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?

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.

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 am not trained in formal logic, so I was hoping you could help me with the moral argument for the existence of God, postulated as follows: 1. If God doesn't exist, then objective moral standards don't exist. 2. Objective moral standards exist. Therefore God exists. I don't really understand why the arguer is allowed to throw in premise 2. It seems that in order to prove that objective moral standards exist, you must first prove that God exists (because the objective moral standards come from God). Since the truth of premise 2 depends on the conclusion of the argument, it seems the argument collapses into a circle. I guess what I'm really saying is that any theist I know would concede that premise 1 is actually an if and only if statement (again, because morality is inextricably linked with God). After all, if you could prove that objective moral standards exist without appealing to God, then you've demonstrated morality's independence from the existence of God and thus nullified the argument. I...

Is it possible to read Kant as holding a position that does not reject the existence of a reality external to mind while maintaining that we can only know representations of that reality not reality as it exists in itself?

Is is philosophicaly valid to ask (and answer) a question based on false or impossible premises? For instance, I could ask something like "If I'm sure that the baby I'm carrying is going to be an evil person, like a new Hitler, or is going to be a mass murderer of serial child molestor, what is the moral thing to do, interrupt the pregnancy or have the baby?" but the premise of this question is false/impossible because there's no way of knowing how a fetus is going to turn out as a person. How do you philosophers deal with these types of questions?

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?

Let us assume science has demonstrated that vegetarians and careful vegans are just as healthy as – indeed, considerably healthier than – meat-eaters. (It has.) Robert Nozick came up with an interesting hypothetical for those who continue to choose meat in a world where this is so – for those today who opt for the real bacon over the soy bacon not because it’s necessary for one’s health, and not because they bear ill-will towards pigs, but simply because they like the taste more: “Suppose . . . that I enjoy swinging a baseball bat. It happens that in front of the only place to swing it stands a cow. Swinging the bat unfortunately would involve smashing the cow’s head. But I wouldn’t get fun from doing that; the pleasure comes from exercising my muscles, swinging well, and so on. It's unfortunate that as a side effect (not a means) of my doing this, the animal's skull gets smashed. To be sure, I could forego swinging the bat, and instead bend down and touch my toes or do some other exercise. But this...

There's no moral obligation on us to bring into existence lives that are good; on the other hand, if we know a life will be bad, perhaps we are under an obligation not to create it. So, perhaps, not knowing whether the lives we introduce will be good or bad, but knowing there's a significant risk they'll be bad, are we morally obliged not to risk introducing such bad lives?

I am looking for books on ethics written in a popular style; understandable for people reading on a high school level. Can you advise?