Per the title, I'll be discussing my own ways of thinking in this post.
If I had to sum it up briefly, I would call myself a moderate liberal rule utilitarian thinker with some empiricism, logic, and methodological naturalism thrown in. That, of course, combines political, ethical, and philosophical ideas, so I'll go ahead and analyze each separately, starting with the last.
The latter half of that last is most closely connected with philosophy, specifically with asking ourselves how we can be certain that what we know matches the actual nature of reality. Logic is the simplest thing I listed, but also the most important. I believe that when it comes down to it, we defend our assumptions about how the world works with logic and evidence, and that we go with the best assumption we have until new evidence comes along. And, given that I mentioned empiricism and methodological naturalism, it is probably obvious that I believe those are currently most supported. I would not, categorically, say that nothing supernatural exists, since it is difficult to say that with certainty. I do, however, believe it is unlikely, with our current understanding, that such things exist, and I believe we can be justified in acting as if that assumption was true, so long as our minds remain open to conflicting evidence.
Next up is the ethical philosophy of utilitarianism. In its most basic form, it focuses on bringing the greatest good to the greatest number. One of its variations is called rule utilitarianism; this theory, instead of focusing on what is right in any specific situation, focuses on creating duties or rules that will promote the greater good overall. Following those rules is then considered good, even if the immediate effect is negative. As with many such ideas, utilitarianism has some problems; in its case, it permits hideous atrocities if the end result brings greater benefit to more people. I, personally, solve this problem by including some details taken from Aristotle's virtues and Kantian ethics, and defining some situations in which the importance of a given duty overrides all potential negative consequences, not just some.
My political philosophy is next. Honestly, there's not too much to say here; I tend to sympathize more with the left as opposed to the right, but I also tend to prefer questioning other people's ideas and ensuring a good debate over defending my own ideals. I'll gladly defend any position I believe I can defend, and I'll gladly argue against any position I think is unsound.
Finally, I'll discuss my own weaknesses. Chief among them is that I am an amateur philosopher at best, and am no better than anyone else at coming up with solid, internally consistent sets of ideas. (Probably the section on my ethics, above, could be taken apart by any actual ethical philosopher.) I am also no better than anyone else at admitting when I'm wrong, and have occasionally realized that I'm being stupid or contradictory in an argument and kept going anyway.
Anyway, that should do for a brief summary. Hopefully it will provide some insight into why I come to the conclusions I draw about others' arguments.