Does Gestalt theory (the whole is greater than the sum of its parts) display one of the limitations of math in general? In other words does gestalt theory show that not all reality can be quantified with mathematical equations? As far as I can see (and I am far from an expert) math is based in deductive reasoning (if all a is b and b is c then a is c). If there are no ‘truths’ (if gestalt theory displays how 1 + 1 does not always equal two) then what does this mean for all the ‘truths’ that mathematics has suggested. Is our reality a construct based on our universal agreement in mathematical ‘truths’ that might not be true? Are we creating the existence of other universes and laws of physics based on inductive reasoning that we constructed to be deductive reasoning?
When we arrive at a conclusion or ‘truth’ using facts, definitions, rules, or properties, it is called Deductive Reasoning… deductive reasoning claims to arrive at a truth with absolute certainty.
Inductive reasoning is when we use observations of apparent consistency to derive a hypothesis about the potential existence of truth… but Inductive reasoning does not claim with absolute certainty that the truth exists.
Gestalt theory suggests that the whole is greater than the sum of its parts. A simple example of this would be a car… if you add all the parts together (paint, metal, rubber, wheels, brakes, gas, etc) you get something which is greater than the sum of its parts (movement, direction, intentionality, a car, transportation, momentum etc). (Paint + metal + rubber does not always = movement or car etc. the product of adding those variables can lead a seemingly infinite amount of results.)
Postmodernism – reality is that which we construct based on agreements; these agreements are transferred through language. Reality is what we choose to believe – there are no absolute truths.
In order to use deductive reasoning (in order for deductive reasoning to be a valid tool of deduction) there must be at least two universal truths in our reality… what are those two universal truths? (In my own philosophical investigations I have not found them… but again I do not claim to be an expert in this area.)
I am absolutely in no way an expert in math, physics, or quantum theory (as a psychotherapist I perhaps have close to the least amount of formal mathematical education for a person with a graduate degree… MA and not a MS) … what I am suggesting is not intended to negate any of the physicists who are surely infinitely more intelligent than I am. Instead, perhaps I am asking for clarification if there is a good answer to my proposal.
I was watching the Colbert report last night (re-run) and one of his guests was a physicist named Brianne Greene who has been using math to come up with hypotheses about the existent of other universes, and alternate ways of explaining what we call reality etc. At one point the physicist talked about how Math can be used to explain every aspect of existence, as math seems to be ‘true’ in our reality… Colbert jokingly (or not… hard to tell) stated that he read a book in which 2 + 2 = 5 (which is sometimes true according to gestalt theory)… the point is that mathematical equations claim to report truth as math uses facts, rules, definitions or properties in reporting answers (this is deductive reasoning) if any of those rules or facts etc was not absolutely a logical certainty then math would be using inductive reasoning as opposed to deductive reasoning… math would then be a tool for speculation and not a tool for truth.
Inductive logic uses observations of consistency to report that something is very likely to be true… then deductive logic can be used to ascertain whether or not it is true. In order for deductive reasoning to be utilized you must have indisputable truths or laws that you can use as an inference…
In short, there must be certain mathematical truths to prove other mathematical truths.
Most high-level equations use inferences in there proofs… this means instead of reproving every mathematical ‘law or truth’ in every equation you use an inference to point to a known truth that was already deduced using a previous proof.
As far as I can see (again… not a mathematician) most sophisticated mathematical equations are in some way based on the ‘truth’ that 1 + 1 = 2….
My question is this… If 1 + 1 is not always 2 then does this rattle the efficacy of all mathematical equations?
“My area of research is superstring theory, a theory that purports to give us a quantum theory of gravity as well as a unified theory of all forces and all matter. As such, superstring theory has the potential to realize Einstein’s long sought dream of a single, all encompassing, theory of the universe. One of the strangest features of superstring theory is that it requires the universe to have more than three spatial dimensions. Much of my research has focused on the physical implications and mathematical properties of these extra dimensions — studies that collectively go under the heading “quantum geometry”.”
I love this stuff… thinking about other universes and such… my question is this… are we constructing these truths these ‘all encompassing theories of the universe” based on premises that we claimed to arrive at deductively when in fact we arrived at then inductively?
Could we change math and change the very make up of our universe? Or is math truly the truth that we can use to display the existence of objectivity?