Reason is used to create the things you name, restating logic over and over, defying time and again axiomas that were considered absolute and trivial truths. There is no holy grail of pure logic.The idea that there is an immutable form of logic that underpins all of reality may be right, not the idea that we can be sure to have found it.Kevin Solway wrote:There are "sytems of logic", but logic itself (ie, A=A) is not one of them. Logic is used to create these systems of logic for use in specific areas of knowledge.Fujaro wrote:There is no trivial intrinsic reason why one logical system should be preferred above another logical systems as underlying reality
Kevin Solway wrote:There is no "real" and "non-real" without logic.Fujaro wrote:Only when it is shown that we can have a mapping from logical enities to real entities.
Real and non-real imho suggest something other than logical vs real. But that aside, I agree that a model of existence is involved. But not that it is based on pure logic. It's in fact a working model for existence that has been around for quite a while and that so far has been substantiated significantly and proven very usefull indeed. According to which logic does from A=A follow that it is usefull to discern logical and real? We should expect that from the pure logic of A=A we can understand why such a perhaps artificial division proves to be usefull to us.
For which part of nature is it truth? One proton added to another proton might give you two protons but then again it might give you completely new particles when you bang ‘m hard together (like soon to be demonstrated in the LHC). Hence pure logic does not map to reality in a straightforward manner at all. You need the context of reality itself to decide on that.Kevin Solway wrote:1 + 1 = 2 is a truth about Nature, and so is 1 + 1 + 1, etc. Hence pure logic can deliver countless truths about nature.Fujaro wrote:Logic and math alone do not, and cannot, generate new truths about nature.
And may I remind you that in the electron example above you have countless electrons. What does it mean to add another electron to it?
So when the Higgs boson is found with LHC, it won’t be the achievement of people only using this very absolute pure logic but it will be the achievement of people making use of all kinds of logic in relation to empirical data, models of reality, trial and error, induction and deduction. And in this process the mappings between reality and logic are not regarded as absolute truths but as tentative mappings. Of course the logical sentence ‘1+ 1’ where every component of the sentence is defined as a logical abstraction within logic itself, still adds up to 2 (ring modulo variants not considered!) . This is the logical conceptual side of it that’s universally true, by which logicians mean that in the form of this abstraction it is always true logically, not that it is necessarily true for things we count in nature. And that’s even true when nature is totally a product of our mind.
Kevin Solway wrote:All logical systems adopt logic, otherwise they wouldn't be logical.Fujaro wrote:The unprovable principle A ≡ A is self-evidently true logically only within the logical system that adopts it.
There is no such thing as a concise superfundamental logic that underpins all logical systems. There are logical systems that don't adopt the logic of the excluded middle or logical systems that leave room for the fact that there is more than one possible state of existence at the same time. That’s all a matter of choice of rules and axiomas by man. You can’t deduce much from A=A alone. It has been shown fruitfull in the past however to choose the axiomas and rules in such a way that these, at least to the human mind, have some resemblance of nature. Euclid’s Geometry was such a choice. It is shown to be complete and consistent in a technical (read: logical) sense. And it still pays of in space flight, but has been shown to not be the final answer about the geometry of nature which is still a part of our existence. The more we know about reality the more elaborate the logical tools have become and the greater the diversity of logical systems used. Logic itself is not an immutable body of thought.
Kevin Solway wrote:A particular system of logic might be limited, but not logic itself.Fujaro wrote:Logic, be it modal logic, propositional logic, paraconsistent logic, multi-valued logic or any other kind of logic one can think of so far, fails to describe all aspects of reality and therefore is incomplete in this sense. It indeed seems that any kind of logic fails to describe the whole of the logical realm, let alone the whole of reality.
The term 'logic itself' can only refer to some specific system of logic or to a container of poorly or undefined mystic logic that can be used as a deus ex machina at any time. Religious logic might be a good name for it. What will it be for you?
Hasn’t it occurred to you that the ‘dealing with’ most of the time takes place after nature has thought us a tough lesson? Logic does not preceed nature. But I agree that with mystified religious logic everything is possible.Kevin Solway wrote:Logic can describe absolutely anything. For example, the emotion of love is described by logic as "the emotion of love". And the Infinite is described by logic as "the Infinite". There is nothing it can't deal with.
The example about love really says it all. It shows exactly how far A=A will take you. Now we only need a project to sum all these usefull absolutely true sentences and all philosophers will be hailed into the cities like Roman emperors returning from campaign. Let’s call it the Human Truth Project and just wait for the funds raised for it by some wealthy endorsers of truth.