In a finite lifetime, you won't be able fully to inspect an object with parts that are infinitely far from you, at least if we assume that you are limited by the speed of light. But there's other evidence. For example, you may be able to measure the gravitational pull of the ladder. If this pull turns out to be exactly what our theory would predict for a ladder that's like the piece of it we have before us (same material, thickness, density, etc.) and infinitely long, then this would be evidence for infinite length. (Note here that the gravitational pull exerted by any one inch of ladder declines with the square of its distance from you. So no matter how long the ladder its, its gravitational pull will not be infinite.) It's also possible that the ladder is expanding (as our universe is), or perhaps contracting. In that case you get a nice Doppler effect: a transformation of light reaching you from distant parts of the ladder -- the farther the light has traveled, the more strongly transformed it arrives. So evidence can provide reasonable assurance. And we have such reasonable assurance now that the universe is in fact finite.

But it's worth noting, as you suggest, that such evidence depends on "reasonable" assumptions. We assume that the laws of nature we've found to hold true around our space-time location also hold millions of light years away and millions of years in the past. Do we have reasonable evidence for this assumption? Well, yes, sort of, if with this assumption we can fit all our observations into one coherent account. Physics hasn't quite achieved this yet. But once physics delivers such a comprehensive theory, then it'll strike us as unreasonable -- bizarre -- to defend an infinite size of the universe by appeal to diverse laws of nature holding at different regions of space-time. But you should ask: the fact that some hypothesis strikes us as bizarre, how much reassurance is this that it's actually false?

In relation to my earlier answer, the following article from the Economist may be of interest. It's advertised as follows: "Can the laws of physics change? Curious results from the outer reaches of the universe." The link is

www.economist.com/node/16941123?story_id=16941123&fsrc=nlw|hig|09-02-2010|editors_highlights

This is not exactly what I had in mind, but relevant nonetheless.

BTW, this question is probably best classified under "physics" rather than "mathematics."

Even if the chords are not presented in the context of a music piece, they are heard in the (more backgrounded) context of music one has heard. Our associations with those pieces of music prime us to hear major versus minor chords in particular ways.

There is also a physical reason for finding major chords to be more settled or stable than minor chords: the wavelengths of a major third match the overtones of the root of a chord more closely than do the wavelengths of a minor third . When we hear a C, for example, it is already producing secondary wavelengths that are those of an E (at a higher octave); the addition of a nearby E thus seems to fit in without added strain.

I think you would really enjoy a new anthology from Wiley-Blackwell--Hunting. It is written largely by and for hunters, and looks at the sort of ethical questions you raise in a way you will find hospitable.

I think hunting is extremely difficult to justify. Though once necessary to obtain necessary nutrients, clothing, etc., killing animals to obtain these things is no longer necessary. It doesn't really help justify hunting/fishing to eat what you kill, if you could have eaten something else.

Even assuming it was necessary to eat meat, it would still be problematic to engage in killing as a recreational leisure activity--which is what hunting/fishing are for most people. If the main goal of sport hunting/fishing are having fun, and food is just a byproduct, something odd is going on (as I argue here). But now getting to you question...

Hunters who are concerned about fairness at least see animals as "subjects" instead of merely as "objects." That's all to the good. Fair hunters will probably kill far fewer animals. But should they really think in terms of fairness? Hunting an animal is not a sport involving two competitors, since the animal doesn't participate voluntarily and has no idea what's going on. In a competition between two humans, fairness is mutually beneficial, but that's not necessarily so in the case of hunting and fishing. The "unfair" hunter at a hunting ranch will lure a tame animal to a hunting station, and then shoot him at close range with a powerful rifle. The "fair" hunter might chase a terrified deer for miles, and then shoot him from a distance with a bow and arrow, so the animal dies a slower death. The extra "fairness" in the second case doesn't benefit the deer, and in fact harms him!

I agree with you that all hunting is not equal, and if one is going to hunt, one should do it "the right way." But the right way, it seems to me, is just less wanton and more humane, not necessarily the way that involves concepts of fairness imported from human sport.

It's not clear what it would mean (or what it would take) to show that there was an effect without a cause (unless we just define an effect as something that is caused, in which case there'd be nothing to show). We certainly have not shown (proven) that every event has a cause in the sense that we have not, and could not, pick out the causes of every event that has ever happened. Rather, we tend to assume that all events have causes, except perhaps those people who assume that free choices are uncaused or who assume that there is a first event that was not caused by any prior event. It's an assumption that tends to work for us--that is, it helps us explain things in science and our everyday life--and it is an assumption that does not have any clear counterexamples (but again, it's not clear what a counterexample would look like). So, as you suggest, this thesis of Universal Causation (UC) might be the most justifiable.

However, one might think that a possible counterexample involves the events described by quantum physics, since it looks like those events are indeterministic: given the exact same prior conditions (or causes) and the same laws of physics, more than one effect might occur. For instance, the electron shot at a barrier might go one way or another and nothing explains (or causes?) which way it goes. However, a better way to describe indeterministic events is that they are probabilistically caused. Quantum physics does not entail randomness--rather it describes objective probabilities between events. So, one can say that the set of events that leads to the electron's hitting the barrier causes it to end up in position 1 (with 50% probability) and causes it to end up in position 2 (with 50% probability). Wherever it ends up, it was caused to end up there by prior effects.

OK, all this is just to set up the take-home message which is that the thesis of UC (Universal Causation), which says that every event--or at least every event after the first event--has a cause, does not entail the thesis of determinism. Determinism is the thesis that: Necessarily, given the same prior events and laws of nature, the same later events occur. UC is consistent with indeterministic causation and hence with the falsity of determinism. So, even if we answer your first two questions 'no', that does not mean we have to answer your third question 'yes'.

Finally, "Hard Determinism" is the thesis in the free will debate that says (a) determinism is incompatible with free will, (b) determinism is true, and therefore (c) free will does not exist. Lots of philosophers (like me) are compatibilists who reject (a) (if interested, see my prior responses to questions in the Freedom category). And most philosophers reject (b) since they accept that the dominant interpretation of quantum physics is indeterministic. But many still think determinism, if true, would rule out free will and do so for reasons that make Universal Causation just as threatening, so indeterminism doesn't help. (Basically, they think that our decisions, like everything else are caused by prior events, ultimately by events over which we have no control, so we do not have ultimate control over our decisions, and they think such ultimate control is required for free will--again, I see no reason to think free will requires such unattainable powers!). These philosophers sometimes call themselves "Hard Incompatibilists" (or Skeptics about free will), and they are the descendants of the Hard Determinists.

This is complicated stuff and I've tried to keep it brief. But I hope this helps!

Philosophers have expressed wide ranging views on the infinite, and even distinguished different kinds of infinites. In terms of the 'infinite' standing for a sequence of events without end, then (just as there is no greatest possible number) it is difficult for someone to claim to have experienced that (experienced all numbers, none of which is lacking in a greater number), though not perhaps difficult for one to claim to understand it (that is, understanding that there is no greatest possible number) or for someone to have an experience of time or space, along with the feeling that this will never end.

There has been some interesting testimony by some philosophers to have experienced soemthing related that may be of interest. Some philosophers have claimed to experience that which is boundless or, in some sense, eternal. Probably the two most famous philosophers to have spoken and analyzed such experiences are Boethius and Augustine. Boethius spoke of God's eternity (and having some experiential acquaintance with God as eternal) in terms of God possessing the 'whole, simultansous, and complete fruition of a life without bounds' (interminabilis vitae tot simul et perfecta possessio'). This would be different from claiming to experience what you might think of as 'forever' or 'endless'; it is more like experiencing an event so overwhelming and perhaps good that you seem to lose track of future and the past. This has been analyzed by some philosophers as experiencing something that is atemporal or beyond metric time or not bound by it. The philosopher A.E. Taylor in an interesting book in the early part of the last century wrote of the experience of eternity in ways that are (to use your term) intense, but more satisfying than jarring or incredible (not worthy of belief). In one example, he describes 'spending an evening of prolonged enjoyment in the company of wholly congenial friends. The past may be represented for us, if we stay to think of it at all, by whatever happened before the party began, the future -but when we are truly enjoying ourselves we do not anticipate it- by what will happen when the gathering is over. The enjoyment of the social evening has, of course, before and after within itself; the party may last two or three hours. But while it lasts and while our enjoyment of it is steady and at the full, the first half-hour in not envisaged as past, nor the third as future, while the second is going on....' Taylor goes on to defend the coherence and importance of experiences that seem to be in response to a value that we wish to last forever or not be bound by time, a state in which one or more people might be completely present to each other that they would never wish it to end. See Taylor's book The Faith of a Moralist --the title is a bit misleading given what we mean by 'moralist' or 'moralistic' today versus when he wrote the book in 1930. It is a good text for thinking about the experience of values and time. (See especially chapters three to six.)