What is truth?
Can we define it in a way that isn't circular? My best attempt is something like this - "truth is the set of patterns that exist."
What is a pattern? I think of patterns as a configuration of data points. I wouldn't limit the definition of patterns to a repetitive design. Patterns are just consistent shapes or behaviors - even if it doesn't repeat into the distance, it repeats across time. In this universe there are patterns for objects - different visual datapoints are associated with each. Perhaps a human has a pattern of 4 limbs and a head. Perhaps a cup has a pattern of a closed cylinder, only open on the top.
My conception of patterns is similar to the Platonic forms. Greek philosophers seemed to like to poke holes in definitional patterns. Is a man a featherless biped? If so, then a plucked chicken could be considered a man! So perhaps "featherless biped" isn't a complex enough pattern to accurately represent the idea of a man.
We can apply the concept of patterns to other possible worlds, or other universes that might have alternate laws of physics. Atoms might be fundamental patterns in our universe, but perhaps “Upside-down-tons” are the fundamental patterns in our opposite universe. Maybe in this universe 1+1=2 because our laws of physics allow singular atoms to bond with each other as opposed to destroy each other. 1 atom joined with 1 atom equals two atoms by virtue of our peaceful laws of physics. But in an alternate universe, when 1 atom is joined to another atom, perhaps they annihilate each other. Creatures in this universe might evolve to see grains of sand annihilate each other upon contact. The idea of a "pile" would be non-existent due to their laws of physics - accumulation is impossible. All there is is annihilation. 1 + 1 = 0 in that universe.
So, when we say "1+1=2 is true" what we are saying is that there is a pattern that exists in our universe where accumulation occurs.
But it gets way more interesting than that. I have been thinking about the ontology of patterns lately. There is a question in the philosophy of math - is math real in an ontological way? Is there preexisting math out there constantly existing and waiting to be discovered? Or is math non-existent, with no objective representation, and only exists in our minds? It’s quite confusing because it seems like both answers are right and wrong at the same time.
We know math is discovered because things like the laws of gravity have always been in effect. Our ignorance of the math doesn't mean that there is no math being played out in the patterns of movement in the universe.
But we also know that there are no subatomic math particles – nothing that represent the elements of math. There is no "+" particle. No "-" particle. No multiplication or division particles. There are just physical particles. These particles have natural behavior patterns. We can use math to describe these patterns, but the patterns aren't fundamentally math. We know this because energetic patterns have a property known as "power" or the ability to do work and move things. There is no property of "power" within math. No matter how much math you write on a piece of paper, the power never appears. Power is inherent in the particles, as energy is its root ontology. So, just as music inherently has power to it, physics inherently has power to it. The notes written down on sheet music describe the music, but they have no power to summon the power of the music. Similarly, math describes the physics, but it has no power to summon the movement of the physics.
But then we have the problem of deduction. When we have a mathematical paradigm, we can apply calculations to deduce truths about the system. When we apply these paradigms to the laws of physics, we can make predictions about the movements of celestial bodies.
This ability to deduce is what gives us the feeling of discovering a preexisting entity. But that is the interesting thing about patterns - their structure allows deduction to take place. By following the pattern, we can see where it leads. So, in effect, by having one pattern exist, deducible patterns simultaneously exist in this abstract space of potential.
One of the weird things about the laws of physics is the concept of potential energy. If potential energy has an ontological status, then perhaps potential patterns have ontological status. This means we can split our ontology into two categories - actual and potential.
Within the category of "truth" there are the actual patterns that ontologically exist, and the potential patterns that ontologically exist by virtue of their deducibility from the actual.
So, within this paradigm, can we say that math ontologically exists? I think that math is far too culturally constructed for us to jump to that conclusion. Math involves human symbols, human axioms, human logic, human functions, and human biases. It’s completely mired in human construction. If we subtract everything human away from math, what is left? Patterns. So, we are back to the beginning. Perhaps math doesn't ontologically exist. But patterns do. And that is the truth we are trying to discover.
Ontology reduces to patterns.
