———— 

Tae! ry; 
iin! 

The Tractatus consists of seven main propositions, 
six of which admit of expansion and aim at saying 
clearly what can be said. The seventh admits no 
expansion. It affirms the limit of what is expressible, 
the inexpressible, and it acquiesces in silence. In 
its form, the Tractatus recalls the Monadology of 
Leibniz; in its content, it approximates, as we have 
indicated, to Spinoza. Logic is the ladder by which 
we rise to a vantage-point from which we survey 
reality, but when we have risen we recognise that 
the logical propositians which have supported us are 
in themselves meaningless: we must throw them away 
in order to see the world rightly, and then, face to 
face with reality, we find it is inexpressible. 
The six main propositions are the rungs in the 
ladder. (1) The world is everything that is the case. 
(2) What is the case, the fact, is the existence of 
atomic facts. (3) The logical picture of the facts is 
the thought. (4) The thought is the significant pro- 
position. (5) Propositions are truth-functions of 
elementary propositions (an elementary proposition 
being a truth-function of itself). (6) The general form 
of truth-function is (omitting the symbols and 
substituting the interpretation) that every proposition 
is the result of successive applications of the operation 
of negating all the propositions making up any set j| 
of propositions, to the elementary propositions. The 
seeming obscurity of this last sentence may perhaps 
be removed by a quotation. “The propositions of 
logic demonstrate the logical properties of propositions, 
by combining them into propositions which say nothing. 
In a logical proposition propositions are brought into 
equilibrium with one another, and the state of the 
equilibrium then shows how these propositions must 
be logically constructed.” 
These six main propositions are not elaborated in 
the deductive or analytic manner, but it is shown that 
a number of propositions depend upon them in a way 
which proves that logic is a constructive process. It 
will be seen, then, that the Tractatus is not a book to 
be read cursorily ; every proposition will only be under- 
stood if the reader succeeds in himself thinking the 
thought of it. Its appearance is a notable event in 
the philosophical world and will be received in many 
quarters as a challenge. 
Probably the central point of interest is the meaning 
which Mr. Wittgenstein attaches to what he calls the 
atomic fact. Outwardly it appears to agree with what 
Mr. Russell describes generally as logical atomism, but 
when we get down to the atomic fact itself, it becomes 
as different from Mr. Russell’s description of the con- 
stituent element as the modern scientific conception of 
NO. 2782, VOL. 111] 
. 

FEsruary 24, 1923] NATURE 247 
two modes of the existence of a being who himself | the atom is different from the Democritean. For Mr. 
exists in infinite modes. ~ Wittgenstein the atomic fact is a system. “ In the 
atomic fact objects. hang one in another like the 
members of a chain.’ Further on he tells us we 
must not say, “ the complex sign aRb says a stands in 
relation R to b”’; what we must say is “ that a stands 
in a certain relation to b says that aRb.” If we accept 
this, what is left of the famous theory of relations ? 
Also to Mr, Wittgenstein those well-known nonsense 
propositions which play so large a réle in the Russellian 
logic are nonsense, that is, they are not propositions, 
they are nothing. 
The interest of the Tractatus will doubtless culminate 
for most students in the mysticism with which it 
concludes. Pure formalism in logic must mean 
mysticism in philosophy. “ Logic is not a theory but 
a reflexion of the world.” It is transcendent. Logic 
is language. It is the clear expression of all that is 
But when we have said all that is sayable 
there remains unexpressed, inexpressible, the will, the 
life, the that we live as distinct from the how we live. 
“Of the will we cannot speak.” “If good or bad 
willing changes the world, it can only change the limits 
of the world, not the facts.” Philosophy when it 
follows the right method and says nothing but what 
can be said, says nothing which concerns philosophy. 
Such is the conclusion of this remarkable, thought- 
provoking book. 
There is one serious omission of the editors which 
at times is embarrassing to the student. Writers are 
referred to whose special theories the reader is presumed 
to know, but there are no references to guide him should 
he wish to consult the originals. 
expressible. 
H. Witpon Carr. 

Outlines of Astronomy. 
General Astronomy. By HH. Spencer Jones. Pp. 
viii+ 392+24 plates. (London: E. Arnold and 
Co., 1922.) 21s. net 
O deal in any adequate sense and in an elementary 
manner with the whole subject of astronomy 
requires both inclinations and aptitudes which are not 
altogether common. It 1s a field in which the greatest 
success may fairly be claimed for English and American 
writers. Thus in France, in spite of a genius for 
scientific romance which serves admirably in an allied 
and more restricted domain, the pen of Arago has 
found no conspicuous successor. Similarly in Germany 
the continued success of “ Newcomb-Engelmann ” is 
not merely a tribute to the original American master- 
piece, but also betrays a native inability to create a 
serious rival. In one case we may suspect a natural 
