But note there's no conflict being saying that "if it's consensual, it's ok" while also saying there can be more to sex than pleasure and a bit of temporary (maybe very, very temporary) bonding. After all, saying something is ok is saying it is permissible, it isn't positively wrong, it isn't to be condemned. And something can be permissible without being optimal; it may not be positively wrong but may fall well short of being particularly to be admired or sought after. Woody Allen jested "Sex without love is an empty experience, but as empty experiences go, it's one of the best". And there's nothing wrong with a fleeting consensual sexual romp (assuming neither partner is committed elsewhere, or is underage, etc. etc.). Which is worth reiterating in the face of the crabbed puritanism of screwed-up moralists, religious or otherwise. And cheap music and cheap booze have their moments too, contrary to other kinds of puritans. But that's quite consistent with the thought that we can and should...

Logic is about what follows from what. But what follows from what isn't always obvious (or else, e.g., pure maths would be a lot easier than it is). So we need ways of demonstrating unobvious entailments. And a standard way of doing this is to show how we can get from the given premisses to the intended conclusion by a sequence of small steps, each of which is guaranteed to be truth-preserving. If we can break down the big inferential leap from premisses to conclusion into smaller inferential moves, each one of which is evidently valid, that shows the big leap is valid too. Now all this applies equally to informal reasoning -- e.g. derivations or proofs in informal mathematics -- and to formally tidied-up reasoning alike. There's nothing mysterious then about derivations in formal logic. They just do in a regimented way, in some tightly constrained formal language, the sort of thing we usually do in a less regimented way. And given a formal version of a proof, we can read back an informal,...

If you have a powerful theory about the smallest building blocks of the world, aboutwhat the laws governing them are, how they combine to generate morefamiliar entities, and this allows you to make more or less successful predictions about the world, then you are presumably giving a scientific account of the natural world. What else? True, these building blocks may not be directly observable, and indeed yourtheory may explain why they can't be observed. But postulating theirexistence may still be the best explanatory game in town by standardscientific criteria. There's nothing 'supernatural' going on -- even if the quantum mechanical laws governing these micro things do make them pretty weird by everyday standards. You jokingly call these ultimate building-blocks "elephants", I call them "quarks" (in fact a name that seems to have originated in another joke). But what's in a word?

Note, desiring something isn't needing it. I may desire a villa in Tuscany, but I don't need one. And, whatever is the case with needs, plainly it isn't the case that for every human desire there is a way of fulfilling it (especially given other people's desires). Maybe lots of us would love a villa in Tuscany; but we can't all get one. And in fact we often desire flatly impossible things. Lots of humans would love totime-travel: but of course that desire doesn't make itpossible. And maybe lots of us would love to live for ever: butthere's no reason to suppose that merely having the desire makes eternal life possibleeither.

I'm really glad you enjoyed the Gödel book! Suppose that S is Goldbach's conjecture. And suppose theory T is your favourite arithmetic (which includes Robinson Arithmetic). Then Theorem 9.3 applies to S . So if not- S is not logically deducible from T , then S must be true. So if we had a proof that S is a "naturally" arising Gödel sentence -- i.e. a demonstration that T proves neither S nor not- S -- we'd ipso facto have a proof that S is true. That means that establishing that that S is a "naturally" arising Gödel sentence for T -- if that's what it is -- is at least as hard as proving Goldbach's Conjecture itself. Which, the evidence suggests, is very hard! As to the "odds": my hunch is that GC is true, and can be proved in PA -- but I wouldn't bet even a decent meal out on it!!

Those who believe that there are contradictions which are true don't think that all contradictions are true. They don't think that "ordinary" contradictions like "the book is fully open and the book is fully closed" can be true. It is only special cases, like Liar propositions and other paradoxical propositions, and perhaps some others, that are claimed to be true and false at the same time. [' Fully open' vs ' fully closed' here, for the reasons that Richard gives in his next posting!]

No, Gödel does not show that there are true claims S that are not provable. He shows rather that, given a consistent formal theory T which contains enough arithmetic, then there will be a true arithmetical "Gödel sentence" G which is not provable in T. But that Gödel sentence G , though it can't be proved in T , can and will be provable in other formal theories (for example, G is provable in the theory that you get by adding to the axioms of T a new axiom Con(T) that encodes the claim that T is consistent). So if we reflect on the axioms of T and accept them as true, and so have good reason to think that T is consistent, we'll have good reason to think T 's Gödel sentence G , which is provable in T + Con(T), is true. (And there's nothing especially mysterious about the notion of truth here: it is the common-or-garden notion of arithmetic truth that is invoked when we say of even the simplest sentence of formal arithmetic, as it might be "1 + 0 ...

Let's make two initial comments to muddy the waters! 1) Accepting some version of a correspondence theory of truth -- e.g. accepting that a true proposition is made true by the existence of a corresponding fact -- doesn't ipso fact make you a realist in your ontology. It will obviously depend what you think about facts ! (You could still be an idealist like Berkeley, and suppose the only facts are ultimately those involving God, other spirits, and their ideas.) 2) Accepting that our knowledge of the world depends on a lot of processing of data by the brain using built-in cognitive mechanisms doesn't make you an anti-realist in epistemology. You could still hold that when those processes are working reliably, they successfully give you epistemic access to facts that obtain independently of you and your cognitive mechanisms. I'd say that talk of a "correspondence theory of truth", "realism about ontology", "conceptual frameworks", and "epistemological anti-realism" is all far too slippery...

Let's agree that, from the moment of conception, we have a living thing -- and, if the parents are human, this living thing belongs to no other species than homo sapiens . So what? That fact doesn't in itself determine the moral status of the product of conception. Here's one possible view: as the human zygote/embryo/foetus develops, its death becomes a more serious matter. At the very beginning, its death is of little consequence; as time goes on its death is a matter it becomes appropriate to be more concerned about. In fact, that view seems to be exactly the one most of us take about the natural death of human zygotes/embryos/foetuses. After all, few of us are worried by the fact that a high proportion of conceptions spontaneously abort: few of us are scandalized if a woman who finds she is pregnant by mistake in a test one week after conception is pleased when she discovers that the pregnancy has naturally terminated a few days later. Similarly for accidental death: suppose a woman...

Evidently something is going pretty badly wrong here. Here's a truth: my laptop computer is right now on my lap as I'm typing this . It doesn't need "precise accuracy without error for an infinite amount of time" to establish that . It's a rough-and-ready proposition about the here-and-now: precise accuracy and infinite amounts of time just don't come into it. Likewise for many common-or-garden truths. Something else is going badly wrong. For here's another truth: it rained here today . Nothing there about the human condition and human behaviour. Just a local meteorological fact. Getting serious about philosophy is nothing to do with "loving a good argument", or trying to make up definitions off the top of your head, any more than getting serious about physics is. It's hard work, and you need to do your homework first in either case. Try this article on truth as a starting point, or Simon Blackburn's Truth .