Can we perceive the natural laws, which have shaped our ability to perceive?

I'm not sure I would use quite the verb "perceive" to describe our cognitive grasp of natural laws, but I don't see any reason why we can't discover at least some natural laws, including those that have shaped our ability to perceive (or discover). That is, I don't see any reason why a natural law's having shaped our ability to perceive should make that natural law especially hard for us to discover. It's not as if we should think of natural laws as having purposely shaped our ability to perceive in order to keep themselves hidden from us.

Skeptical theism states that if we cannot tell whether any of the evils in our world are gratuitous, then we cannot appeal to the existence of gratuitous evil to conclude that God does not exist. However, I can't help but think that we can. The rules of probability tell us that that individual probabilities can be quite low, but their disjunction can be very high. For instance, there may be only a small chance that you will be involved in an automobile accident on a given day, but if you drive every day, the chances are pretty good that you will be in one on some day in your lifetime. Similarly, even if the chance that a given instance of a trillion cases of suffering is gratuitous is quite low, the chance that one of that trillion is gratuitous can be can be very high, and it only takes one instance of gratuitous evil to rule out the existence of God. Coming from someone who is not a philosophy major, am I right in my criticism of skeptical theism or is it too naive?

The theism part of skeptical theism, at least if it's classical theism, must say that the probability that God allows suffering without having an adequate moral justification for allowing it is well-defined and zero, just as you suspect. But the skeptical part of skeptical theism, as I understand it, says that we can't properly assign any probability at all to the claim that a given case of suffering is in fact gratuitous (i.e., such that God, if God exists, has no adequate moral justification for allowing it). We can't, according to the skeptical part, because we can't presume to know the full range of justifications at God's disposal, if God exists. So we have to enter a "?" rather than a number (or range of numbers) into our calculation of the probability of the disjunction, which of course renders the calculation impossible. I don't mean to suggest that I accept the skeptical part of skeptical theism, but that's what it says, if I understand it correctly.

so What is more real? The number two or my two feet?

Why must either be "more real" than the other? I can't make sense of "more real," anyway, as a comparison. Are shadows less real than the 3D objects that cast them? Shadows are dependent in a way in which 3D objects are not, but I don't see how that makes shadows any less real when they exist. Some philosophers say that the number 2, being an abstract object, exists necessarily (i.e., in all possible circumstances), whereas your two feet exist only contingently (i.e., in some but not all possible circumstances). But that view does not imply that the number 2 is any more real than your two feet. Other philosophers say that the number 2 exists but not your two feet, because they say that "anatomical foot," being a linguistically vague term, fails to denote anything in the world. (I think they're mistaken.) Still other philosophers would say that neither the number 2 nor your two feet exist. But none of that, I think, implies that one is more real than the other. Is Donald Trump more real than the...

Hi! I wonder what "knowledge" is. I heard the JTB argument that says knowledge must be a justified, true belief. Then there is the Gettier problem in which JTB is not sufficient to describe knowledge. But I suppose, to say that "JTB is not enough for knowledge", one must have a definition of knowledge in the first place which is not "justified, true belief". So I was so curious what the definition of knowledge, about which philosophers have been discussing so long, actually is?

You're right that according to the JTB analysis of the concept of knowledge (it's really an analysis rather than an argument), propositional knowledge is identical to justified, true belief. Gettier cases, as you say, are meant to show that knowledge requires more than justified, true belief. But Gettier cases don't proceed by assuming a different analysis (or definition) of knowledge than the JTB analysis: if they did that, they would be guilty of begging the question against the JTB analysis. Instead, Gettier cases involve scenarios in which intuitively the subject lacks knowledge of a proposition despite having a justified, true belief of the proposition. We're supposed to agree that, intuitively, Smith doesn't know the proposition Jones owns a Ford or Brown is in Barcelona , even if we don't have in mind any specific definition of "knowledge." Compare: If I propose an analysis of the concept of a lie on which a lie is nothing more than a false utterance, you can refute my analysis by...

Do these two sentences mean the same thing?- a) If I feel better tomorrow, I'll go out. b) Unless I feel better tomorrow, I won't go out.

I'd say that they have different meanings. I interpret (a) as implying that your feeling better tomorrow is a sufficient condition (all else equal, presumably) for your going out, whereas (b) implies that your feeling better tomorrow is a necessary but maybe not sufficient condition for your going out. That is, (b) seems more cautious, more hedged: (b) allows that you may not go out even if you do feel better tomorrow. Compare: (c) If you feed your pet goldfish, it will flourish; (d) Unless you feed your pet goldfish, it won't flourish. Given how easy it is to overfeed a pet goldfish, (c) is doubtful: your pet goldfish may not flourish even if you feed it. Given that pet goldfish depend on being fed, (d) isn't at all doubtful.

Representation of reality by irrational numbers. In the world there are an infinite number of space/time positions represented by irrational numbers. I should think that all these positions are real, even though they cannot be precisely described mathematically. Does this mean that mathematics cannot fully describe reality? What are the philosophical implications of this?

I would question your assumption that positions, magnitudes, etc., whose measure is irrational "cannot be precisely described mathematically." Consider a simple-minded example: In a given frame of reference, some point-particle is located exactly pi centimeters away from some other point-particle. I think that counts as a precise mathematical description of the distance between the two particles, even though it uses an irrational (indeed, transcendental) number, pi, to describe the distance. It's true that any physical measurement of that distance -- say, 3.14159 cm -- will be precise to only finitely many decimal places and therefore will be only an approximation of the actual distance. But the description "pi centimeters apart" is itself perfectly precise, despite the irrationality of pi.

In my opinion, one of the reasons that we argue around determinism is that it seems to have some disturbing implications with regards to fatalism: if determinism is true, then everything is predetermined since the origin of the universe. That is to say that given enough information about the state of the original universe, it is possible to 'calculate' what is going to happen thereafter, because determinism means everything is strictly causally determined by its prior events. And because of this, in a strictly deterministic universe, there is only one 'fate' for anyone, and the disturbing implication that seems to follow is that since there is one fate for me, there is not much point for me make any decisions, because I'm not really making decisions, as everything I will do, or want, is already determined. How might a compatibilist, who thinks that humans are still capable of free will and are capable of making decisions, refute the above argument for fatalism? p.s.: this is a follow-up from the question...

Thanks for following up. I'm pleased that you found my earlier answer helpful. Above you wrote, "the disturbing implication that seems to follow is that since there is one fate for me, there is not much point for me make any decisions, because I'm not really making decisions, as everything I will do, or want, is already determined." I'd like to make two points in reply. (1) It's crucial not to confuse determinism with "your fate." Your fate is supposed to be the fixed outcome that you'll encounter regardless of anything you do in the meantime. So, according to the story, Oedipus is fated to kill his father and marry his mother, regardless of any actions Oedipus takes beforehand, including any attempts he makes to avoid that fate. Determinism is, if anything, the opposite doctrine. According to determinism, whom you marry (if anyone) depends crucially on your actions beforehand: every link in the causal chain is essential, no link is superfluous, and those links include your carefully considered...

My question arises in free will and compatibilism. Basically, according to the compatibilists, the actions driven by 'internal factors' can be considered as free. Is this truly the kind of free will that people want to establish in the first place? Isn't this more of a compromise, rather than solution? I would have thought that the free will we are trying to seek is the capability to do otherwise, but I think internally driven actions are still determined, i.e. the agent could not have done otherwise. Moreover, is it right to seek free will as in 'the capability to do otherwise'? Is this truly meaningful? I feel like the whole deterministic and incompatible theory is somewhat dodgy in its logic: what does it mean that we cannot have done otherwise?

I would have thought that the free will we are trying to seek is the capability to do otherwise... The capability to do otherwise, full stop, or the capability to do otherwise had we wanted to do otherwise? Today I saw my neighbor and gave him a friendly greeting because I wanted to. Even if determinism is true, had I wanted not to give him a friendly greeting -- imagine that he had rudely blasted his stereo and woken me at 3:00am -- there's no reason to think I would have given him a friendly greeting anyway. That is, determinism is compatible with the claim that my desire to give my neighbor a friendly greeting played an essential role in my actually giving him a friendly greeting. Indeed, I want my action to be under the effective control of my desire: I don't want indeterminism to pop up in between the two. For suppose that, despite my wanting to give him a friendly greeting, something indeterministic popped up and resulted in my screaming obscenities at him instead. I would hardly...