(Let me just add to what TheOtherKawoomba already said)
This is an infinity, and therefore I have an infinity of beliefs. Is that wrong?
If that were so, then "I believe the sky is blue" would mean "I have an infinity of beliefs about the sky, namely that it is blue, so it also is "not blue+1/nth the distance to the next color" (then vary the n).
A student writing down "x>2" would have stated an infinity of beliefs about the answer. Does that seem like a sensible definition of belief? Say I picked one out of your infinite beliefs about the car's weight. Where is it located in your brain? Which synapses encode it? It would have to be the same ones also encoding an infinity of other beliefs about the car's weight. Does that make sense? I plead the Chewbacca defense.
There's another problem if you consider all the implications as if they were your beliefs, even if you've not explicitly followed the implication. Propositions in math simply follow from axioms, i.e. are implications of some basic beliefs. Yet for some of those their truth value is famously not yet known. If you held all beliefs which were logically implied by stated beliefs to also be your beliefs just the same, you'd face a conundrum - you'd be uncertain about such famous - yet unknown - propositions. Yet that uncertainty isn't in the territory - either the proposition is implied by the axioms or it isn't. Yet you couldn't build the "beliefs implied by this belief". So would you just follow "trivial" implications such as in your example? You'd still need to evaluate them, and it is that simple fact of having to evaluate whether an implication actually is one, or even if 99 is actually smaller than 100 - however trivial it seems - that is the basis for the new (derived) belief, the reason you cannot automatically follow an infinity of implications simultaneously. Since you cannot evaluate an infinity of numbers, you cannot hold an infinity of beliefs.
If that were so...
Agreed. Edit: I don't think the one claim means the other, but I do agree that the one (in this case) implies the other. Do you believe that the sky's being blue excludes its being (at the same time and in the same respect) red?
A student writing down "x>2" would have stated an infinity of beliefs about the answer.
Well, the student could be said to believe an infinity of things about the answer, not that the student has stated such an infinity. We agree that to state (or explicitly think about) an infinity of beliefs wo...
A few notes about the site mechanics
A few notes about the community
If English is not your first language, don't let that make you afraid to post or comment. You can get English help on Discussion- or Main-level posts by sending a PM to one of the following users (use the "send message" link on the upper right of their user page). Either put the text of the post in the PM, or just say that you'd like English help and you'll get a response with an email address.
* Normal_Anomaly
* Randaly
* shokwave
* Barry Cotter
A note for theists: you will find the Less Wrong community to be predominantly atheist, though not completely so, and most of us are genuinely respectful of religious people who keep the usual community norms. It's worth saying that we might think religion is off-topic in some places where you think it's on-topic, so be thoughtful about where and how you start explicitly talking about it; some of us are happy to talk about religion, some of us aren't interested. Bear in mind that many of us really, truly have given full consideration to theistic claims and found them to be false, so starting with the most common arguments is pretty likely just to annoy people. Anyhow, it's absolutely OK to mention that you're religious in your welcome post and to invite a discussion there.
A list of some posts that are pretty awesome
I recommend the major sequences to everybody, but I realize how daunting they look at first. So for purposes of immediate gratification, the following posts are particularly interesting/illuminating/provocative and don't require any previous reading:
More suggestions are welcome! Or just check out the top-rated posts from the history of Less Wrong. Most posts at +50 or more are well worth your time.
Welcome to Less Wrong, and we look forward to hearing from you throughout the site!
Note from orthonormal: MBlume and other contributors wrote the original version of this welcome post, and I've edited it a fair bit. If there's anything I should add or update on this post (especially broken links), please send me a private message—I may not notice a comment on the post. Finally, once this gets past 500 comments, anyone is welcome to copy and edit this intro to start the next welcome thread.