I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to that or some truer method of philosophy.

Rational mechanics must be the science of the motions which result from any forces, and of the forces which are required for any motions, accurately propounded and demonstrated. For many things induce me to suspect, that all natural phenomena may depend upon some forces by which the particles of bodies are either drawn towards each other, and cohere, or repel and recede from each other: and these forces being hitherto unknown, philosophers have pursued their researches in vain. And I hope that the principles expounded in this work will afford some light, either to this mode of philosophizing, or to some mode which is more true.

I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions.

We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.

The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

But it is not to be conceived that mere mechanical causes could give birth to so many regular motions: since the Comets range over all parts of the heavens, in very eccentric orbits. For by that kind of motion they pass easily through the orbs of the Planets, and with great rapidity; and in their aphelions, where they move the slowest, and are detain'd the longest, they recede to the greatest distances from each other, and thence suffer the least disturbance from their mutual attractions.

Idolatry is a more dangerous crime because it is apt by the authority of Kings & under very specious pretenses to insinuate it self into mankind. Kings being apt to enjoyn the honour of their dead ancestors: & it seeming very plausible to honour the souls of Heroes & Saints & to believe that they can heare us & help us & are mediators between God & man & reside & act principally in the temples & statues dedicated to their honour & memory? And yet this being against the principal part of religion is in scripture condemned & detested above all other crimes. The sin consists first in omitting the service of the true God.

The other part of the true religion is our duty to man. We must love our neighbour as our selves, we must be charitable to all men for charity is the greatest of graces, greater then even faith or hope & covers a multitude of sins. We must be righteous & do to all men as we would they should do to us.

Yet sometimes vegetables and animals are, by certain epithets or circumstances, extended to other significations; as a Tree, when called the tree of life or of knowledge; and a Beast, when called the old serpent, or worshiped. When a Beast or Man is put for a kingdom, his parts and qualities are put for the analogous parts and qualities of the kingdom; as the head of a Beast, for the great men who precede and govern; the tail for the inferior people, who follow and are governed; the heads, if more than one, for the number of capital parts, or dynasties, or dominions in the kingdom, whether collateral or successive, with respect to the civil government; the horns on any head, for the number of kingdoms in that head, with respect to military power...

When a man is taken in a mystical sense, his qualities are often signified by his actions, and by the circumstances of things about him. So a Ruler is signified by his riding on a beast; a Warrior and Conqueror, by his having a sword and bow; a potent man, by his gigantic stature; a Judge, by weights and measures... the affliction or persecution which a people suffers in laboring to bring forth a new kingdom, by the pain of a woman in labor to bring forth a man-child; the dissolution of a body politic or ecclesiastic, by the death of a man or beast; and the revival of a dissolved dominion, by the resurrection of the dead.

I can calculate the motions of erratic bodies, but not the madness of a multitude.

There's no objective morality, but that's not the real point. It's not the point that morality has to somehow be a stone, or something that can be touched. 

The options that are available to choose are determined to a point, and this is the objective aspect of morality, ethics, goodness, fairness, justice. 

The subjective aspect can still remain subjective, but that doesn't mean goodness is relative.....at all. The measure of a man is a man.

There is one ethical principle, either you are preserving life generally, or you aren't. Preserving life in your ends and your means determines whether you are good or evil.

There are two kinds of people, killers, and everybody else.

Pure justice emerges from symmetry applied human life, and human beings as ends in themselves.

To conclude: there are two well-known minor ways in which language has mattered to philosophy. On the one hand there is a belief that if only we produce good definitions, often marking out different senses of words that are confused in common speech, we will avoid the conceptual traps that ensnared our forefathers. On the other hand is a belief that if only we attend sufficiently closely to our mother tongue and make explicit the distinctions there implicit, we shall avoid the conceptual traps. One or the other of these curiously contrary beliefs may nowadays be most often thought of as an answer to the question Why does language matter to philosophy? Neither seems to me enough.

Well, he wasn't a relativist. There's a long and complicated story of the rise of a desire for scientific relativism. Part of it may well be simply sort of rage against reason, the fear of the sciences and a kind of total dislike of the arrogance of a great many scientists who say we're finding out the truth about everything-and here [with Kuhn] there was a way to undermine that arrogance.

There are two ways in which a science develops; in response to problems which is itself creates, and in response to problems that are forced on it from the outside.

Pascal is called the founder of modern probability theory. He earns this title not only for the familiar correspondence with Fermat on games of chance, but also for his conception of decision theory, and because he was an instrument in the demolition of probabilism, a doctrine which would have precluded rational probability theory.

Opinion is the companion of probability within the medieval epistemology.

Many modern philosophers claim that probability is relation between an hypothesis and the evidence for it.

Until the seventeenth century there was no concept of evidence with which to pose the problem of induction!

A single observation that is inconsistent with some generalization points to the falsehood of the generalization, and thereby 'points to itself'.

Much early alchemy seems to have been adventure. You heated and mixed and burnt and pounded and to see what would happen. An adventure might suggest an hypothesis that can subsequently be tested, but adventure is prior to theory.

Statistics began as the systematic study of quantitative facts about the state.

When land and its tillage are the basis of taxation, one need not care exactly how many people there are.

Probability fractions arise from our knowledge and from our ignorance.

From any vocabulary of ideas we can build other ideas by formal combinations of signs. But not any set of ideas will be instructive. One must have the right ideas.

We favor hypotheses for their simplicity and explanatory power, much as the architect of the world might have done in choosing which possibility to create.

To sum up: we have seen that of the three notions of 'partial interpretation' discussed, each is either unsuitable for Carnap's purposes (starting with observation terms), or incompatible with a rather minimal scientific realism; and, in addition, the second notion depends upon gross and misleading changes in our use of language. Thus in none of these senses is 'a partially interpreted calculus in which only the observation terms are directly interpreted' an acceptable model for a scientific theory.

In sum, a theory is only accepted if the theory has substantial, non-ad hoc, explanatory successes. This is in accordance with Popper; unfortunately, it is in even better accordance with the 'inductivist' accounts that Popper rejects, since these stress support rather than falsification.

In summary, then, the set theoretic 'needs' of physics are surprisingly similar to the set theoretic needs of pure logic. Both disciplines need some set theory to function at all. Both disciplines can 'live' - but live badly - on the meager diet of only predicative sets. Both can live extremely happily on the rich diet of impredicative sets. Insofar, then, as the indispensability of quantification over sets is any argument for their existence - and we will discuss why it is in the next section - we may say that it is a strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets.

Truth and falsity are the most fundamental terms of rational criticism, and any adequate philosophy must give some account of these, or failing that, show that they can be dispensed with.

In short, analytic statements are statements which we all accept and for which we do not give reasons. This is what we mean when we say that they are true by 'implicit convention'. The problem is then to distinguish them from other statements that we accept, and do not give reasons for, in particular from the statements that we unreasonably accept. To resolve this difficulty, we have to point out some of the crucial distinguishing features of analytic statements (e.g. the fact that the subject concept is not a law-cluster concept), and we have to connect these features with what, in the preceding section, was called the 'rationale' of the analytic-synthetic distinction. Having done this, we can see that the acceptance of analytic statements is rational, even though there are no reasons (in the sense of' evidence') in connection with them.

On another possible world or another planet a word might be associated with much the same stereotype and much the same criteria as our term 'water', but it might designate XYZ and not H₂O. At least this could happen in a prescientific era. And it would not follow that XYZ was water; it would only follow that XYZ could look like water, taste like water, etc. What 'water' refers to depends on the actual nature of the paradigms, not just on what is in our heads.

Even if we consider not words by themselves but rules deciding what words may appropriately be produced in certain contexts - even if we consider, in computer jargon, programs for using words - unless those programs themselves refer to something extra-linguistic there is still no determinate reference that those words possess. This will be a crucial step in the process of reaching the conclusion that the Brain-in-a-Vat Worlders cannot refer to anything external at all (and hence cannot say that they are Brain-in-a-Vat Worlders).

What we have is a device for producing sentences in response to sentences. But none of these sentences is at all connected to the real world. If one coupled two of these machines and let them play the Imitation Game with each other, then they would go on 'fooling' each other forever, even if the rest of the world disappeared! There is no more reason to regard the machine's talk of apples as referring to real world apples than there is to regard the ant's 'drawing' as referring to Winston Churchill.

To me, believing that some correspondence intrinsically just is reference (not as a result of our operational and theoretical constraints, or our intentions, but as an ultimate metaphysical fact) amounts to a magical theory of reference. Reference itself becomes what Locke called a 'substantial form' (an entity which intrinsically belongs with a certain name) on such a view. Even if one is willing to contemplate such unexplainable metaphysical facts, the epistemological problems that accompany such a metaphysical view seem insuperable. For, assuming a world of mind- independent, discourse-independent entities (this is the presupposition of the view we are discussing), there are, as we have seen, many different 'correspondences' which represent possible or candidate reference relations (infinitely many, in fact, if there are infinitely many things in the universe).

Even though the model referred to satisfies the theory, etc., it is 'unintended'; and we recognize that it is unintended from the description through which it is given (as in the intuitionist case). Models are not lost noumenal waifs looking for someone to name them; they are constructions within our theory itself. and they have names from birth.

If reason is both transcendent and immanent, then philosophy, as culture-bound reflection and argument about eternal questions, is both in time and eternity. We don't have an Archimedean point; we always speak the language of a time and place; but the rightness and wrongness of what we say is not just for a time and a place.

To require that all of these must be reducible to a single version is to make the mistake of supposing that 'Which are the real objects?' is a question that makes sense independently of our choice of concepts.

The problem with all this--the problem I discussed in the first lecture--is that if the causes/background conditions distinction is fundamentally subjective, not descriptive of the world in itself, then current philosophical explanations of the metaphysical nature of reference are bankrupt.

Now, moral philosophers generally prefer to talk about virtues, or about (specific) duties, rights, and so on, rather than about moral images of the world. There are obvious reasons for this; nevertheless, I think that it is a mistake, and that Kant is profoundly right. What we require in moral philosophy is, first and foremost, a moral image of the world, or rather--since, here again, I am more of a pluralist than Kant--a number of complementary moral images of the world.

No sane person should believe that something is 'subjective' merely because it cannot be settled beyond controversy.

What I am saying, then, is that elements of what we call "language" or "mind" penetrate so deeply into what we call "reality" that the very project of representing ourselves as being "mappers" of something "language-independent" is fatally compromised from the very start. Like Relativism, but in a different way, Realism is an impossible attempt to view the world from Nowhere. In this situation it is a temptation to say, "So we make the world," or "our language makes up the world," or "our culture makes up the world"; but this is just another form of the same mistake. If we succumb, once again we view the world-the only world we know-as a product. One kind of philosopher views it as a product from a raw material: Unconceptualized Reality. The other views it as a creation ex nihilo. But the world isn't a product. It's just the world.

Philosophers today are as fond as ever of apriori arguments with ethical conclusions. One reason such arguments are always unsatisfying is that they always prove too much; when a philosopher 'solves' an ethical problem for one, one feels as if one had asked for a subway token and been given a passenger ticket valid for the first interplanetary passenger-carrying space ship instead.

Part of what makes moral philosophy an anachronistic field is that its practitioners continue to argue in this very traditional and aprioristic way even though they themselves do not claim that one can provide a systematic and indubitable 'foundation' for the subject. Most of them rely on what are supposed to be 'intuitions' without claiming that those intuitions deliver uncontroversial ethical premises, on the one hand, or that they have an ontological or epistemological explanation of the reliability of those intuitions, on the other.