He believes this logic doctrine results from the philosophy of mathematics on the basis of a certain metaphysic. It is called atomistic because he believes in many separate things in constrast to the absolute idealists. He won't prove this but he will advocate a result from undeniable data. Not necessarily true data but undeniable data as that is a psychological term, it is the sort of thing that nobody is going to deny. It does not follow that it is true though we will think its true and that is as close to truth as we can get.
Considering any form of knowledge we are inevitably connected with subjectivity and we ask "What can I know of the world?" not simply what is true. The data one always starts with are rather vague and ambiguous like "There are a number of people in this room at this moment." But when you try and define a room and what it is for a person to be in a room you find you did not really know what you meant. He thinks philosophizing is passing from these vague sentences into something precise, clear, definite. He believes it is impossible to be free from error. Facts are what they are no matter what we choose to believe about them.
Beliefs refer to facts and are either true or false. He wants to give an explanation of fact rather than a definition. A fact is the kind of thing that makes a proposition true or false. We express a fact by saying that something has a certian property or that it has a certain relation to another thing. A thing by itself is not a fact. Facts belong to the external world. Facts are just as much a part of the world as particulars. Facts are involved equally when we speak truly or falsely, because it is an objective fact which makes what we say false. There are many kinds of facts. Particular facts "this is white", general facts "All men are mortal", and more. One cannot only use particular facts to describe the world for in making this list you would have to include a general fac. "These are all the particular facts there are." There are positive facts "Socrates is alive", negative facts "Socrates is not alive". Then there are facts concerning particular relations or qualities. THe general facts one has in logic. There are facts about properties of single things, and then facts between a number of different things. There are not true and false facts, just facts. True and false are correlatives so you say things are true if they could be false. A proposition is indicative, it asserts something. A proposition is a complex symbol, i.e. it has parts that are also symbols. Unless one is aware of the relation of the symbol to what it symbolizes one will attribute properties of the symbol to the thing. Thinking about the symbols is easier because they are tangible. Good philosophers every so often think about the thing symbolized. Bad philosophers never do. There are different kinds of symbols, different relationships between them, and fallacies arise unless this is realized.
He thinks absolute idealism is the result of making a mistake in symbolism. Symbolism includes all languages. A symbol is something that means something else. He doesn't tackle meaning at this time. He says that there are infinite meanings. Socrates means a particular man, mortal means a certain quality, and "Socrates is mortal" means a certain fact, but meaning isn't the same in each of these cases. It is very important to not think that just one thing is meant by "Meaning". And therefore there is just one sort of relation of symbol to what is symbolized. A name is proper symbol for a person. A sentence is proper symbol for a fact. A belief or statement is always involves a proposition. Propositions are not names for facts, which Wittgenstein pointed out to him, because there are two propositions for every fact "Socrates is dead" and "Socrates is not dead", there is ony one fact that makes one true and the other false. The relationship of proposition to fact is then nearly different from name to thing named. A name can just name a particular, if it does not it is not a name, just a noise, it must have that one particular relation, where as a proposition doesn't cease to be if it is false. You cannot properly name a fact, you cannot put the sort of thing that makes a proposition true or false in the position of logical subject, only have it there to be something asserted or denied.
In the philosophy of logical atomism one has accepted that the world can be analyzed into a number of separate things with relations. A few questions that must be answered are:
1. Are the things that really are logically complex entities really complex?
2. Are they really entities?
3. What can be taken as prima facie examples of logically complex entities?
These aren't precise because he believes that one cannot start with precision but must acquire it as they go along. It appears that there are complex entities from #3 everywhere around us. Chairs, tables, Socrates all seem to be complex systems bound together into a unity, and he thinks that this is why monists view the universe as being a unity. Russell doesn't believe in complex entities of those kinds. For example, if we said "Picadilly is a pleasant street." We could analyze this statement and one will find that the fact corresponding to your statement does not contain any constituent corresponding to the word "Picadilly". There is no single constituent simple or complex in the facts corresponding to the word Picadilly. If you define Picadilly one would have to define it as a series of classes of material entitites, so that if you hold Picadilly as real you also have to hold those series and classes as real. Russell holds series and classes as fictions so he also holds Picadilly as a fiction, and the same problems exist with other entities, even Socrates. The rejection of these leads us to other complex entities. In order to give a complete account of the world you must also mention the relations of particular things and their properties all of which are facts, and so facts seem much more complex and much less able to be explained away than things like Socrates. So we begin by analyzing facts. Russell seems to think that because we don't know exactly what Socrates is we don't know what "Socrates" means. A fact is obviously complex because a proposition requires many words to express it. He makes a point of showing that facts can be analyzed on 161 against those who think analysis is impossible. One can understand a proposition if you know the words that compose it even if you've never heard the proposition before. This is a mark of the complexity of propositions contrasted with words which are simple. Take the word "red" which stands for a particular color. One can only understand the meaning of "red" by seeing red things. One can give a definition like "the longest visible wavelength" but not an analysis which is only possible with that which is complex and it depends upon direct acquaintance with the objects of certain simple symbols. One defines symbols not things. Those objects which are impossible to symbolize other than by simple symbols are called simple, those which can be symbolized by a combination of symbols is called complex. And the definition of red above does not constitute the meaning of "red" in the slightest. The two create two different propositions. The definition is actually a true description. Russell says that it is quite fortunate that different individuals don't mean exactly the same things by their words (163) because meaning of words depends on the nature of objects one is acquainted with and different people are acquainted with different objects and they would not be able to talk to one another. In order to analyze the components of a proposition are the symbols we must understand in order to understand the proposition. The components of the fact which makes a proposition true or false, as the case may be, are the meanings of the symbols which we must understand in order to understand the proposition. With obvious exceptions to words like "or", "not", etc. This complexity of the proposition shows that the corresponding fact is complex as well. The reason why we are going from proposition to fact is because symbols are easier to deal with. He also doubts that we cannot analyze the complexity of facts in themselves. Therefore, when one cannot get a real proper analysis of a thing, it is better to talk around it without professing an exact definition.
In Lecture VII, he argues that a logically correct symbolism there will always be a certain fundamental identity of structure between symbol and fact. And that their complexities are very similar as well. For example, it is obviously objectively complex that one object is to the left of another. In a logically perfect language the words in a proposition would correspond one to one with the omponents of the fact with the exception of "or", "not", etc. which have different functions. There would be exactly one word for every simple object, and everything not simple would be expressed by a combination of words. This type of language would give us a glimpse of the logical structure of the facts. If normal languages were this way their vocabulary would make them a private language. The simplest imaginable facts are those which consist in the possession of a quality by some particular thing like "this is white" referring to what you see not the thing itself. Next would be a relation between two facts "this is to the left of that." Then it gets increasingly complicated the more relations there are between greater numbers of facts. These are all the simplest form of fact called an atomic fact expressed by atomic propositions. Atomic facts contain a relation and a term, from one up, these terms are defined as particulars. Particulars = terms of relations of atomic facts. This definition is purely logical. The word expressing a monadic relation is a "predicate". The words that are not the verb or predicate may be called the subject. Only proper names can stand for a particular. One cannot talk about a particular particular except by means of a proper name. One cannot use general words except by way of description. An atomic proposition uses names of particulars because he thinks that is the only way to mention particulars.
He says our everyday language has lots of names for particulars, but in actuality names like Socrates are really abbreviations for descriptions of complicated systems of classes or series not a particular. He says a name can only be applied to a particular with which the speaker is acquainted. With Socrates we don't use the name in its proper sense. So there are very few names in the logical sense of the word, only words uses properly as names are "this" and "that". In "this is white" using "this" as what you presently see, is a proper name, but one cannot apprehend this proposition. If one means the piece of chalk as physical object, "this" is not a name. It is only a proper name when standing for an actual object of sense. This is ambiguous in that it means different things to different people but it is still a proper name in the logical sense. Particulars stand entirely alone and is completely self-subsistent, each one is logically independent of every other, each one might be the whole universe, it is merely an empirical fact that this isn't the case, this is a peculiarity of particulars. All that is required to understand a name of a particular is to be acquainted with it, then you have a full, adequate, and complete understanding of the name and no further info is required. No further info of the facts of that particular allow you to have a fuller meaning of the name.
Excursis into Metaphysics
Russell thinks that all traditional metaphysics are filled with mistakes due to bad philosophical grammer. He doesn't think numbers are real entities because they are classes of classes, and classes are logical fictions. He has tried to justify that we can get down in theory if not in practice to ultimate simples, out of which the world is built. These simples are of infinite number of sorts. There are particulars and qualities and relations of various orders.
Other than simples there are only facts but they are not properly entities in the same sense like their constituents are, that is shown because you can't name them. But in order to know the world you must know both through knowing a simple is different from knowing facts.
A phrase may be denoting, yet not denote anything. A phrase may denote one definite object. A phrase may denote ambiguously. There is a distinction between acquaintance and knowledge about something, the latter we only reach through means of denoting phrases.
His theory is that the denoting phrase is meaningless, only the proposition it is in is meaningful. He uses a variable C(X) that can be put in three propositions all building off of the first one ‘C (everything) means “C(x) is always true”’, which is taken as ultimate and indefinable; from that proposition we can make ‘ “C (nothing) is false” is always true’; and from that proposition we can make ‘It is false that “C (x) is false” is always true’.
“I met a man” then becomes ‘ “I met X, and X is human” is not always false’.
“The” implies uniqueness.
He says the evidence for his theory is that contradictions result from the other theories where denoting phrases stand for genuine constituents. So ‘round square’ is supposed to be an object.