Hi Harv again! continuing from part one:
Quote: "In the case of abstract objects and rules, we cannot reduce these abstractions to anything other than abstractions".
I do not think so. Given the building of life-experiences argument above........... (one might say "abstract" and "concrete" are "one".................? So I defer to quoting "If You have faith as a grain of mustard seed; you could say "move" to this mountain, and it would move". It's not that I am "evangelising" unreasonably; if I find words attributed to Jesus Christ appear most apt why not quote them? It would be censorship to deny His voice.....
Quote: "That's okay if we want to believe something that requires an abstraction since many very important concepts of the world fall into this category, but when defining an abstract concept like truth with the hope of giving us a sound definition (remember a definition is a reduction to something more tangible), then we must meet a higher criteria than just axiomizing terms".
What is "definition"? It requires giving a context to something; a "SAME" background against which it can be seen from DIFFERENT perspectives without getting muddled with those other things it is being "met" by?
Example: definition of "car" must allow you to "see" "car" against say variations in wheel design without getting muddled between "car" and "wheel".
You require a "tangibility" to "definition"? Well one might include life-experience background; YOUR historical world-interaction basckground, to impart more tangibility?
Quote: " These terms must take on something we can directly experience and experience in a manner which doesn't allow for inconsistencies"
Very good point it seems......
But that requires "total recall": if you are fully conscious of your own world-interaction history and personal experiences; you are not going to get muddled? In full consciousness you are free from confusion.... as surely everthing is as defined as it needs to be within the limits of freedom of definition....
Quote: "If inconsistencies exist (e.g., everyone has a vague or varying definition of the term 'lie'), then obviously you haven't defined your terms".
Quote: "This is a key impediment to defining mathematical truth since this is what we cannot accomplish".
Well; I think that it is possible to expose the nature of math; it appears to have a shell or skeleton-like structure reminiscent of a pyramid of layers of "ones"; it appears to involve a "Zeno's arrow" like self-referential character; it appears to be about sticking labels to things and grouping them together; where it is used with algebra or concepots seems to be where physics governs it as "math INSIDE math". Example: "a physics concept" becomes a counting system of its own; each timne you find that concept you are counting by its math redistributing in your regular math......
Quote: "Now, I think it's true that nothing in our world is really fully defined. There's a word trick we can all play where we could define a word and then ask to define that word, etc. At some point we simply run out of words to define the remaining words (i.e., without mentioning words that were already used). Nevertheless, the words that are more common in our usage (e.g., 'he', 'her', 'them', etc) can be further defined by pointing at the actual reference".
I call this "comparing and matching patterns".
Quote: "With that kind of ostensive definition, a picture is worth a thousand words and a better understanding is obtainable".
It occurs to me that "E = mc squared" translates to "a picture is worth a thousand words" in general terms. "Alternatives = freedom of definition of comparison compared" where "E" becomes "alternatives"; "m" becomes "freedom of definition"; "c" becomes "speed of speed" or "comparison of comparison" as by simple Newtonian relativity we can say "speed" involves "things moving relative to each other while still differentiable (not muddled)...."
Quote: "The reason why this is important is because with good definitions (good reductions), we can hopefully eliminate concepts that otherwise might disrupt our understanding".
Quote: "For example, if mathematical truth is some kind of Tarskian 'M2' instead of its truth conditions (e.g., if A then B), then we don't look to understand mathematical truths by their truth conditions".
You still do: "conditions" in math-world are still conditions that must be met.
Quote: "The definition (reduction) avoids looking in the wrong direction".
Well you can look from one layer in the pyramid of life-experience to another? You seem to be proposing looking from "math statement" to "rule about math statement" instead of looking to "how I built these ideas as a child" .....? But ultimately......the child is still there.......
Quote: " "Touch" is not necessary; they need only be defined as MEETING within a certain context which might be quite generally defined for math purposes. This allows transferability of concept between more specified geometries.
'Meeting' or 'touching' are English terms that have reference to tangible events that take place in reality."
This is a very curious comment; how do you define "meeting"? I and a planet around some star in the milky way galaxy....have I met it?
Maybe life is about discovering what meeting IS? It seems that creation involves meeting things.....
Quote: "But, we presumably aren't talking about reality, so you have to explain what you mean - otherwise the terms don't have enough meaning to understand the Tarskian quantifiers that we are placing as truth quantifiers".
I would say that everything is "real". Music from a CD player is real; real CD-music. It is not a live band; but it is really what it is though...
Quote: "What happens if someone says "excuse me, the term 'meeting' is a symbolic word that can be reduced to an actual meeting in the real world, that's how we can understand what a 'meeting' is if there's any doubt. But, when you talk about two objects meeting in abstract space, you have no way to reduce that further beyond the symbolic meaning of the words".
This is very curious .....how about: if you even mention or think of two things: they have met (in your head!).
Meeting is always true by virtue of its own occurence! So it needs no definition; it is already "definition" itself; as to think of combining two items is to already combine them as possibly combined---they have already been partially "defined" as capable of being thought about by you? I'm reluctant to use the word "defined" here.... we do not usually go into describing every thing a thing meets as a part of its definition....
Quote: "However, the words 'meeting' in terms of abstract objects meeting and 'meeting' in terms of physical objects meeting cannot mean the same thing since by the mere fact that the former has no physical reference like the latter".
It does have a physical reference: they meet in your thoughts....
Quote: "Doesn't that mean that the former 'meeting' is just an empty word having no real meaning? Couldn't you just say two objects 'snubblebun' together and wouldn't that mean basically the same thing. The word 'snubblebun' has no physical reference, and the term is empty in terms of physical meaning. It seems that's about all you can say about two objects meeting - they are 'snubblebunning' together."?
Whatever language you use: if you think of two things; they are together thought of by you.
Quote: "You see Alan, if someone made this claim, they would be perfectly correct".
internet place closing...