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Logic
Science

To whom it may concern; I thank you in advance for your assistance. I had a discussion with some of my colleagues regarding a problem that I identified. Basically, I got two different and contradictory results of the same problem (i.e., a paradox) using different but equally valid methodologies and rationales in our area of research. I propose to resolve this paradox by making some adjustments to the methodologies in order to make them consistent. As you know, when paradoxes are found, solutions have to be advanced in order to resolve the inconsistencies, and this in turn strengthens the whole methodology. The problem is that I identified the aforementioned paradox by means of a simulated, laboratory-type of study, in which ideal conditions are assumed and simulated. Since my area of research is business studies, my colleagues allege that the “paradox” I found is not valid, because it is not based on data from real firms. They added that for the paradox to be valid, real data would have to be used. I...

I don't think that there is or could be a general principle that says that a paradox arising from idealizations will inevitably carry over (much less become worse) when the idealizations are relaxed. In some cases, the paradox will disappear when the idealizations are removed. In other cases, the paradox will persist (or become worse). There is no general rule here. It depends entirely on the details of the case. For example, various paradoxes result in classical electromagnetic theory when pointlike charged particles are used. Point charges are a convenient idealization for many purposes, but the energy in such a field is undefined (the integral blows up). However, if we go to charge densities and extended charged bodies rather than point charges, these problems disappear. Likewise, in cosmology, Newtonian gravitational theory is afflicted with various paradoxes if we assume an infinite universe with a homogeneous, isotopic distribution of matter. Remove these idealizations and the problems go...
Knowledge
Logic

In a debate about faith and doubt in which I was doubting all existence and my friend argued in favor of existence, he challenged my rationalistic perspective by asking me this: Your reasoning depends upon the rules of logic, but there is a problem: how do you KNOW, conclusively, that the rules of logic are sound? Isn't that an act of faith? Can't you conceive of a universe in which logic *appears* to work, but in which logic is actually an illusion? How do you know that you don't live in that universe? Cogito ergo sum did not cover this one. I was stumped. Can you help me out?

If a logical principle such as "F, therefore F or G" is false in some universe, then that universe contains a contradiction, and contradictions are impossible. So no universe containing a violation of logic could exist.
Logic

I can recognize the importance of logic in argument but it never seems to apply in the 'real' world. You never see headlines along the lines of SYMBOLIC LOGIC REFUTES SENATOR Z'S CLAIMS ABOUT DEPLOYMENT OF TROOPS IN IRAQ SHOCK, followed by 'if A then not B' stuff. No political columnist ever cites logical validity or fallacies to support their view or dismiss the views of others - it is all opinion and anecdote (even if they did, few would get their point) - so how does logic work outside of the rarefied realm of philosophy?

Well, I happen to think that it would be better if political columnists DID point out logical mistakes in the arguments made by public officials. There is no shortage of mistakes to point out. Of course, to point out mistakes in the arguments made by politicians, there would have to be arguments to begin with, and they too are in perilously short supply. Perhaps more attention to logic would encourage participants in public debates to offer arguments instead of appeals to emotion, innuendo, name-calling, and sanctimonious prattle. Logic concerns how we ought to reason. Perhaps your logic course will lead you to demand that public figures offer you arguments that stand up under logical scrutiny. I, for one, would consider as highly successful any logic course that encouraged students to do that, even if they did not remember what modus ponens was after the final exam was over.
Logic
Physics

Could a newly discovered law of physics ever change/affect a law of logic?

Very good question! Let's begin by drawing an important distinction. By "changing a law of logic", you might mean (i) our changing our minds about what the laws of logic are, or (ii) the actual laws of logic changing -- one set of laws was in force at one time and another set is in force at another time. I will assume you had option (i) in mind, since the idea that the laws of logic change is at least as weird as the idea that the laws of physics change (which is to say: pretty weird), and in any case, the change would surely not be a result of something as cosmically inconsequential as our making a certain scientific discovery! So, your question now is: Could we be justified in changing our minds about what the laws of logic are as a result of a discovery in physics? This is a controversial question. Some philosophers have said that we know the laws of logic a priori -- that is, independent of sensory input. In general, such philosophers do not think that we could justly change our minds...
Knowledge
Logic

I once took a graduate course in education in which I was the only non-teacher. One day, I disagreed with something said by another student, and her response has always baffled me. She said: "Who are you? You can't question me until you've walked in my shoes." In other words, she felt that I was unqualified to question her, to cast doubt on anything she said. Who was I to say? Well of course her response was nonsense but how so? As a matter of logic or illogic, was her remark an example of an appeal to authority? She certainly felt that she was an authority.

I agree that the student's response was rude. Not knowing the precise topic of your discussion in class, I am unable to say much. But it seems like the student could have done a great deal more to explain the basis for her view, and it seems like a good teacher would have required her to do so. However, an appeal to authority is not always inappropriate. Suppose an art expert tells me that a certain recently discovered painting is by Botticelli. I could ask the art expert to explain the justification for her view. She might reply that the brushstrokes or the treatment of the hair are characteristic of Botticelli's work, and she might even point out to me the similarities between the given painting and others firmly attributed to Botticelli. But suppose I do not perceive those similarities. I just don't see the "characteristic brushstrokes", for instance. It might well be entirely appropriate for the art expert to say, "Well, I've done my best to show you what I see. But it took me years to perfect...