Ludwig Wittgenstein was
born in 1889 to one of the wealthiest families in Europe. He was a
contemporary of Frege and Bertrand Russell, and his work on logic is
related to both of those previous philosophers. He's an important
philosopher, and one of his book, the Philosophical Investigations,
was published posthumously in 1953 – he had died two years earlier
– and is regarded as the most important book of 20th
century philosophy. His work can be divided into his early work and
his later work. The Tractatus is one of his early works and was
written during the first world war. It was published in 1922, ten
years after Russell's great work, the Principia Mathematica.
By Wittgenstein's own
words, the Tractatus can be summed up in a single sentence:
What can be said at
all can be said clearly, and what cannot be said at all should pass
over in silence.
The point of his work,
thus, is to define the boundaries of logic and of language, because
language, by his definition, is the medium of logic. What are the
limits of thought? This is the question Wittgenstein tries to answer.
He states in the
preface that “its purpose would be achieved if it gave pleasure to
one person who read and understood it”. While it's difficult,
The book is split into
seven short chapters. Each chapter is again split into smaller
sections, so that you have chapter 1, then chapter 1.1, then point
1.11 and 1.12 and so on. Each 'chapter' and 'point' are at most only
three or four sentences long.
Wittgenstein sought out
to define the limits of thought within language in his book and
masterfully uses as few words as possible to deliver his strong
points.
So, Chapter 1 begins
with the statement that the world is the totality of facts, not of
things
I
think what Wittgenstein means here is that 'things' are described as
'facts', and these facts determine how and what a thing is. For
example, the thing that is a swan was originally named and
categorised for the fact that it is white. Facts are the how of
things that define them. More on that later though.
The
chapter's ending statement leads directly into Chapter 2.
Wittgenstein
states that 'the world divides into facts', and he goes to say that
any one can either be the case or not be the case, and everything
else remain the same. What does that mean?
2.
What is the case, the fact, is the existence of atomic facts.
So
there is half the answer. 2.1 states that we make for ourselves
pictures of facts. Here, Wittgenstein is putting to paper the logic
behind thought. Thought, and imagination, are the logical
representations of facts within our mind.
Defining
what an atomic fact is, he calls it a combination of objects, which
are entities and things.
The
object is a simple thing, while atomic facts link with one another,
like a chain. The totality of this chain, that is, the entirety of
these atomic facts is the world. You might think of it as objects and
things being like the cells that together make up the human body,
with the body being the totality of these cells. He even states that
it is 'essential' of a 'thing' that it can be a constituent part of
an atomic fact. A thing or object is thus defined by its relation
to other things or objects.
So
the totality of existent atomic facts determine which atomic facts,
or chains of ideas, do not exist. The existence and non-existence of
atomic facts is how we define reality. He calls the existence of an
atomic fact a 'positive fact', and the non-existence a 'negative
fact'. So one could say that the economic crisis is a positive fact,
while the statement that dinosaurs are still roaming the earth today
is a negative fact.
In
2.013, he states that everything is in a space of possible atomic
facts. One can think of this space as empty, but cannot think of the
thing without space. This is just another wording of the old 'No one
is on the road' problem: We cannot think of there being nobody, we
can only think of the lack of somebody in the space that is the
road.. Wittgenstein's explanation goes:
Just
as we cannot think of spatial objects apart from space, or temporal
objects apart from time, so we cannot think of any
object apart from the possibility of its connections with other
things
Our
understanding of things is based upon their interactions with other.
Objects,
he says, contain the possibility of all states of affairs. They are
essentially the building blocks of all complex ideas. The possibility
of an object's occurrence in an atomic fact, is the form of the
object. To put in another way, an object's interaction and
differentiation with the world around it, is the definition of the
object, or so I understand.
The
object is the simplest form of substance in the world. It cannot be a
compound – for example, you can have the object of a sheep and the
object of a tree. But you cannot have a tree that is also a sheep.
However, you can have a sheep standing beneath a tree, and
that would be an atomic fact, as it is a combination of two simple
objects.
Objects
can only differentiated from one another by how they are different.
Either something has unique properties which make it distinguishable,
or there is a group of things which have most of their properties in
common, and are thus impossible to distinguish from one another.
Going back to our sheep example, a single black sheep in a crowd of
white sheep is distinguished and defined by its colour, while the
crowd of white sheep cannot be discerned from one another.
He
defines how we picture things in our minds, calling pictures models
of reality. The logical picture can depict the world. The picture
agrees with reality or doesn't, it is either true of false. Thus can
one imagine something that doesn't exist, such as a sheep that is
also a tree. But to discover whether a picture is true or false we
have to compare it with reality. It cannot be discovered from a
picture alone whether or not it is true or false, probably because we
can't imagine a picture without some basis in reality to begin with.
As Wittgenstein puts it, there
is no picture which is a truth a priori.
This relates somewhat back to Locke's idea that we are all blank
slates, and is a refutation of the in-born knowledge of God that
Descartes pronounced.
For
example, if I ask you to picture an alien unique to itself with no
reference to the world you know, it is impossible. You cannot picture
its form without it resembling some object you know, or the texture
of its body without reference to soft or course. You cannot picture
it being a colour outside of the red-to-violet spectrum we know. It
is impossible to picture such a thing, because all our thoughts,
however imaginative they are, are grounded in the real world.
Now
we come to chapter 3, which states that the logical picture of the
facts is the thought.
“An
atomic fact is thinkable”, meaning that we can imagine it. We can't
think something unlogical, because we would have to think
unlogically. We cannot do that, because unlogic is incomprehensible
to us. He says that to present in language anything which
“contradicts logic” is as impossible as in trying to present a
figure which cannot exist in space by its coordinates in geometry.
Language is how we express logic.
I'm
not sure I can quite come to grips with this, as if I were to ask
someone “On a scale of one to ten, yes or no?”, my words would
make no logical sense. Isn't that the same as writing an incorrect
geometric proof? You're using the expression of logic, language,
incorrectly, and it comes to be meaningless.
Talking about language more, he states that a
propositional sign consists of words combined in a definite way. This
sign is a fact, and the proposition is articulate. For example, “the
sheep has white wool” is an articulate propositional sign that is a
fact.
On the topic of names, he states that a name
represents an object only. Names are primitive signs that do not
describe how a thing is,
which is what Wittgenstein's logical language is interested in. He is
interested in the composition of a thing, which the name cannot
define. For example, 'tree' is the name of an object, but it is the
branches and the roots and so on that assert how
a tree is a tree.
As only a
proposition has sense, only in the context of this proposition does a
name have meaning. For example, we can make sense of the name 'tree'
when we say “a tree is a thing with branches and roots”.
Otherwise, it is an arbitrary label.
For the remainder of chapter 3, he goes into the detail of what makes a name meaningless except as a label, and the logic behind a proposition.
Chapter 4 states
that the thought is the
significant proposition.
A
proposition presents the existence and non-existence of atomic facts.
To remind you, an atomic fact is the possibilities of the sum of the
objects. These atomic facts can either have a true or false value.
Wittgenstein
states that people construct languages in which every sense can be
expressed, but without fully understanding how the words and language
work, just as how we can make the sounds of our language without
being fully conscious of how we're making them. Like Frege, he
believed that language disguises thought, especially colloquial
language – what Frege would have called colour.
Like
Russell, he states that most philosophical writings are senseless.
Most questions and propositions of philosophers result from the lack
of understanding most of us have of language. Thus the deepest
problems are often not problems at all. Personally, I don't quite
understand how this makes sense.
5,
Propositions are truth-functions of elementary propositions. An
elementary proposition is a truth-function of itself.
In this chapter Wittgenstein talks more about the logic underlying the makeup of propositions, that is, sentences. I have to admit that the further I read into the book, the less it makes sense to me. This chapter deals greatly with mathematical proofs of 'truth-functions', which so far as I understand are the justifications for your propositions. but chapter 5's final point, 5.6, puts things in layman's terms that anyone can understand:
The limits of my language mean the limits of my world.
What
that means is that your perception and understanding of the world
ends where your language ends. If someone from Rome of 2000 years ago
saw modern technology, then went to tell his friends, he would not be
able to properly describe what he saw because he has no word for
computer or aeroplane. His understanding of these things are limited
by his language.
Chapter
6's title-sentence gives us the mathematical form of truth-functions
and states that this
is the general form of proposition.
He gives more proofs as to this general form of the proposition and states now that propositions of logic are actually tautologies – that is, phrases that say the same things in different ways. But he defends these tautologies. They show the formal, logical, properties of language.
Chapter 7 is the shortest in the book, being only a sentence long. It states: whereof one cannot speak, thereof one must be silent.
If
you can't form a logical proposition on something, then you can't
express it. If it is unlogical, it cannot be propositioned, and it
cannot be said. This seems to me to be a law of language and speech.
Going back to that alien which has no worldly properties, I can only
speak of it in terms of how it differentiates from everything else.
But I cannot picture it, and I cannot describe it, therefore I cannot
talk about it except in this theoretical sense. I must be silent
about it, because there's nothing I can say.
Thus ends Wittgenstein's Tractatus. It is an analytical work picking apart the construction of thought and language in order to understand and talk with logic. It seems an evolution of Frege's work, which was robotic in its form of logic. Wittgenstein's logic, on the other hand, is more flexible in that it can make sense of every-day logic and language – what Frege called colour. In fact, logical statements and 'colour' don't necessarily seem to be distinguished by Wittgenstein, as they all follow some basic laws of logic.
There are no universal facts or objects. The world is the structure of your ideas
Engineeer background – you need rules and composite parts.
To
understand what people are saying you can break down each of their
sentences. We're none the wiser about the universe than we were 2000
years ago. We cannot work out anything, nihilistic. Nothing stands
still. Cannot analyse what people say – plus psychology shows a
whole kind of secret world of thought behind thought.
