Hi again; before reading through your reply I wish to complete "reply part three"......
Quote: "H: " Who's mathematical abstract reality? Is everyone's reality the same as everyone else's abstact reality?" Two meet: they are different; but one meeting.......
The objection is that we haven't even defined what an mathematical abstract reality is".
In specific cases "mathematical abstract reality " gets defined as "rules" to be followed? As "dots to be joined"; as patterns to be matched......fitted together without contradicting...............
Quote: "Definitions require some reduction in order to be sensical. If we just want to form a belief from some abstract stance, that's fine. There's nothing wrong to holding beliefs in abstract things. But, if we want to precisely define something such that the definition helps us to better grasp what it is we are saying such that there is no confusion, etc, then we need our definition to lock in on some kind of consistent usage."
"Consistent usage" implies a "SAME" background; a "freedom surface" against which the definition can interact with things without being lost.
Quote: "An abstract object is always at least a mental object held by someone's belief system, and if that's what you mean, then you have to state it and explain how consistency can occur from one person to the next".
How do you verify you both have the same background? How do you know a Korean-speaker understands English language when you speak to them in English? Trial and error? But more basically-- mutual access to a common consciousness.......
Quote: "Platonists try to explain mathematical truth by saying that abstract objects exist outside the mind, and that when talking about an abstract mathematical reality, we are indeed talking about a universe of such objects. This is a better definition that lays the groundwork for a mathematical definition of truth since it doesn't rely on human images which are subject to change from person to person, as well as be distorted by the person's mental composure (e.g., drug use, alcohol use, etc)."
But is Platonistic perspective projected from human imagining and human experience......................? Is not for example the "ideal square shape" a combination of actual life experiences shared among Platonists, and acknowledging an eternal template idea for "square shapes"?
Reality a two-way (or multi-way) street.............?
Quote: "H: "This might seem unfair to throw these kind of issues in the middle of a simple mathematical attempt to set-up an abstract situation, however this is the result of trying to establish a definition of mathematical truth if one chooses to do so." You appear to have substituted "corespondence with the facts" with "correspondence with rules of math-world".
No. I am concentrating on a Tarskian framework by which to understand how to define mathematical truth. The truth conditions of mathematics is entirely an epistemological issue, and we don't need to discuss those issues since this is what mathematics are doing - and are doing it very well. However, when talking about mathematical truth ontology, then quantifiers are needed in order to specify how the T schema can be a definition of truth, and this is where one runs into trouble."
But epistemology and ontology appear to merge; by proposing an abstract mathematical world to which math statements must correspond to get your Tarski-template for "correspondence theory"; you have made the ontological conditions (nature of being) for math truth become the epistemological conditions for math truth (method of knowing).
Quote: "As you can see from 'M2', it quickly moves toward the path toward Platonism, although one could take a nominalistic approach to mathematical truth and say that mathematical abstract reality is a 'particular' in each person's imagination. This is a valid approach, and one in which many philosophers have taken. The definition of mathematical truth for the nominalists will be highly focused on particulars and the universals (e.g., object, plane, lie, etc) all become abstractions of particulars that people encounter in their lives. That's the beautiful thing about the Tarskian approach, it provides the kind of versatility for a nominalist, or a platonist, minimalist, etc to approach the subject matter of truth definition in a slightly different manner."
The correspondence idea of Tarski thus involves here the issue of correspondence between individual viewpoints...
Quote: "As you can see, it's because of these many differing positions that mathematical truth becomes a philosophical quagmire and the reason why philosophers of mathematics debate it with so much passion.
So he [Hilbert, sic] kept definitions broad enough to allow concept transferability among different more specified contexts? But in so far as he had defined his rules; these became axioms?
These weren't definitions that he provided or kept broad. He simply used words without defining them. This is allowable in mathematics since math is about truth conditions and just as long as you don't start trying to define these terms you don't get into trouble".
That is apparently a default definition by usage, making math similar to a language........
Quote: "It's only when people find out how great mathematics is at creating consistent and useful structures that we start saying "hmm... this mathematical stuff is pretty good stuff. I wonder if we can state that truth is mathematical...". Once that philosophy gets going, then the can of worms have been opened, and that's when we need to carefully look at the issues of proper truth definitions and what we mean by references, etc."
One needs to be aware of the Zeno's Arrow way numbers appear to be built...
Quote: "H: " Truth in mathematics remains undefined, but the conditions of truth (truth functionals) is of course the heart and soul of mathematics and logic." I do not think so: a minimaly defined rule is still defined. Truth needs no definition by math; truth is what/ who exists. In math as elsewhere; as you judge, so you are judged.
Excuse me for being frank, but Alan you just have other agendas that you are evangelizing that severly taint your view. The fact of the matter is that you aren't giving any credence to any philosophical position other than your logicist views, and that position is not very representative of the philosophical work made in this avenue. I am giving just the tip of the iceberg reply to these issues. Unfortunately, you have so much interest in logicism, that it is apparent to me that you cannot think straight."
What is "logicism"? It is straight thinking isn't it? Are you promoting being "illogical"!!!!? Consider here the law of non-contradiction..........
Quote: "In fact, your 'religious talk' is so tainting that it makes you appear a little fanatical. I guess since we are talking about truth, a little of that should come out."
I am interested in discussing without evading or censoring. It would be misleading to boycott perspectives because they are deemed to be "too religious"...
Quote: "I presume by "truth functionals" you mean "structures in keeping with not contradicting the rules upon which they are built"?
Truth functionals are quantified or connected structures with individual true elements in that structure using functional operators (connectives and quantifiers)".
That sounds like it fits what I said?
Further on entropy and time:
"Entropy": suppose one say hold this concept as a constant; as a background; to see or count time.
"Time": suppose one say hold this concept as a background to see or count entropy?
Entropy: involves "breaking up".
Time: involves "breaking up"?
Hold time as unbroken (or "equal spaced, so Zeno's Arrow effect say) and you see entropy break up (so entropy increases). Because to even detect the concept "entropy" requires a before and after; but if you hold time as constant you mix before and after; you feed entropy back on itself by saying you can see it but can not see its direction anymore so by definition you juggled time. You mixed past and future when you claim to detect entropy in the lab but claim time held as constant?