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Single Idea 7311
[filed under theme 5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
]
Full Idea
In all knowledge that can be expressed in words - with the exception of "this" and "that", and a few other such words - no genuine proper names occur, but what seem like genuine proper names are really descriptions
Gist of Idea
The only genuine proper names are 'this' and 'that'
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVI)
Book Ref
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.178
A Reaction
This is the terminus of Russell's train of thought about descriptions. Suppose you point to something non-existent, like a ghost in a misty churchyard? You'd be back to the original problem of naming a non-existent!
The
54 ideas
from 'Introduction to Mathematical Philosophy'
8468
|
The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false
[Russell, by Orenstein]
|
8469
|
Russell's proposal was that only meaningful predicates have sets as their extensions
[Russell, by Orenstein]
|
13414
|
For Russell, numbers are sets of equivalent sets
[Russell, by Benacerraf]
|
14420
|
Infinity and continuity used to be philosophy, but are now mathematics
[Russell]
|
8745
|
Classes are logical fictions, and are not part of the ultimate furniture of the world
[Russell]
|
14421
|
Discovering that 1 is a number was difficult
[Russell]
|
14424
|
Numbers are needed for counting, so they need a meaning, and not just formal properties
[Russell]
|
14423
|
'0', 'number' and 'successor' cannot be defined by Peano's axioms
[Russell]
|
14422
|
Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms
[Russell]
|
14425
|
A number is something which characterises collections of the same size
[Russell]
|
14430
|
If a relation is symmetrical and transitive, it has to be reflexive
[Russell]
|
14426
|
A definition by 'extension' enumerates items, and one by 'intension' gives a defining property
[Russell]
|
14427
|
We can enumerate finite classes, but an intensional definition is needed for infinite classes
[Russell]
|
14428
|
Members define a unique class, whereas defining characteristics are numerous
[Russell]
|
14429
|
Classes are logical fictions, made from defining characteristics
[Russell]
|
14431
|
The definition of order needs a transitive relation, to leap over infinite intermediate terms
[Russell]
|
14441
|
The formal laws of arithmetic are the Commutative, the Associative and the Distributive
[Russell]
|
10450
|
Russell admitted that even names could also be used as descriptions
[Russell, by Bach]
|
13510
|
Could a number just be something which occurs in a progression?
[Russell, by Hart,WD]
|
14432
|
'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a
[Russell]
|
14435
|
The essence of individuality is beyond description, and hence irrelevant to science
[Russell]
|
14433
|
Mathematically expressed propositions are true of the world, but how to interpret them?
[Russell]
|
14434
|
What matters is the logical interrelation of mathematical terms, not their intrinsic nature
[Russell]
|
14438
|
New numbers solve problems: negatives for subtraction, fractions for division, complex for equations
[Russell]
|
14436
|
A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum
[Russell]
|
14439
|
A complex number is simply an ordered couple of real numbers
[Russell]
|
14440
|
We may assume that there are infinite collections, as there is no logical reason against them
[Russell]
|
14442
|
If straight lines were like ratios they might intersect at a 'gap', and have no point in common
[Russell]
|
14443
|
The British parliament has one representative selected from each constituency
[Russell]
|
14444
|
Choice is equivalent to the proposition that every class is well-ordered
[Russell]
|
14445
|
Choice shows that if any two cardinals are not equal, one must be the greater
[Russell]
|
14446
|
We can pick all the right or left boots, but socks need Choice to insure the representative class
[Russell]
|
14447
|
Infinity says 'for any inductive cardinal, there is a class having that many terms'
[Russell]
|
14449
|
There is always something psychological about inference
[Russell]
|
12197
|
Inferring q from p only needs p to be true, and 'not-p or q' to be true
[Russell]
|
14450
|
All forms of implication are expressible as truth-functions
[Russell]
|
14451
|
Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts
[Russell]
|
14454
|
An argument 'satisfies' a function φx if φa is true
[Russell]
|
14453
|
The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M?
[Russell]
|
14452
|
All the propositions of logic are completely general
[Russell]
|
14456
|
'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity
[Russell]
|
14458
|
Asking 'Did Homer exist?' is employing an abbreviated description
[Russell]
|
12444
|
Logic is concerned with the real world just as truly as zoology
[Russell]
|
14457
|
Names are really descriptions, except for a few words like 'this' and 'that'
[Russell]
|
7311
|
The only genuine proper names are 'this' and 'that'
[Russell]
|
14455
|
'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not
[Russell]
|
14459
|
Reducibility: a family of functions is equivalent to a single type of function
[Russell]
|
14461
|
Propositions about classes can be reduced to propositions about their defining functions
[Russell]
|
14460
|
If something is true in all possible worlds then it is logically necessary
[Russell]
|
14465
|
Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men'
[Russell]
|
14462
|
In modern times, logic has become mathematical, and mathematics has become logical
[Russell]
|
14464
|
Logic can be known a priori, without study of the actual world
[Russell]
|
10057
|
Logic can only assert hypothetical existence
[Russell]
|
14463
|
Existence can only be asserted of something described, not of something named
[Russell]
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