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Single Idea 18738
[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
]
Full Idea
We say we get nearer to root-2 by adding further figures after the decimal point: 1.1412.... This suggests there is something we can get nearer to, but the analogy is a false one.
Gist of Idea
We don't get 'nearer' to something by adding decimals to 1.1412... (root-2)
Source
Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], Notes)
Book Ref
Wittgenstein,Ludwig: 'Lectures in Cambridge 1930-32', ed/tr. Lee,Desmond [Blackwell 1980], p.114
The
219 ideas
from Ludwig Wittgenstein
6318
|
The doctrine of indeterminacy of translation seems implied by the later Wittgenstein
[Wittgenstein, by Quine]
|
22419
|
'I' is a subject in 'I am in pain' and an object in 'I am bleeding'
[Wittgenstein, by McGinn]
|
16010
|
While faith is a passion (as Kierkegaard says), wisdom is passionless
[Wittgenstein]
|
18704
|
Philosophy tries to be rid of certain intellectual puzzles, irrelevant to daily life
[Wittgenstein]
|
18706
|
Words of the same kind can be substituted in a proposition without producing nonsense
[Wittgenstein]
|
18705
|
Words function only in propositions, like levers in a machine
[Wittgenstein]
|
18707
|
All thought has the logical form of reality
[Wittgenstein]
|
18708
|
Infinity is not a number, so doesn't say how many; it is the property of a law
[Wittgenstein]
|
18709
|
Laws of logic are like laws of chess - if you change them, it's just a different game
[Wittgenstein]
|
18727
|
A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied
[Wittgenstein]
|
18710
|
Philosophers express puzzlement, but don't clearly state the puzzle
[Wittgenstein]
|
18711
|
A proposition is any expression which can be significantly negated
[Wittgenstein]
|
18712
|
Understanding is translation, into action or into other symbols
[Wittgenstein]
|
18713
|
If an explanation is good, the symbol is used properly in the future
[Wittgenstein]
|
18719
|
Grammar says that saying 'sound is red' is not false, but nonsense
[Wittgenstein]
|
18714
|
We already know what we want to know, and analysis gives us no new facts
[Wittgenstein]
|
18715
|
Using 'green' is a commitment to future usage of 'green'
[Wittgenstein]
|
18716
|
A machine strikes us as being a rule of movement
[Wittgenstein]
|
18717
|
Thought is an activity which we perform by the expression of it
[Wittgenstein]
|
18718
|
Saying 'and' has meaning is just saying it works in a sentence
[Wittgenstein]
|
18720
|
Explanation gives understanding by revealing the full multiplicity of the thing
[Wittgenstein]
|
18721
|
Explanation and understanding are the same
[Wittgenstein]
|
18723
|
We may correctly use 'not' without making the rule explicit
[Wittgenstein]
|
18724
|
In logic nothing is hidden
[Wittgenstein]
|
18725
|
A proposition draws a line around the facts which agree with it
[Wittgenstein]
|
18726
|
For each necessity in the world there is an arbitrary rule of language
[Wittgenstein]
|
18728
|
The meaning of a proposition is the mode of its verification
[Wittgenstein]
|
18729
|
Part of what we mean by stating the facts is the way we tend to experience them
[Wittgenstein]
|
18730
|
The history of philosophy only matters if the subject is a choice between rival theories
[Wittgenstein]
|
18732
|
We don't need a theory of truth, because we use the word perfectly well
[Wittgenstein]
|
18731
|
There is no theory of truth, because it isn't a concept
[Wittgenstein]
|
18733
|
Laws of nature are an aspect of the phenomena, and are just our mode of description
[Wittgenstein]
|
18734
|
If you remember wrongly, then there must be some other criterion than your remembering
[Wittgenstein]
|
18735
|
Talking nonsense is not following the rules
[Wittgenstein]
|
18736
|
Contradiction is between two rules, not between rule and reality
[Wittgenstein]
|
18737
|
There are no positive or negative facts; these are just the forms of propositions
[Wittgenstein]
|
18738
|
We don't get 'nearer' to something by adding decimals to 1.1412... (root-2)
[Wittgenstein]
|
18280
|
We live in sense-data, but talk about physical objects
[Wittgenstein]
|
6563
|
'And' and 'not' are non-referring terms, which do not represent anything
[Wittgenstein, by Fogelin]
|
23481
|
Propositions assemble a world experimentally, like the model of a road accident
[Wittgenstein]
|
23500
|
My main problem is the order of the world, and whether it is knowable a priori
[Wittgenstein]
|
22323
|
The philosophical I is the metaphysical subject, the limit - not a part of the world
[Wittgenstein]
|
18276
|
A statement's logical form derives entirely from its constituents
[Wittgenstein]
|
16908
|
We can dispense with self-evidence, if language itself prevents logical mistakes
[Jeshion on Wittgenstein]
|
18274
|
Analysis complicates a statement, but only as far as the complexity of its meaning
[Wittgenstein]
|
4678
|
Absolute prohibitions are the essence of ethics, and suicide is the most obvious example
[Wittgenstein]
|
23472
|
The sense of propositions relies on the world's basic logical structure
[Wittgenstein]
|
22312
|
Facts can be both positive and negative
[Wittgenstein, by Potter]
|
3596
|
Total doubt can't even get started
[Wittgenstein, by Williams,M]
|
4721
|
If you are not certain of any fact, you cannot be certain of the meaning of your words either
[Wittgenstein]
|
3597
|
Foundations need not precede other beliefs
[Wittgenstein]
|
7055
|
Externalist accounts of mental content begin in Wittgenstein
[Wittgenstein, by Heil]
|
12576
|
Possessing a concept is knowing how to go on
[Wittgenstein, by Peacocke]
|
23450
|
Wittgenstein rejected his earlier view that the form of language is the form of the world
[Wittgenstein, by Morris,M]
|
6567
|
For Wittgenstein, words are defined by their use, just as chess pieces are
[Wittgenstein, by Fogelin]
|
6501
|
As sense-data are necessarily private, they are attacked by Wittgenstein's objections
[Wittgenstein, by Robinson,H]
|
18743
|
Wittgenstein says we want the grammar of problems, not their first-order logical structure
[Wittgenstein, by Horsten/Pettigrew]
|
4136
|
To imagine a language means to imagine a form of life
[Wittgenstein]
|
4137
|
In the majority of cases the meaning of a word is its use in the language
[Wittgenstein]
|
4138
|
Is white simple, or does it consist of the colours of the rainbow?
[Wittgenstein]
|
4139
|
Naming is a preparation for description
[Wittgenstein]
|
4140
|
The standard metre in Paris is neither one metre long nor not one metre long
[Wittgenstein]
|
4141
|
Various games have a 'family resemblance', as their similarities overlap and criss-cross
[Wittgenstein]
|
4946
|
A name is not determined by a description, but by a cluster or family
[Wittgenstein, by Kripke]
|
2512
|
Philosophy is a battle against the bewitchment of our intelligence by means of language
[Wittgenstein]
|
6566
|
The problem is to explain the role of contradiction in social life
[Wittgenstein]
|
4142
|
To understand a sentence means to understand a language
[Wittgenstein]
|
6165
|
Every course of action can either accord or conflict with a rule, so there is no accord or conflict
[Wittgenstein]
|
4143
|
One cannot obey a rule 'privately', because that is a practice, not the same as thinking one is obeying
[Wittgenstein]
|
6169
|
We do not achieve meaning and understanding in our heads, but in the world
[Wittgenstein, by Rowlands]
|
6166
|
Was Wittgenstein's problem between individual and community, or between occasions for an individual?
[Rowlands on Wittgenstein]
|
4144
|
Common human behaviour enables us to interpret an unknown language
[Wittgenstein]
|
11049
|
To communicate, language needs agreement in judgment as well as definition
[Wittgenstein]
|
4145
|
How do words refer to sensations?
[Wittgenstein]
|
5676
|
To say that I 'know' I am in pain means nothing more than that I AM in pain
[Wittgenstein]
|
7875
|
If a brilliant child invented a name for a private sensation, it couldn't communicate it
[Wittgenstein]
|
4146
|
We cannot doublecheck mental images for correctness (or confirm news with many copies of the paper)
[Wittgenstein]
|
4147
|
If we only named pain by our own case, it would be like naming beetles by looking in a private box
[Wittgenstein]
|
5659
|
If the reference is private, that is incompatible with the sense being public
[Wittgenstein, by Scruton]
|
5663
|
It is irresponsible to generalise from my own case of pain to other people's
[Wittgenstein]
|
19272
|
To imagine another's pain by my own, I must imagine a pain I don't feel, by one I do feel
[Wittgenstein]
|
4148
|
What is your aim in philosophy? - To show the fly the way out of the fly-bottle
[Wittgenstein]
|
4149
|
We don't have 'meanings' in our minds in addition to verbal expressions
[Wittgenstein]
|
4150
|
Asking about verification is only one way of asking about the meaning of a proposition
[Wittgenstein]
|
15106
|
Essence is expressed by grammar
[Wittgenstein]
|
4151
|
Grammar tells what kind of object anything is - and theology is a kind of grammar
[Wittgenstein]
|
4152
|
Getting from perceptions to words cannot be a private matter; the rules need an institution of use
[Wittgenstein]
|
4153
|
Are sense-data the material of which the universe is made?
[Wittgenstein]
|
4154
|
Why are we not aware of the huge gap between mind and brain in ordinary life?
[Wittgenstein]
|
4155
|
We all seem able to see quite clearly how sentences represent things when we use them
[Wittgenstein]
|
6600
|
The belief that fire burns is like the fear that it burns
[Wittgenstein]
|
4156
|
Make the following experiment: say "It's cold here" and mean "It's warm here"
[Wittgenstein]
|
4157
|
Concepts direct our interests and investigations, and express those interests
[Wittgenstein]
|
7092
|
If individuals can't tell if they are following a rule, how does a community do it?
[Grayling on Wittgenstein]
|
4158
|
An 'inner process' stands in need of outward criteria
[Wittgenstein]
|
6658
|
What is left over if I subtract my arm going up from my raising my arm?
[Wittgenstein]
|
22490
|
Bring words back from metaphysics to everyday use
[Wittgenstein]
|
11079
|
How do I decide when to accept or obey an intuition?
[Wittgenstein]
|
12606
|
Man learns the concept of the past by remembering
[Wittgenstein]
|
19273
|
I don't have the opinion that people have minds; I just treat them as such
[Wittgenstein]
|
4159
|
The human body is the best picture of the human soul
[Wittgenstein]
|
4160
|
One can mistrust one's own senses, but not one's own beliefs
[Wittgenstein]
|
4161
|
If a lion could talk, we could not understand him
[Wittgenstein]
|
7392
|
If a lion could talk, it would be nothing like other lions
[Dennett on Wittgenstein]
|
18282
|
You can't believe it if you can't imagine a verification for it
[Wittgenstein]
|
22320
|
An 'object' is just what can be referred to without possible non-existence
[Wittgenstein]
|
18283
|
Language pictures the essence of the world
[Wittgenstein]
|
6606
|
Consider: "Imagine this butterfly exactly as it is, but ugly instead of beautiful"
[Wittgenstein]
|
18281
|
In mathematics everything is algorithm and nothing is meaning
[Wittgenstein]
|
11073
|
Two and one making three has the necessity of logical inference
[Wittgenstein]
|
11074
|
'It is true that this follows' means simply: this follows
[Wittgenstein]
|
7536
|
If you hope to improve the world, all you can do is improve yourself
[Wittgenstein]
|
7085
|
The main problem of philosophy is what can and cannot be thought and expressed
[Wittgenstein, by Grayling]
|
23463
|
Atomic facts correspond to true elementary propositions
[Wittgenstein]
|
23490
|
A thought is mental constituents that relate to reality as words do
[Wittgenstein]
|
7084
|
What can be said is what can be thought, so language shows the limits of thought
[Wittgenstein, by Grayling]
|
17665
|
The 'Tractatus' is instrumentalist about laws of nature
[Wittgenstein, by Armstrong]
|
6849
|
Wittgenstein hated logicism, and described it as a cancerous growth
[Wittgenstein, by Monk]
|
7090
|
The 'Tractatus' is an extreme example of 'Logical Atomism'
[Wittgenstein, by Grayling]
|
23507
|
Unlike the modern view of a set of worlds, Wittgenstein thinks of a structured manifold of them
[Wittgenstein, by White,RM]
|
7088
|
Logic and maths can't say anything about the world, since, as tautologies, they are consistent with all realities
[Wittgenstein, by Grayling]
|
23479
|
The Tractatus aims to reveal the necessities, without appealing to synthetic a priori truths
[Wittgenstein, by Morris,M]
|
9810
|
The 'Tractatus' is a masterpiece of anti-philosophy
[Badiou on Wittgenstein]
|
10910
|
The best account of truth-making is isomorphism
[Wittgenstein, by Mulligan/Simons/Smith]
|
18349
|
All truths have truth-makers, but only atomic truths correspond to them
[Wittgenstein, by Rami]
|
10967
|
Wittgenstein's picture theory is the best version of the correspondence theory of truth
[Read on Wittgenstein]
|
7087
|
Language is [propositions-elementary propositions-names]; reality is [facts-states of affairs-objects]
[Wittgenstein, by Grayling]
|
4702
|
The account of truth in the 'Tractatus' seems a perfect example of the correspondence theory
[Wittgenstein, by O'Grady]
|
7537
|
Wittgenstein convinced Russell that logic is tautologies, not Platonic forms
[Wittgenstein, by Monk]
|
6428
|
Wittgenstein is right that logic is just tautologies
[Wittgenstein, by Russell]
|
9467
|
Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions
[Wittgenstein, by Jacquette]
|
13830
|
Logical truths are just 'by-products' of the introduction rules for logical constants
[Wittgenstein, by Hacking]
|
13429
|
The identity sign is not essential in logical notation, if every sign has a different meaning
[Wittgenstein, by Ramsey]
|
18154
|
The sign of identity is not allowed in 'Tractatus'
[Wittgenstein, by Bostock]
|
23499
|
This book says we should either say it clearly, or shut up
[Wittgenstein]
|
23459
|
This work solves all the main problems, but that has little value
[Wittgenstein]
|
13133
|
The world is facts, not things. Facts determine the world, and the world divides into facts
[Wittgenstein]
|
22311
|
The world is determined by the facts, and there are no further facts
[Wittgenstein]
|
23462
|
He says the world is the facts because it is the facts which fix all the truths
[Wittgenstein, by Morris,M]
|
11027
|
To know an object you must know all its possible occurrences
[Wittgenstein]
|
22321
|
To know an object we must know the form and content of its internal properties
[Wittgenstein, by Potter]
|
23470
|
Each thing is in a space of possible facts
[Wittgenstein]
|
23465
|
The 'form' of an object is its possible roles in facts
[Wittgenstein]
|
23467
|
Objects are simple
[Wittgenstein]
|
6429
|
All complex statements can be resolved into constituents and descriptions
[Wittgenstein]
|
23466
|
Objects are the substance of the world
[Wittgenstein]
|
23469
|
An imagined world must have something in common with the real world
[Wittgenstein]
|
12869
|
Two objects may only differ in being different
[Wittgenstein]
|
23468
|
Apart from the facts, there is only substance
[Wittgenstein]
|
23464
|
In atomic facts the objects hang together like chain links
[Wittgenstein]
|
23471
|
The structure of an atomic fact is how its objects combine; this possibility is its form
[Wittgenstein]
|
23473
|
Do his existent facts constitute the world, or determine the world?
[Morris,M on Wittgenstein]
|
22313
|
The existence of atomic facts is a positive fact, their non-existence a negative fact
[Wittgenstein]
|
23482
|
The 'form' of the picture is its possible combinations
[Wittgenstein]
|
7056
|
Pictures reach out to or feel reality, touching at the edges, correlating in its parts
[Wittgenstein]
|
23483
|
Proposition elements correlate with objects, but the whole picture does not correspond to a fact
[Wittgenstein, by Morris,M]
|
23486
|
Pictures are possible situations in logical space
[Wittgenstein]
|
23485
|
No pictures are true a priori
[Wittgenstein]
|
23487
|
What is thinkable is possible
[Wittgenstein]
|
7089
|
A name is primitive, and its meaning is the object
[Wittgenstein]
|
23506
|
Names are primitive, and cannot be analysed
[Wittgenstein]
|
2939
|
If a sign is useless it is meaningless; that is the point of Ockham's maxim
[Wittgenstein]
|
23492
|
Our language is an aspect of biology, and so its inner logic is opaque
[Wittgenstein]
|
23510
|
Most philosophical questions arise from failing to understand the logic of language
[Wittgenstein]
|
18268
|
Apparent logical form may not be real logical form
[Wittgenstein]
|
8172
|
To understand a proposition means to know what is the case if it is true
[Wittgenstein]
|
23488
|
Propositions are understood via their constituents
[Wittgenstein]
|
23489
|
We translate by means of proposition constituents, not by whole propositions
[Wittgenstein]
|
23511
|
Propositions use old expressions for a new sense
[Wittgenstein]
|
10905
|
My fundamental idea is that the 'logical constants' do not represent
[Wittgenstein]
|
22314
|
On white paper a black spot is a positive fact and a white spot a negative fact
[Wittgenstein]
|
23508
|
Science is all the true propositions
[Wittgenstein]
|
7968
|
A relation is internal if it is unthinkable that its object should not possess it
[Wittgenstein]
|
7969
|
The order of numbers is an internal relation, not an external one
[Wittgenstein]
|
7784
|
'Object' is a pseudo-concept, properly indicated in logic by the variable x
[Wittgenstein]
|
21682
|
If a proposition is elementary, no other elementary proposition contradicts it
[Wittgenstein]
|
22319
|
Analysis must end in elementary propositions, which are combinations of names
[Wittgenstein]
|
18277
|
If q implies p, that is justified by q and p, not by some 'laws' of inference
[Wittgenstein]
|
21683
|
Nothing can be inferred from an elementary proposition
[Wittgenstein]
|
16907
|
If the truth doesn't follow from self-evidence, then self-evidence cannot justify a truth
[Wittgenstein]
|
23493
|
'Not' isn't an object, because not-not-p would then differ from p
[Wittgenstein]
|
11062
|
Logic is a priori because it is impossible to think illogically
[Wittgenstein]
|
16909
|
Logic is a priori because we cannot think illogically
[Wittgenstein]
|
6056
|
Identity is not a relation between objects
[Wittgenstein]
|
22322
|
You can't define identity by same predicates, because two objects with same predicates is assertable
[Wittgenstein]
|
6057
|
Two things can't be identical, and self-identity is an empty concept
[Wittgenstein]
|
23498
|
The modern idea of the subjective soul is composite, and impossible
[Wittgenstein]
|
23475
|
The form of a proposition must show why nonsense is unjudgeable
[Wittgenstein]
|
2938
|
The limits of my language means the limits of my world
[Wittgenstein]
|
23502
|
Logic fills the world, to its limits
[Wittgenstein]
|
23497
|
Solipsism is correct, but can only be shown, not said, by the limits of my personal language
[Wittgenstein]
|
2940
|
The subject stands outside our understanding of the world
[Wittgenstein]
|
23501
|
There is no a priori order of things
[Wittgenstein]
|
23503
|
Strict solipsism is pure realism, with the self as a mere point in surrounding reality
[Wittgenstein]
|
18153
|
A number is a repeated operation
[Wittgenstein]
|
18160
|
The concept of number is just what all numbers have in common
[Wittgenstein]
|
18161
|
The theory of classes is superfluous in mathematics
[Wittgenstein]
|
18162
|
The propositions of logic are analytic tautologies
[Wittgenstein]
|
23495
|
The tautologies of logic show the logic of language and the world
[Wittgenstein]
|
15089
|
Logical proof just explicates complicated tautologies
[Wittgenstein]
|
19292
|
Logic doesn't split into primitive and derived propositions; they all have the same status
[Wittgenstein]
|
23509
|
The logic of the world is shown by tautologies in logic, and by equations in mathematics
[Wittgenstein]
|
23504
|
Logic concerns everything that is subject to law; the rest is accident
[Wittgenstein]
|
2941
|
Induction accepts the simplest law that fits our experiences
[Wittgenstein]
|
9442
|
The only necessity is logical necessity
[Wittgenstein]
|
17673
|
The modern worldview is based on the illusion that laws explain nature
[Wittgenstein]
|
23496
|
Two colours in the same place is ruled out by the logical structure of colour
[Wittgenstein]
|
2942
|
The sense of the world must lie outside the world
[Wittgenstein]
|
2943
|
Ethics cannot be put into words
[Wittgenstein]
|
2944
|
If a question can be framed at all, it is also possible to answer it
[Wittgenstein]
|
6591
|
Doubts can't exist if they are inexpressible or unanswerable
[Wittgenstein]
|
7086
|
Good philosophy asserts science, and demonstrates the meaninglessness of metaphysics
[Wittgenstein]
|
23512
|
Once you understand my book you will see that it is nonsensical
[Wittgenstein]
|
6870
|
I say (contrary to Wittgenstein) that philosophy expresses what we thought we must be silent about
[Ansell Pearson on Wittgenstein]
|
2937
|
What we cannot speak about we must pass over in silence
[Wittgenstein]
|
10710
|
We accept substance, to avoid infinite backwards chains of meaning
[Wittgenstein, by Potter]
|
6569
|
'This sentence is false' sends us in a looping search for its proposition
[Wittgenstein, by Fogelin]
|
2626
|
A philosopher is outside any community of ideas
[Wittgenstein]
|
3790
|
Causes of beliefs are irrelevant to their contents
[Wittgenstein]
|