Tutor profile: John H.
Why can’t I say “he did it by thinking” in Latin as “Cogitanti id fecit”?
"Cogitanti" is a present participle. A present participle, such as “running” in “a running horse is hard to catch,” is not the same as a gerund, as running in “running is a very healthy habit.” The participle modifies a noun the way an adjective does; the gerund is like a noun, denoting the act itself. English is the only language in the world that makes the present participle look like the gerund: “running” in both cases. To understand Latin (or French or German) we have to keep these two things separate. So “he did it by thinking” would have to be something like “Cogitando fecit” with a gerund.
Why would someone (for example, an idealist) say that the world is basically mental, not material?
If you think about everything we know about something, say a desk in front of you, you will find that what you know is what is looks like, what it feels like, what laws of nature it obeys, and so forth. All these things are experiences or thoughts, of the nature of the mind. The belief that there is something beyond these mental things, a material object, is a faith-based belief. The idealist declines to share this belief.
What's a derivative?
It’s the rate of change. Think of speed. When you’re driving and the speedometer says 52 miles per hours at exactly 3:02 pm, what does that mean? Speed is distance divided by time, but at exactly 3:02 pm, the time interval is zero seconds. Do we have to divide by zero? No, When we take a derivative we let the time interval we’re talking about get less and less – 1 second, half a second, one quarter second… -- and watch what happens to the distance covered. In this example, we’ll find that the distance divided by the time gets closer and closer to 52. That’s a derivative!
needs and John will reply soon.