The least of things with meaning is worth more in life than the greatest of things without it.
Carl Jung, Modern Man In Search Of A Soul.
The least of things with meaning is worth more in life than the greatest of things without it.
Carl Jung, Modern Man In Search Of A Soul.
Where there is no hope, it is incumbent on us to invent it. You can’t create experience, you undergo it.
Albert Camus, The Fall.
…what is pretty cannot be beautiful.
Ludwig Wittgenstein, Reflections On Reality In It’s Various Manifestations.
Founders of religion and philosophers come into the world to shake him out of his torpidity and show him the high significance of existence: philosophers for the few, the emancipated; founders of religion for the many, humanity at large. For a philosophical crowd is impossible…
Arthur Schopenhauer, On Religion.
02.11.21 I Day 18 out of 100
I’m gonna be a senior year and I’ve been buying books to help me start planning my senior thesis. I’m been interesting and I hope it will be worth it.
✔️Daily Morning Habits
✔️Rights Readings
✔️Reading for Honors
✔️Meeting with Professor
✔️Meal Prep
✔️Painting
~MP
It is society, our tame, mediocre, castrated society, in which an untutored son of nature who comes to us from his mountains or from his adventures at sea, must necessarily degenerate into a criminal.
Friedrich Nietzsche, The Criminal And His Like.
…everything that guarantees the future involves pain…
Friedrich Nietzsche, The Twilight Of The Idols.
The progress of life shows a man the stuff of which he is made.
Arthur Schopenhauer, Counsels And Maxims.
Objective judgement, now, at this very moment. Unselfish action, now at this very moment. Willing acceptance— now, at this very moment—of all external events. That’s all you need.
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Marcus Aurelius, The Meditations.
The largest library in disorder is not so useful as a smaller but orderly one; in the same way the greatest amount of knowledge, if it has not been worked out in one’s own mind, is of less value than a much smaller amount that has been fully considered.
Arthur Schopenhauer, On Thinking For Oneself.
(Pictured: The multitalented Ada Lovelace (b. 1815) was a mathematician and is often regarded as the world’s first computer programmer.)
What are numbers? You can’t think them into existence mentally. You can’t bump into them physically. And you’d be wild to follow Plato in believing they exist as changeless abstract objects outside of spacetime. So what are they?!
Let’s start with 2.
‘“2” denotes a pair of things,’ you might say, pointing two fingers from a clutched hand.
But that’s cheating! Here ‘pair’ signifies what 2 is, ensuring your definition is circular, like a serpent eating its tail. The challenge applies to all numbers, not just 2, all the way to infinity.
[Cantor to the rescue!]
Mathematician Georg Cantor offered an interesting solution with his theory of infinite sets.
Sets are definable collections of things, not just numbers. For example, take teacups, black cats, and books. Each collection is a set because its members share something in common: they are all kinds of teacups, black cats, or books. In set-theoretic notation we might group together a set M of mathematicians, {Euclid, Lovelace, Turing . . . }, in which Lovelace, l, is a member. Thus l ∈ M (‘l is a member of M’).
We use the same syntax for numbers.
Let’s start with absolutely nothing (zero) and symbolise it with ‘Ø’.
Then let’s say ‘1’ is the set of nothing, {Ø}.
Nice.
Then let’s say ‘2’ is the set of ‘1’, {{Ø}} …
Woo! Can you see what’s happening? We’re actually defining 2 without reference to itself! And we can go on infinitely (in theory)!
Numbers, Cantor thought, are expressions of sets of sets of sets … each a distinct object.
His philosophy on the nature of numbers was a precursor to further work, in which he claimed mathematicians were free to posit the existence of abstract things so long as they were devoid of internal contradiction.
However, Cantor’s view is controversial: if you think about it, he argued that Ø—nothing!—founds all other numbers like 1, 2, and 3. This is a bit absurd, don’t you think?
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I am need of your assistance. Are there any philosophy studyblrs out there or any tags I can follow for philosophy. I’m taking an honors course and my brain already hurts after one week of classes. I need to self-study this asap. Thanks in advance!
- Sam
It is pleasure for all poor devils to grumble, it gives them a little intoxicating sense of power.
Friedrich Nietzsche, Twilight Of The Idols.
We are lived by powers we pretend to understand.
W.H Auden, In Memory Of Ernst Toller.
Today we travel back to Ancient Greece to the times of Eubulides of Miletus, who is usually credited with ‘sorites paradox’, which goes like this.
Picture a single grain of something—say, rice, wheat, or sand. Let’s go with sand. Start with one grain. Then add one grain at a time to your collection. Here’s the paradox.
In our description, when does the collection of grains become a heap? It never seems to. According to the language we used to describe the collection—through ‘grain’—the sand always remains granular, no matter how many grains we add.
We can work in reverse, too: if we start with a heap of sand and take one grain away at a time, we are always left with a heap.
Thus, howsoever we start in our description, sand always remains as either a collection of grains or a heap: it cannot change from one to the other. Intuitively, this doesn’t sit well: we ordinarily put so much trust into language—and then it goes and lets us down like this!
‘Heap’, then, is a ‘lazy term’; and, with it, sorites paradox exposes the vagueness of language (whereas the last two paradoxes we discussed expose limitations of mathematics and epistemology). Like ‘old’, ‘tall’, ‘bald’, ‘grey’, and many other terms, ‘heap’ is used in predicates (e.g. ‘is a heap’ or ‘is heap-ish’). But in doing so we elicit the blurred boundaries of our descriptions—we aren’t describing anything properly!
To conclude, ‘sorites’ derives from ‘soros’ and translates from Greek to English as ‘heap’; but turning a description of grains of sand into a heap of sand, or vice versa, isn’t so easy a translation.
So next time you describe something, TRY NOT TO BE SO LAZY and just say exactly how many grains there are!
they say that you’re not truly dead until someone says your name for the last time. that latin is a dead language, because it hasn’t been spoken in 1500 years. yet, it lives on: in the crevices of our minds, in the utterances of our language. latin is not dead, it has only adapted.
—when i am asked why i study latin.
Our knowledge of the external world is typically much more acute and thorough than our knowledge of what is closest to us namely ourselves.
Friedrich Nietzsche, Genealogy Of Morals.
(Pictured: We tie knots in our minds from our misunderstandings of language, according to Wittgenstein. He wanted ‘to shew the fly the way out of the fly-bottle’: liberate us from cases like Moore’s paradox by making language less ambiguous and more truth-apt.)
Named after G.E. Moore, Moore’s paradox illustrates how it may be possible to make logically valid statements containing contradictory beliefs. To borrow Moore’s own example, ‘It is raining but I do not believe it is raining’: ‘P and I believe not-P’. Intuitively, this seems bizarre! How is that statement valid?!
Belief isn’t a simple statement of facts. The paradox rests on there being a genuine belief about the world (it’s an epistemic paradox). It arises from your believing something in contradiction to what you just said.
Moore suggested that the solution is to say P isn’t an assertion but an implication: it’s not contradictory to undermine only an implication. However, fellow analytic philosopher Ludwig Wittgenstein, who was greatly influenced by this paradox, offered a different take.
He blamed language in the first-person point of view for the source of Moore’s paradox, which doesn’t arise in the third person (‘It is raining but she does not believe it is’) or past tense (‘It was raining but I did not believe it was’).
Wittgenstein thus called for clarification of the expression ‘I believe’, arguing that it isn’t intelligible: things are either true or they’re not. In Philosophical Investigations he writes:
‘How did we ever come to use such an expression as “I believe … ”? … Did we observe ourselves and other people and so discover belief?’
Hence ‘I believe’ is really just equivalent to ‘This is the case’. Thus ‘P’ and ‘I believe not-P’ are just two propositions of the same kind which do contradict each other, dispelling an unavoidable paradox.
Belief, true or false, is usually taken to be meaningful: it’s matched up against some kind of objectivity (e.g. through justification). This undermines Wittgenstein’s view that false beliefs aren’t possible. But, when we lift all of our pride about it, can we say such objectivity exists? Wittgenstein’s own version of truth is ‘deflationary’. For him, truth has no explicit meaning (e.g. it’s not verifiable). Rather, it is implicitly fixed to its own conditions for being true, making it superficial and expressive.
But isn’t it radical for Wittgenstein to deny the meaning of ‘I believe’? We mentally report on what we think to be true every day …
Either way, feel free to ignore Ludwig’s advice and commit Moore’s paradox.
Will you?
You will and I believe you won’t.