Logic has a tendency to correct, first, inaccuracy of thought, secondly, inaccuracy of expression. Many persons who think logically express themselves illogically, and in so doing produce the same effect upon their hearers or readers as if they had thought wrongly.

In a logically perfect language the words in a proposition would correspond one by one with the components of the corresponding fact, with the exception of such words as ‘or,’ ‘not,’ ‘if,’ ‘then,’ which have a different function. In a logically perfect language there will be one word and no more for every simple object, and everything that is not simple will be expressed by a combination of words, by a combination derived, of course, from the words for the simple things that enter in, one word for each simple component. A language of that sort will be completely analytic, and will show at a glance the logical structure of the facts asserted or denied. The language which is set forth in Principia Mathematica is intended to be a language of that sort. […] Actual languages are not logically perfect in this sense, and they cannot possibly be, if they are to serve the pur- poses of daily life.

Once master the machinery of Symbolic Logic, and you have a mental occupation always at hand, of absorbing interest, and one that will be of real use to you in any subject you take up. It will give you clearness of thought – the ability to see your way through a puzzle – the habit of arranging your ideas in an orderly and get-at-able form – and, more valuable than all, the power to detect fallacies, and to tear to pieces the flimsy illogical arguments, which you will so continually encounter in books, in newspapers, in speeches, and even in sermons, and which so easily delude those who have never taken the trouble to master this fascinating Art. Try it. That is all I ask of you!

The propositions of philosophy are not factual, but linguistic in character – that is, they do not describe the behaviour of physical, or even mental, objects; they express definitions, or the formal consequences of definitions. Accordingly we may say that philosophy is a department of logic.

It needs must be that what can be thought and spoken of is;
for it is possible for it to be, and it is not possible for, what is
nothing to be. This is what I bid thee ponder. I hold thee
back from this first way of inquiry, and from this other also,

upon which mortals knowing naught wander in two minds; for
hesitation guides the wandering thought in their breasts, so that
they are borne along stupefied like men deaf and blind.
Undiscerning crowds, in whose eyes the same thing and not the
same is and is not, and all things travel in opposite directions!

Being is that which belongs to every conceivable term, to every possible object of thought – in short, to everything that can possibly occur in any proposition, true or false, and to all such propositions themselves. Being belongs to whatever can be counted. If A be any term that can be counted as one, it is plain that A is something, and therefore that A is. “A is not” must always be either false or meaningless. For if A were nothing, it could not be said not to be; “A is not” implies that there is a term A whose being is denied, and hence that A is. Thus unless “A is not” be an empty sound, it must be false – whatever A may be, it certainly is. Numbers, the Homeric gods, relations, chimeras and four-dimensional spaces all have being, for if they were not entities of a kind, we could make no propositions about them. Thus being is a general attribute of everything, and to mention anything is to show that it is.

The propositions of philosophy are not factual, but linguistic in character – that is, they do not describe the behaviour of physical, or even mental, objects; they express definitions, or the formal consequences of definitions. Accordingly we may say that philosophy is a department of logic.

That we can form no idea of its content is […] no reason for denying all meaning to a word, or for excluding it from our vocabulary. We are indeed only imposed on by the opposite view because we will, when asking for the meaning of a word, consider it in isolation, which leads us to accept an idea as the meaning. Accordingly, any word for which we can find no corresponding mental picture appears to have no content. But we ought always to keep before our eyes a complete proposition. Only in a proposition have the words really a meaning. It may be that mental pictures float before us all the while, but these need not correspond to the logical elements in the judgement. It is enough if the proposition taken as a whole has a sense; it is this that confers its parts also to their content.