance, now,’ she went on, sticking a large piece of plaster on her finger as she spoke, ‘there’s the King’s Messenger. He’s in prison now, being punished: and the trial doesn’t even begin till next Wednesday: and of course the crime comes last of all.’
‘Suppose he never commits the crime?’ said Alice.
‘That would be all the better, wouldn’t it?’ the Queen said, as she bound the plaster round her finger with a bit of ribbon.
Alice felt there was no denying that. ‘Of course it would be all the better,’ she said: ‘but it wouldn’t be all the better his being punished.’
‘You’re wrong there, at any rate,’ said the Queen. ‘Were you ever punished?’
‘Only for faults,’ said Alice.
‘And you were all the better for it, I know!’ the Queen said triumphantly.
‘Yes, but then I had done the things I was punished for,’ said Alice: ‘that makes all the difference.’
‘But if you hadn’t done them,’ the Queen said, ‘that would have been better still; better, and better, and better!’ Her voice went higher with each ‘better’, till it got quite to a squeak at last.
Alice was just beginning to say ‘There’s a mistake somewhere —,’ when the Queen began screaming, so loud that she had to leave the sentence unfinished. ‘Oh, oh, oh!’ shouted the Queen, shaking her hand about as if she wanted to shake it off. ‘My finger’s bleeding! Oh, oh, oh, oh!’
Her screams were so exactly like the whistle of a steam-engine, that Alice had to hold both her hands over her ears.
‘What is the matter?’ she said, as soon as there was a chance of making herself heard. ‘Have you pricked your finger?’
‘I haven’t pricked it yet,’ the Queen said, ‘but I soon shall — oh, oh, oh!’
‘When do you expect to do it?’ Alice said, feeling very much inclined to laugh.
‘When I fasten my shawl again,’ the poor Queen groaned out: ‘the brooch will come undone directly. Oh, oh!’ As she said the words the brooch flew open, and the Queen clutched wildly at it, and tried to clasp it again.
‘Take care!’ cried Alice. ‘You’re holding it all crooked!’ And she caught at the brooch; but it was too late: the pin had slipped, and the Queen had pricked her finger.
‘That accounts for the bleeding, you see,’ she said to Alice with a smile. ‘Now you understand the way things happen here.’
‘But why don’t you scream now?’ Alice asked, holding her hands ready to put over her ears again.
‘Why, I’ve done all the screaming already,’ said the Queen. ‘What would be the good of having it all over again?’

Kant’s Prolegomena continues…

§ 10. We can intuit things a priori only through the mere form of sensuous intuition. In so doing, we can only know objects as they appear to us, not as they are in themselves, apart from our sensations. Mathematics is not an analysis of concepts. Mathematical concepts are constructed from a synthesis of intuitions. Geometry is based on the pure intuition of space. The arithmetical concept of number is constructed from the successive addition of units in time. Pure mechanics uses time to construct motion. Space and time are pure a priori intuitions. They are the mere forms of our sensations and exist in us prior to all of our intuitions of objects. Space and time are a priori knowledge of a sensed object as it appears to an observer.

§ 11. The problem of a priori intuition is solved. The pure a priori intuition of space and time is the basis of empirical a posteriori intuition. Synthetic a priori mathematical knowledge refers to empirically sensed objects. A priori intuition relates to the mere form of sensibility; it makes the appearance of objects possible. The a priori form of a phenomenal object is space and time. The a posteriori matter of a phenomenal object is sensation, which is not affected by pure, a priori intuition. The subjective a priori pure forms of sensation, namely space and time, are the basis of mathematics and of all of the objective a posteriori phenomena to which mathematics refers.

§ 12. The concept of pure, a priori intuition can be illustrated by geometrical congruence, the three–dimensionality of space, and the boundlessness of infinity. These cannot be shown or inferred from concepts. They can only be known through pure intuition. Pure mathematics is possible because we intuit space and time as the mere form of phenomena.

§ 13. The difference between similar things which are not congruent cannot be made intelligible by understanding and thinking about any concept. They can only be made intelligible by being intuited or perceived. For example, the difference of chirality is of this nature. So, also, is the difference seen in mirror images. Right hands and ears are similar to left hands and ears. They are not, however, congruent. These objects are not things as they are apart from their appearance. They are known only through sensuous intuition. The form of external sensible intuition is space. Time is the form of internal sense. Time and space are mere forms of our sense intuition and are not qualities of things in themselves apart from our sensuous intuition.

Part one of the main transcendental problem. How is pure mathematics possible?

http://en.wikipedia.org/wiki/Prolegomena_to_Any_Future_Metaphysics#Part_one_of_the_main_transcendental_problem._How_is_pure_mathematics_possible.3F

§ 6. Mathematics consists of synthetic a priori knowledge. How was it possible for human reason to produce such a priori knowledge? If we understand the origins of mathematics, we might know the basis of all knowledge that is not derived from experience.

The origin of mathematics lies in the synthetic geometry of Euclid’s Elements. When Descartes converted these ideas into his Analytic Geometry, he used numbers and equations as a shorthand method for describing geometric forms. However, the signifier ’1′  (and likewise all numbers and mathematical operators) has no natural referent in the world of experience and is therefore meaningless by itself. 1 + 1 = 2 is nothing but a tautology when considered a priori and Russell and Whitehead’s ‘Principles of Mathematics’ is a complete trainwreck as are all critiques of the Enlightenment which are Numerocentric in thinking.

I can pick 1 or 2 apples from a tree. But I cannot pick a 1 or 2 from a tree.

More, unless I have witnessed someone picking 1 or 2 apples from a tree, or I had prior knowledge of the quantify signified by those numerical signifiers, when commanded “Go and pick 2 apples from that tree,” I would have no idea what to do.

However, if I was commanded “Go and pick the best apple from that tree,” it is quite likely I would pick the one I found to be most aesthetically pleasing, that is the roundest most geometrically perfect apple, free from bruises cuts or deformations. This is because I would somehow understand, as synthetic a priori, that objects closer to ideal geometric forms are more aesthetic and thus ‘better’ than those which are deformed. And this is knowledge that is intrinsically shared by all mankind.

I once thought still life paintings quite silly. Now I see them as representations of the most basic and beautiful truths available to us.

 

From Kant’s Prolegomena

2. Mathematical judgments are all synthetical. This fact
seems hitherto to have altogether escaped the observation of
those who have analyzed human reason; it even seems directly
opposed to all their conjectures, though incontestably certain,
and most important in its consequences. For as it was found that
the conclusions of mathematicians all proceed according to the
law of contradiction (as is demanded by all apodictic certainty),
men persuaded themselves that the fundamental principles were
known from the same law. This was a great mistake, for a
synthetical proposition can indeed be comprehended according to
the law of contradiction, but only by presupposing another
synthetical proposition from which it follows, but never in
itself.

     First of all, we must observe that all proper mathematical
judgments are a priori, and not empirical, because they carry
with them necessity, which cannot be obtained from experience.
But if this be not conceded to me, very good; I shall confine my
assertion pure Mathematics, the very notion of which implies that
it contains pure a priori and not empirical cognitions.

     It might at first be thought that the proposition 7 + 5 = 12
is a mere analytical judgment, following from the concept of the
sum of seven and five, according to the law of contradiction. But
on closer examination it appears that the concept of the sum Of
7+5 contains merely their union in a single number, without its
being at all thought what the particular number is that unites
them. The concept of twelve is by no means thought by merely
thinking of the combination of seven and five; and analyze this
possible sum as we may, we shall not discover twelve in the
concept. We must go beyond these concepts, by calling to our aid
some concrete image [Anschauung], i.e., either our five fingers,
or five points (as Segner has it in his Arithmetic), and we must
add successively the units of the five, given in some concrete
image [Anschauung], to the concept of seven. Hence our concept is
really amplified by the proposition 7 + 5 = I 2, and we add to
the first a second, not thought in it. Arithmetical judgments are
therefore synthetical, and the more plainly according as we take
larger numbers; for in such cases it is clear that, however
closely we analyze our concepts without calling visual images
(Anscliauung) to our aid, we can never find the sum by such mere
dissection.

     All principles of geometry are no less analytical. That a
straight line is the shortest path between two points, is a
synthetical proposition. For my concept of straight contains
nothing of quantity, but only a quality. The attribute of
shortness is therefore altogether additional, and cannot be
obtained by any analysis of the concept. Here, too, visualization
[Anschauung] must come to aid us. It alone makes the synthesis
possible.

     Some other principles, assumed by geometers, are indeed
actually analytical, and depend on the law of contradiction; but
they only serve, as identical propositions, as a method of
concatenation, and not as principles, e. g., a=a, the whole is
equal to itself, or a + b > a, the whole is greater than its
part. And yet even these, though they are recognized as valid
from mere concepts, are only admitted in mathematics, because
they can be represented in some visual form [Anschauung]. What
usually makes us believe that the predicate of such apodictic5
judgments is already contained in our concept, and that the
judgment is therefore analytical, is the duplicity of the
expression, requesting us to think a certain predicate as of
necessity implied in the thought of a given concept, which
necessity attaches to the concept. But the question is not what
we are requested to join in thought to the given concept, but
what we actually think together with and in it, though obscurely;
and so it appears that the predicate belongs to these concepts
necessarily indeed, yet not directly but indirectly by an added
visualization [Anschauung].