Sex

When I read contemporary theories of sexual ethics, they all seem to boil down to "if it's consensual, it's okay." I'm not religious, but this sounds awfully reductionist to me. Isn't there more to sex than just pleasure and emotional bonding? I could go hiking with a woman and that would be pleasurable and bonding. Are there any significant differences between sex and hiking? Or am I appealing to a baseless intuition?

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...

What do derivation systems in a formal logical language tell us about logic? Or about the propositions in the proof? Are their purpose only to show us that a particular proof or argument can be demonstrated using that particular language? IN other words, why do we have derivations in formal logic ... what is their grand purpose?

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 I make a claim, based on empirical evidence, that itself invokes the existence of unobservable entities (e.g., those which are very small) am I making a supernatural claim? For example, if I claim that there are tiny elephants which act as the smallest building blocks of all that exists, is this supernatural or is it simply a scientific claim, given that we currently do not possess the means to observe existence at this level but we might eventually develop such means?

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?

Is this argument evidence of the existence of heaven: "For every need humans have there is a corresponding means of fulfillment. There is hunger and so there is food, there is lust and therefore sex. Finally there is desire for eternal happiness, therefore there must be heaven." I don't think that this is a good argument but I don't know how to refute it. Thanks.

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.

This question is directed (mainly) to Peter Smith. I've read you "Introduction to Gödel's Theorems" (that's how I ended up here) and found it fascinating. At a certain point it the book, it is asserted that G (that is, a Gödel Sentence) is Goldbach type. My question is the following, what are the odds (I don't mean statistically, just your opinion) that the Goldbach conjecture is in some manner an example of a Gödel Sentence naturally (?) arising? I am aware that most mathematicians believe the Goldbach Conjecture to be true, even if all attempts to prove it have failed so far. So, could it be that it actually is true, but to be proven, additional axioms would have to be added to regular arithmetic, or the former would have to be modified in some fashion? Has anyone tried to prove this? Have they succeeded? Sorry for the messy English, I hope my question can be understood, and thanks for writing such an interesting book.

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!!

I always assumed that there could be no contradictions -- that the principle of non-contradiction was absolute, so to say. Recently, however, I read about dialetheism and paraconsistent logic and realized that some philosophers disagreed. It seems all of logic falls apart if contradictions are permitted. I fail to understand how their position makes any sense (which could admittedly be just a failure on my part). So is it possible someone could better explain their viewpoint? Surely none of them believe that, say, one could simultaneously open and close a book, right?

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!]

I know that Gödel shows that there are true claims S that are not provable. The epistemic question is "How do we know S is true". Is it "true" in the same way that axioms of Euclid's geometry are true?

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 ...

I have been reading a little about realism and anti-realism which has left me thinking that my metaphysical beliefs put me in both camps? Let me explain. I'm inclined to accept the correspondence theory of truth which, I think, puts me in the realism camp as to my ontology. However, while I believe there exists a world external to mind, I do not think we come to know that world directly. Our experience and knowledge of the world is mediated by the brain which uses conceptual frameworks to make sense of all the raw data we are bombarded with daily. So it would seem, ontologically I'm a realist but epistemologically I'm an anti-realist. Does this make any sense?

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...

A friend of mine recently gave me a copy of an official report released by the United States Senate Subcommittee. Apparently they invited medical and scientific officials from all across the world to discuss the scientific status of a fetus. There wasn’t any debate. All agreed that human life began at some point during the initial conception except one who said he didn’t know. Here’s a quote from the report. “Physicians, biologists, and other scientists agree that conception marks the beginning of the life of a human being - a being that is alive and is a member of the human species. There is overwhelming agreement on this point in countless medical, biological, and scientific writings.” Subcommittee on Separation of Powers to Senate Judiciary Committee S-158, Report, 97th Congress, 1st Session, 1981 I did some further snooping on the internet and found that the medical and scientific community is in universal agreement on the fact that human life begins upon conception. This leads me to a few...

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...

I attempted to define 'Truth' today and so far the best I can come up with is: In order to really understand and analyse exactly what truth is; we first need to explore the idea of truth in its purest form. The Compact Oxford English dictionary suggests that Truth is 'that which is fact or can be accepted as true.' In this sense, I would first suggest that, philosophically, truth falls more aptly into the area of faith and belief as opposed to anything definitive. This is due to the fact that nothing can be proven to be precisely accurate without error for an infinite amount of time. In fact, even if something were theoretically created at a point in time that was, at that point in time, precisely accurate it cannot be proven to be accurate for an infinite amount of time as, by definition, you would need to test the theory or creation infinitely. We can thus resolve that, despite common definition, truth is a label given to an abstract, repetitive belief specifically in relation to the human condition...

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 .

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