" **2 " means raised to the second power (i.e. squared). So " **3 " means raised to the third power, etc. This is standard scientific notation. — EricH
I don't know how to do that on my keyboard, but now that you've shown the way I can cut & paste from your example. :clap:2² = 4 — flannel jesus
Show your math. — wonderer1
Regardless of philosophical issues, we can in fact experimentally verify, to some reasonable degree of precision, that bowling balls and pool balls both accelerate toward the ground when dropped. If you have philosophical problems with the concept of acceleration, you should separate that from your ability to look at that evidence and see what does, in fact, happen — flannel jesus
Why don't you try answering his question? — tim wood
Maybe you should read it. Here, from your reference (italics added):Our mathematical representation of it is very problematic. Read the following: https://en.wikipedia.org/wiki/The_Analyst — Metaphysician Undercover
Yes, that's what I said, truth means corresponding with reality, therefore I'm using "truth" in the sense of correspondence theory. — Metaphysician Undercover
"Truth" implies an understanding of what is going on, which takes us beyond the ability to predict. — Metaphysician Undercover
Yes of course, such objects accelerate. They must, in order to get from zero velocity to having some velocity. The problem is that we as human beings, do not have a very accurate understanding of acceleration. Our mathematical representation of it is very problematic. Read the following: https://en.wikipedia.org/wiki/The_Analyst
Notice that the article says that Berkeley's criticism of Newton was resolved with the concept of "limits". But this really doesn't solve the problem of acceleration because it places zero as a boundary, limit, which is never obtained. So the principle utilized is that there is no point in time when the object changes from being at rest to being in motion, because an infinite amount of time would pass before the boundary is crossed. So the crossing of that boundary, between rest and motion is never actually obtained by the mathematical representation. — Metaphysician Undercover
In 1966, Abraham Robinson introduced Non-standard Analysis, which provided a rigorous foundation for working with infinitely small quantities. This provided another way of putting calculus on a mathematically rigorous foundation, the way it was done before the (ε, δ)-definition of limit had been fully developed. — tim wood
And it is equally clear that, short as the article is, you did not understand any of the rest of it either. "Berkeley did not dispute the results of calculus; he acknowledged the results were true. The thrust of his criticism was that Calculus was not more logically rigorous than religion. Berkeley concluded that the certainty of mathematics is no greater than the certainty of religion." Berkeley was writing as a Christian apologist. — tim wood
Any claim of yours, then, of any problem with the maths in question here, whether mathematical, philosophical, or metaphysical, is ignorant, stupid, self-serving, and that you used it to evade a fair question on your inconsistent usages of "truth," I call vicious. — tim wood
These are incompatible. Reconcile them! — tim wood
Regardless, this is irrelevant to the point I was making. I said "truth" implies understanding. But for someone to say "I agree that this is true", and for it to actually be true, are two different things. So "I agree that X is true" does not imply understanding in the way that truth itself implies understanding. — Metaphysician Undercover
I already told you the problem with the "rigorous" solutions. They are not real solutions because they allow "infinite" which is fundamentally unintelligible, as indefinite, into the mathematical representations. So any mathematical model employed, using these axioms which are designed to produce a "rigorous foundation" will have indefiniteness, which is a form of unintelligibility, built into it. — Metaphysician Undercover
If there is coherency within the logical system it produces truth. — Metaphysician Undercover
To represent reality in the way of correspondence (truth), requires necessarily that one has some understanding of the reality being represented. Therefore "truth" in the sense of correspondence, implies understanding. — Metaphysician Undercover
You don't need to understand acceleration to agree with some basic observable facts about how bowling balls fall. — flannel jesus
What math? It's a philosophical problem, one which mathematics has not resolved. Look, there's a point in time, when a body at rest becomes a body accelerating. The body changes from being at rest, to being in motion at some point in time. Since the rate of increase of velocity (acceleration) is expressed as over a period of time, at this point in time, when the body changes from being at rest to being in motion, the rate of increase must be infinite because it's a number expressed over zero, x/0. — Metaphysician Undercover
I think it's incredibly feasible to agree to the truth of something without fully understanding it. — flannel jesus
The same is true for the example given before about acceleration. You may not understand or even philosophically agree with certain aspects of acceleration mathematically, but without that understanding you can still acknowledge observations that say, "after dropping the bowling ball, it was going at about 9.8m/s downward after 1 second , and it was going about 19.6m/s downward after 2 seconds , and it was going about 29.4m/s downward after 3 seconds". — flannel jesus
So, the solutions offered as such by mathematics are not solutions? What do you imagine mathematics and solutions to be? — tim wood
"In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world."
Now you are introducing the notion of understanding into the mix - and it's not clear to me what you mean here. If by the word "understanding" you mean that a statement is grammatically and syntactically correct and expresses a thought/notion that could potentially be real? Then that is trivially correct. — EricH
But if by "understanding" you mean something more than our shared understanding of the plain language meaning of words, then this raises all sorts of questions - what do you mean by "understanding"? Can we ever fully understand anything at all? Warning! Warning! Infinite regress ahead! — EricH
It's starting to appear as if you don't know how to apply math to the situation. (Not that there is anything wrong with that.) — wonderer1
No, that's the point, I would not agree to this. I would want to see the measuring technique, the justification for this claim, that "it was going at about 9.8m/s downward after 1 second", etc.. What I said, is that some others might accept this, as a matter of faith in some principles they hold, but I am not inclined to accept things on faith. — Metaphysician Undercover
What's all this talk about faith? You think people came up with the 9.8 number on faith? — flannel jesus
I really do not believe that there is a way to successfully apply math to the situation. That's the point, it's a philosophical problem which math cannot resolve. math has its limits, and there are many problems which it cannot resolve. — Metaphysician Undercover
Now, whether you think they're actually capable of being done to your satisfaction is entirely different question from your ability to imagine a scenario where they were done to your satisfaction. — flannel jesus
I'm also genuinely quite amazed at the conspiratorial nature of your approach to acceleration due to gravity. Do you really not think there's sufficient evidence for it? Are the physicists of the last hundreds of years incompetent or just lying? How did we manage to make it to the moon, or send rovers to Mars, if we don't even grasp the very basics of gravity? I can't tell how sincere you are about all this. — flannel jesus
But we know you, MU - and these others don't although they're learning - that you do not agree even that 2+2=4. — tim wood
Mathematics, as used in the sciences at least, is the language used to try to describe with some rigor, precision, accuracy, and consistency what is happening in nature, and when done well, called a solution — tim wood
Btw, as you well know there are at least several mathematicians who post here, and a characteristic of their work is the effort to demonstrate and make clear their own arguments and points about their topic, to educate and contribute to a general clarity and understanding. You on the other hand pontificate without substance, demonstration, evidence, clarity, or proof. And while you claim to understand that this is a philosophy site, you consistently refuse any substantive reply to the question, "How do you know?" — tim wood
Ultimately you're a waste of time, and I would like you to stop it! — tim wood
I thought I explained this . The current state of "mathematics", the axioms and rules which are the current conventions, make it impossible that this could be done to my satisfaction. So I cannot imagine this scenario. You are asking me to imagine something which I am saying is impossible for me to imagine. For me to imagine this being done to my satisfaction would be to imagine it being done with something other than "mathematics". — Metaphysician Undercover
Notice your use of "try", and "a solution" only occurs when "done well". And, as I've described using English, one of very many languages used to describe what is happening in nature, there are aspects of nature (such as acceleration) which cannot be described by the current grammar of this language called "mathematics". — Metaphysician Undercover
And this you exactly do not know. You may suspect; the logic may be suggestive or it may point or provide clues, but not knowledge-of. Or, perhaps you will make explicitly clear how logic might have this power of constitution that you appear to suppose it has.We know from logic that it is there, whether it best be represented as "aether" or as "field", or whatever term. — Metaphysician Undercover
I would like you to reflect a bit more on what you're posting, with respect to the subject matter; to be as exact with language as your views require, and to stop wasting time with nonsense.Why do you keep asking me questions if you want me to stop posting? Your use of language demonstrates a base irrationality. — Metaphysician Undercover
This is exactly what Socrates demonstrated many years ago, that when people are doing things, they really cannot accurately describe what they are doing, and this means that they do not know what they are doing. — Metaphysician Undercover
Can you give an example of a statement involving the mathematical measurement of some physical property of an object that you would consider to be a true statement - per the correspondence theory of truth? — EricH
This seems like you're still overthinking it. You're focusing so much on abstract mathematics and not enough on concrete measurements. Galileo didn't discover acceleration due to gravity via abstract mathematics, he measured it. If you can't imagine measurements, then let me do the imagining for you. I don't believe it's particular challenging. — flannel jesus
So, we start out by asking, how fast was it falling approximately at 1s? We look at our high speed footage and we measure is position at 0.9s and 1.1s. We find the positions are 3.97 and 5.93 respectively (measured in meters from the starting point). So we find out that in that 0.2s time frame, it travelled about 1.96m, which means it was going about 9.8m/s. — flannel jesus
So we get all our results together, and quickly notice that every time a second passes, the cube seems to be traveling 9.8m/s faster than it was traveling the previous second.
Why are these sorts of measurements, and this sort of experiment, unimaginable to you? Are they still unimaginable to you now? — flannel jesus
But you are dismissive of the map because it is not the territory, and that is an unseemly and unaccountable (on rational terms) error for someone like yourself. — tim wood
As with the 2+2=4, you say that the 2+2 does not represent the same thing as 4, and of course it exactly represents the same thing as 4. — tim wood
And I refute this thus: When they are doing something, are they doing that thing, or are they doing something else? If you had read a little more closely, you would have seen that Socrates did indeed find people who knew what they were doing, but not wise, because they, knowing something, thought that they knew more that they did, thus knowing something, but not wise. That is, the Oracle had told Socrates that he was the wisest, and Socrates had to discover that wisdom and knowledge are not the same thing. — tim wood
And, a misleading map gets people lost. — Metaphysician Undercover
That's an assumption YOU made, not me. I said APPROXIMATE speed. I didn't say constant. I don't know why you would assume it's constant, the data doesn't say that.Well, look what you have shown me. Between .9s and and 1.1s the object was moving at a constant speed. — Metaphysician Undercover
Or you're just immune to science. — flannel jesus
I, am an impenetrable fortress. Nothing, I repeat nothing, from that "external world" can infiltrate my defenses, and move me. All which exists within my mind comes from the inside. Thus is my reality.
There is however, a sense in which ideas come to my mind from somewhere other than my mind. Since they cannot penetrate through my fortress, and enter from the external, and "ghostly phenomena" is silly talk, I conclude that they enter my mind through "inner space". And since the ideas which enter my mind through inner space seem to be very similar to the ideas which enter your mind through inner space, I can conclude that we are very well connected through inner space. — Metaphysician Undercover
I said APPROXIMATE speed. — flannel jesus
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