What is the best way to combat grade inflation? I'm teaching a course (first semester organic) right now for 265 undergraduates. Traditionally an average score in this course earns you a B+. Even more ridiculously, based on the last three years, being two standard deviations below the mean will generally earn you a C. There is no such thing as a D (or failure), assuming you sit for one (of three) midterms and the final.Best way to combat grade inflation? Teach logic.
What is the basis of the baseball rule that requires a batter to be tagged out if he/she strikes out and the catcher drops the pitch? What does this rule accomplish? I can see the logic behind the fourth out rule. I can also understand the infield fly rule. However, I have no idea why a batter is not out until tagged when first base is open and the catcher drops the third strike pitch.The rule does seem odd in that once the batter swings and misses, his turn at bat should be over, yet play continues beyond the strike. It is odd to think the ball is still in play after the whiff, although the foul tip is still in play with two strikes and the catcher holding it is sufficient for a strike out, too. Yet, it is only with two strikes that the ball is live if it gets away from the catcher, the batter only becomes a base runner after he is seemingly out and not before. Yeah, sporting rules are arbitrary, but generally there is a coherent logic to them. I'm with you that this seems a bit bizarre.
In the semantic view of theories, how are we take the word "model"? Set theoretically? If so, what advantages does that give us over the syntactic view?The semantic view of theories is a position that derived from Bas van Fraassen's constructive empiricism in the 80s and was championed by a number of really smart philosophers of science like Nancy Cartwright, Patrick Suppes, Frederick Suppe, who argued that the traditional view of scientific theories as sets of sentences that were individually testable or testable as a group was wrongheaded. Science is not about finding true statements about the world, but about finding models that fit well and scientific theories were to be thought of, not as set of true or false propositions, but as sets of models. Better theories represent the natural system better, but it becomes a question of usefulness, not of correspondent truth.
I propose that we regard the simple harmonic oscillator and the like as abstract entities having all and only the properties ascribed to them in the standard texts. The distinguishing feature of the simple harmonic oscillator, for example, is that it satisfies the force law F = -kx. The simple harmonic oscillator, then, is a constructed entity. Indeed, one could say that the systems described by the various equations of motion are socially constructed entities. They have no reality beyond that given to them by the community of physicists.So I think that the logician's notion of a model is not far from mind and in the case of formalizable mathematical models like we see in physical theories, it is exactly what they mean, but I think the idea is kept looser to account for things like scale models in chemistry and computer models.
I suggest calling the idealized systems discussed in mechanics texts ?theoretical models? or, if the context is clear, simply ?models.? This suggestion fits well with the way scientists themselves use this (perhaps overused) term. Moreover, this terminology even overlaps nicely with the usage of logicians for whom a model of a set of axioms is an object, or a set of objects, that satisfies the axioms. As a theoretical model, the simple harmonic oscillator, for example, perfectly satisfies its equations of motion.
The relationship between some (suitably interpreted) equations and their corresponding model may be described as one of characterization, or even definition. We may even appropriately speak here of ?truth.? The interpreted equations are true of the corresponding model. But truth here has no epistemological significance. The equations truly describe the model because the model is defined as something that exactly satisfies the equations.
The statements used to characterize models come in varying degrees of abstraction. At its most abstract the linear oscillator is a system with a linear restoring force, plus any number of other, secondary forces. The simple harmonic oscillator is a linear oscillator with a linear restoring force and no others. The damped oscillator has a linear restoring force plus a damping force. And so on. Similarly, the mass-spring oscillator identifies the restoring force with the stiffness of an idealized spring. In the pendulum oscillator, the restoring force is a function of gravity and the length of the string. And so on.