I read that Gödel's incompleteness theorems don't effect Peano Arithmetic that doesn't include multiplication sign. This confuses me, since multiplication can be defined through addition. So, even if "PA without multiplication" doesn't have multiplication sign in itself, it provides everything that's needed for defining mul. sign. So what's the difference? That is, why is "PA without multiplication" (but that contains everything needed for defining mul.) different from PA (that already has multiplication defined)? From "Gödel without tears": "The formalized interpreted language L contains the language of basic arithmetic if L has at least the standard rst-order logical apparatus (including identity), has a term '0' which denotes zero and function symbols for the successor, addition and multiplication functions defined over numbers - either built-in as primitives or introduced by definition - and has a predicate whose extension is the natural numbers." Is there any difference between having those...

Is it unethical to look at a woman's breasts? What if she has cleavage?

Can ethics be a sufficient condition for becoming a lifelong "law-abiding" citizen? What ethical standards could be there to ensure life under legal boundaries? Or if one needs some very basic legal knowledge to achieve that being, what combination of ethics and law is most sensible for someone not pursuing a career in law? Or perhaps the question should be posed as, "How much law do we need to know in our lives, and how much do we use ethics to fill the rest of our moral consciousness?" Thank you!

I hope this is not too general of a question, but the more I thought about it the more I realised it was a very difficult question to answer. It does not necessarily pertain to anything religious, but I believe in a God who is eternally good, just so you know the angle that I'm coming from. Anyway, here is my question: Would the idea of something or someone being truly 'good' have ever come about if it never had the contrast of something 'bad' or 'evil' to compare it to? Hypothetically speaking, if someone were to never experience anything bad, would they ever have the understanding of something being good?

Do people who are blind, deaf and mute since birth dream? If so how?

"Scepticism arises because 'for so long as men thought that real things subsisted without the mind, and that their knowledge was only so far forth real as it was conformable to real things, it follows, they could not be certain they had any real knowledge at all. For how can it be known, that the things which are perceived, are conformable to those which are not perceived, or exist without the mind?' The nub of the problem is that if we are acquainted only with our own perceptions, and never with the things which are supposed to lie beyond them, how can we hope for knowledge of those things, or even be justified in asserting their existence?"--A.C. Grayling quoting Berkeley My question is: Isn't one answer to this problem re representationalism that concerns Berkeley that if we were seriously out of sync with the real (mind-independent) world, then how could we have survived as well as we have? If I reach for an object,it's always there (unless I hallucinate).---If it's ALL a "Matrix" world then I can...

It makes sense to me that there should be nothing rather than anything. I find this issue rather mind boggling because obviously there is something. Fortunately I'm able to dismiss this issue and go on to other things. My only hope is that if there is an afterlife, and there are orientation sessions I will ask the lecturer (an angel?) about it. I'm just afraid that his reply will be a board with a bunch of incomprehensible formulae. My question is do philosophers deal with this issue or has it already been dismissed as undealable.

Is democracy a just form of government because it leads to the fairest results, or because it is inherently most fair to let everyone have an equal say in the decision-making process? In a situation where the population overwhelmingly makes a decision that will harm them in the long-term and reduce everyone's standard of living (for example, when the population votes for parties whose policies lead to individual freedom in the short term but collective suffering via environmental decay, financial crisis, war and poverty in the long term), are we witnessing a failure of democracy to do what it is supposed to do (i.e. create the fairest possible society), or are we witnessing democracy doing exactly what it is supposed to do (i.e. let everyone have a fair say in the decision-making process)?

I'm interested to know about the capability of philosophize. Because in my own experience, noticed that when I were a teenager (13-15) I had a strong insight and I started to feel and thought the philosophie even did not reading books, only by my experience of just living. However after had grown up, this ability became even more weak until it disapeared. Today, when I can read the text of the philosophers, I can see all that I thought but not feel as I could feel. Now it seems that the poetic powers are gone. My question is if we can philosophize again (as Schopenhauer says that the Philosophy that chooses the time to come and show us the world in its inner) or just reproduce the quotes of other writers?

Is it possible to perceive something unconsciously?