# For some reason, the sorites paradox seems quite a bit like the supposed paradox of Achilles and the turtle with a head start: every time Achilles reaches where the turtle had been, the turtle moves a little bit forward, and so by that line of reasoning, Achilles will never be able to reach the turtle. Yet, when we watch Achilles chase the turtle in real life, he catches it and passes it with ease. By shifting the level of perspective from the molecular to the macro level, so to speak, we move beyond the paradox into a practical solution. If we try to define "heap" by specifying the exact number of grains of sand it takes to differentiate between "x grains of sand" and "a heap of sand," aren't we merely perpetuating the same fallacy, albeit in a different way, by saying that every time Achilles reaches where the turtle had been, the turtle has moved on from there? If not, how are the two situations qualitatively different? Thanks.

### In my opinion, the reasoning

In my opinion, the reasoning that generates the paradox of Achilles and the tortoise isn't nearly as compelling as the reasoning that generates the sorites paradox. The Achilles reasoning overlooks the simple fact that Achilles and the tortoise are travelling at different speeds : if you graph the motion of each of them, with one axis for distance and the other axis for elapsed time, the two curves will eventually cross and then diverge as Achilles pulls farther and farther ahead of the tortoise. All of this is compatible with the fact that, for any point along the path that's within the tortoise's head start, the tortoise will have moved on by the time Achilles reaches that point: that's just what it means for the tortoise to have a head start. It's not that the Achilles reasoning is good at the micro level but bad at the macro level. It's just bad. By contrast, the only thing overlooked by the sorites reasoning is the principle that a small quantitative change (e.g., the loss of one grain of...

# Recently, I noticed about sorites problem. I thought that problem is serious to all of philosophical endeavor, but my friend told me that is problematic when you assume some kind of platonism. Is he right? Or is it equally problematic when we assume nominalism?

### I think that the sorites

I think that the sorites paradox is a problem even for nominalists. Suppose we line up 101 North American men by height, starting with the shortest man (who's 125 cm tall) and ending with the tallest man (who's 225 cm tall). Let's also suppose that each man except the shortest man is 1 cm taller than the man to his right. Clearly the shortest man is short. If 1 cm in height never makes the difference between a short man in the lineup and one who isn't short, then the tallest man is also short, which is clearly false. So there must be a tallest short man in the lineup. But who could that be? If we can't know who it is, then why not? I think I've managed to state the problem in terms that even a nominalist can accept. If nominalism, as such, evades the problem, then I'd love to know how it does.

# Is it right to call a believer rational even if she cannot prove articulately or give good arguments for her belief in God? Let's just say I ask a believer "Why do you believe in God?" and she simply answered, "Because I've experienced God's grace in my life," and she needs no arguments or other evidences for her belief, is her position justifiable? I personally thinks it is but if that is the case, then what would make belief in God irrational, if simply certain personal experiences can justify such belief?

If she had reasons to believe, it would not be faith that she had but knowledge. I respectfully reject the implicit reasoning in Prof. Marino's claim. Someone's having reasons to believe may make her belief rational or epistemically justified, but her belief is knowledge only if her belief is true , and its truth doesn't follow from her having reasons to believe. [A]s human beings we still have to decide whether or not [to] believe in what falls outside the bounds of reason. Does what falls outside the bounds of reason also fall entirely within the bounds of reason? If no, why not? If yes, then how can anyone understand the statement of Prof. Marino's that I just quoted?

# The universe appears to behave in logical ways. All of the individual physical components of the universe, as far as we can tell, are likely governed by logically consistent laws of physics. According to physicalism, human beings are nothing more than complex physical systems. That means that the physical components and functions of a human being, including those that give rise to human thought, are governed by the same logically consistent laws that govern the behavior of electrons, etc. If the physical processes that give rise to thought are rational how can a human being have an irrational thought? Where in the system does irrationality arise? It seems that human beings are in fact capable of irrational thought. If two people hold mutually exclusive ideas then at least one of them must be wrong. But if irrational thought is possible where does it come from? Is this an argument against physicalism? Does it mean we are more than just bits of matter? Or does it mean that the universe itself doesn't...

You asked, "If the physical processes that give rise to thought are rational, how can a human being have an irrational thought?" You might be misinterpreting the claim that "the physical processes...are rational." Presumably what's meant by the claim is that the physical processes can be discovered and understood by rational means , such as empirical investigation and logical reasoning. The claim doesn't mean to attribute rationality to the physical processes themselves: the processes don't literally investigate or reason, either well or badly. So the fact that the physical processes can be discovered and understood rationally doesn't imply that irrational thoughts can't result from those processes. Furthermore, we can rationally investigate the physical causes of irrational thoughts, even if science isn't very far down that road at present. In any case, we should resist the suggestion that the universe sometimes violates the laws of logic: that suggestion is either impossible or not even...

# It seems to me that today's rationality is completely irrational in a sense that it attacks everything that is not rational. But who define what is rational? For example, many people like to back up their beliefs by scientific arguments or by pointing on the bad parts of religion. Yet in 19. century frenology was considered science. Today we call it pseudoscience. Is it lacking humility for most people or something else that they cannot accept that in 200 years people will laugh at our modern "science"? And, if we are so deeply influenced by beliefs of our times why wouldnt relativism allow for more open minded approach in a sense that it would allow people to believe anything they want (without the need for justification) instead of using relativism primarily for attacking "old" beliefs (example would be the view that christianity is obsolete)?

Your comment seems to be in tension with itself. You end it by suggesting that we adopt a version of relativism "that...would allow people to believe anything they want (without the need for justification)." Yet you begin your comment by apparently condemning, as "completely irrational," the beliefs of those who think pseudoscience or religion are irrational. I don't think you can have it both ways: relativism for their judgments, objectivism for your own. You ask, "Who defines what is rational?" I take it you have some definition in mind when you describe critics of pseudoscience and religion as "completely irrational." Relativism has an undeserved reputation for being open-minded. Those who think that they can "believe anything they want (without the need for justification)" should feel no pressure to keep their minds open to any evidence or arguments against what they believe.

# I understand that mathematical induction is deductive reasoning (but why doesn't it have another name?!). But I wonder if there can be true induction based only on reason. Here is an example: I may think about a possible practical problem and think what I would do in many variants of it. I can also ask other people to imagine other variants and I can ask them help about what to do in all those variants. After all this thinking, it is possible that one notices a general rule about what to do with that problem, and come to believe that that rule would be good for every variant of it, even for those variants we didn't check. Wouldn't that be an inductive conclusion? And do you think that this conclusion would be less acceptable than inductive conclusions in the natural sciences?

It's not clear to me how your example counts as "induction based only on reason." As I understand it, the process you imagine involves asking other people to think about the problem and then share with you their advice. Even if you stick entirely to your own thoughts about the problem, they'll no doubt be informed by your experience with practical problems of a similar kind. Either of those methods is at least partly empirical rather than "based only on reason." You would indeed be drawing conclusions inductively rather than (purely) deductively. As for the reliability of the results, I prefer a method in which various possible solutions to a type of practical problem are actually tried out rather than merely thought about. As anyone who's tried DIY renovations can tell you, there's a world of difference between thinking about how a practical problem should be solved and seeing how it actually gets solved once you put your thoughts into practice!

# Is it rational to believe that some of my beliefs are false? This seems like a reasonable claim. After all, most people have some false beliefs, and I know that I've had plenty of beliefs in the past which I later learned were false. On the other hand, I obviously believe that each of my beliefs is true (otherwise, they wouldn't be my beliefs). So how could I also believe that some unspecified beliefs among them are false?

It certainly looks like the height of rationality for you to believe that at least some of your beliefs are false. Yet, as you point out, there's no particular belief of yours that you regard as false. Any given belief of yours you regard as true; otherwise, it wouldn't be a belief of yours. This pair of attitudes gives rise to what's usually called the "Paradox of the Preface." One place to start looking is the SEP entry on "Epistemic Paradoxes," available here , which contains both discussion and references.

# I've heard it asserted several times in quite different contexts that "people make decisions primarily using emotional criteria, and only after the fact do they then use reason to justify this decision." I'm curious both to hear your response(s) in general, and perhaps also in a more specific context. If I understand Karl Marx' economic theory correctly, he asserts that the foundation of all social relationships is technology, or economic relationships, or how people earn a living. Social, political, religious, and governmental structures then develop as a justification of the fundamental underlying economic relationships. I'm curious on philosophical responses to this assertion, because it seems to me that it is the basis for the crucial argument that then follows. He then asserts that, because technology is constantly evolving, while bureaucratic structures are static, that a "dissonance" develops over time, which must eventually result in a re-balancing. so that the other structures are then in...

Regarding whether it's true that "people [in general] make decisions primarily using emotional criteria, and only after the fact do they then use reason to justify this decision": This question is empirical, and it belongs to psychology. I wouldn't trust any philosopher as such to answer it. I'm not sure that psychology, in its present state of development, can answer it either, but philosophy as such doesn't have a hope of answering it. The claims you attribute to Marx are also empirical, and in this case best evaluated by economic historians. The claims are so sweeping that I myself would need an awful lot of evidence before I'd accept them. I'm not sure how we'd even get reliable evidence that "the foundation of all social relationships is technology, or economic relationships, or how people earn a living": the claim is not only sweeping but also ill-defined (what's meant by "foundation"?). Philosophers as such aren't equipped to answer empirical questions. But I think they...

# I often read that we must judge arguments or claims based on their own merits, rather than on the quality of the person presenting them. This is fine in realms such as logic or everyday life, where we can all have access to the relevant information, but how does this play out in complex domains, such as science? For instance, suppose I am reading two books on the health effects of different nutrients, such as animal fat. One author claims all animal fat is harmful, the other claims that some animal fats, such as fish fat, is fine in moderation. Both cite studies supporting their views, but one author is a spokesperson for PETA and the other is a senior researcher at a well-known university. As somebody who doesn't have access to biology laboratories to conduct experiments, and who perhaps doesn't have the time to read every source cited, critique every study made and read every attack made on both author's views, what is the best thing for me to do? Should I simply decide not to believe anything at...

Your question touches on two much-discussed philosophical topics: the epistemology of (expert and non-expert) testimony and the epistemology of disagreement . You can find accessible discussions of those topics here and here . I won't opine about those topics in general except to say that the academic credentials and scholarly independence of anyone making a scientific claim are highly relevant and worth checking. Fortunately, the particular example you gave is fairly tractable: the issue "Is all animal fat harmful even if consumed in moderation?" In fact, the debate you referred to is even more tightly focused: "Is fish fat, even in moderation, harmful?" Thanks to that tight focus, you can narrow your search to sources answering that particular question. The web makes such a search easier than ever before. Start with the most recent peer-reviewed articles you find, because they're supposed to take account of and respond to earlier articles; their conclusions will be summarized...

# According to the Stanford Encyclopedia of philosophy Schopenhauer was one of the first philosophers to advocate for the idea that the universe was not something "rational" What is an "irrational" universe then? Is there a difference between a universe being beyond the grasp of human reason and saying that the universe is "irrational"? Does he mean to say that the universe can do things that are illogical such as have square triangles?

I'm also no scholar of Schopenhauer, but from what I remember he's claiming that our universe is at bottom non-rational -- fundamentally arising from causes rather than from reasons . The universe isn't, on this view, irrational if that means 'capable of reasoning but bad at it' or 'containing logical inconsistencies'. I take it that Schopenhauer is rejecting a theistic or deistic view that sees reason (and not causation) as fundamental to our universe. I agree with Professor Manter that neither Schopenhauer's view nor the view he's rejecting allows for inconsistent things such as square triangles. Can I take this opportunity to grind an axe? Advocates of a supernatural (theistic or deistic) origin of our universe often claim that only their view -- rather than metaphysical naturalism -- gives us hope of achieving a rational understanding of the universe by investigating it. They say that only if the universe was rationally intended can we hope to understand it. I think the...