Your conclusion on sheep is a physical state in your mind, generated by physical processes. But the sheep still exist outside of your mind.
Restating my claim in terms of sheep: The identification of a sheep is a state change within a context of evaluation that implements sheep recognition. So a sheep exists in that context.
Physical reality however does not recognize sheep; it recognizes and responds to physical reality stuff. Sheep don’t exist within physical reality.
“Sheep” is at a different meta-level than the chain of physical inference that led to that classification.
That “truth” in the map doesn’t imply truth in the territory, I accept. That there is no truth in the territory, I vehemently reject.
“Truth” is at a different meta-level than the chain of physical inference that lead to that classification. There is no requirement that “truth” is in the set of stuff that has meaning within the territory.
When you look at the statement 2+2=4 you think some form of “hey, that’s true”. When I look at the statement, I also think some form of “hey, that’s true”. We can then talk and both come to our own unique conclusion that the other person agrees with us. This process does not require a metaphysical arithmetic; it only requires a common context.
For example we both have a proximal existence within the physical universe, we have a communication channel, we both understand English, and we both understand basic arithmetic. These types of common contexts allow us make some very practical and reasonable assumptions about what the other person means.
Common contexts allow us to agree on the consequences of arithmetic.
The short summary is that meaning/existence is formed by contexts of evaluation, and common contexts allow us to communicate. These processes explain your observations and operate entirely within the physical universe. The concept of metaphysical existence is not needed.
When you look at the statement 2+2=4 you think some form of “hey, that’s true”. When I look at the statement, I also think some form of “hey, that’s true”. We can then talk and both come to our own unique conclusion that the other person agrees with us.
I think your argument involves reflection somewhere. The desk calculator agrees that 2+2=4, and it’s not reflective. Putting two pebbles next to two pebbles also agrees.
Look at the discussion under this comment; I maintain that cognitive agents converge, even if their only common context is modus ponens—and that this implies there is something to be converged upon. At the least, it is ‘true’ that that-which-cognitive-agents-converge-on takes the value that it does (rather than any other value, like “1=0”).
These processes explain your observations and operate entirely within the physical universe. The concept of metaphysical existence is not needed.
Mathematical realism also explains my observations and operates entirely within the mathematical universe; the concept of physical existence is not needed. The ‘physical existence hypothesis’ has the burdensome detail that extant physical reality follows mathematical laws; I do not see a corresponding burdensome detail on the ‘mathematical realism hypothesis’. Thus by Occam, I conclude mathematical realism and no physical existence.
I am not sure I have answered your objections because I am not sure I understand them; if I do not, then I plead merely that it’s 8AM, I’ve been up all night, and I need some sleep :(
I think your argument involves reflection somewhere. The desk calculator agrees that 2+2=4, and it’s not reflective. Putting two pebbles next to two pebbles also agrees.
Agreement with statements such as 2+2=4 is not a function that desk calculators perform. It is not the function performed when you place two pebbles next to two pebbles.
Agreement is an evaluation performed by your mind from its unique position in the universe.
… this implies there is something to be converged upon.
The conclusion that convergence has occurred must be made from a context of evaluation. You make observations and derive a conclusion of convergence from them. Convergence is a state of your map, not a state of the territory.
Mathematical realism also explains my observations and operates entirely within the mathematical universe; …
Mathematical realism appears to confuse the map for the territory—as does scientific realism, as does physical realism.
When I refer to physical reality or existence I am only referring to a convenient level of abstraction. Space, time, electrons, arithmetic, these all are interpretations formed from different contexts of evaluation. We form networks of maps to describe our universe, but these maps are not the territory.
Gottlob Frege coined the term context principle in his Foundations of Arithmetic, 1884 (translated). He stated it as “We must never try to define the meaning of a word in isolation, but only as it is used in the context of a proposition.”
I am saying that we must never try to identify meaning or existence in isolation, but only as they are formed by a context of evaluation.
When you state:
Putting two pebbles next to two pebbles also agrees.
I look for the context of evaluation that produces this result—and I recognize that the pebbles and agreement are states formed within your mind as you interact with the universe. To believe that these states exist in the universe you are interacting with is a mind projection fallacy.
Restating my claim in terms of sheep: The identification of a sheep is a state change within a context of evaluation that implements sheep recognition. So a sheep exists in that context.
Physical reality however does not recognize sheep; it recognizes and responds to physical reality stuff. Sheep don’t exist within physical reality.
“Sheep” is at a different meta-level than the chain of physical inference that led to that classification.
“Truth” is at a different meta-level than the chain of physical inference that lead to that classification. There is no requirement that “truth” is in the set of stuff that has meaning within the territory.
When you look at the statement 2+2=4 you think some form of “hey, that’s true”. When I look at the statement, I also think some form of “hey, that’s true”. We can then talk and both come to our own unique conclusion that the other person agrees with us. This process does not require a metaphysical arithmetic; it only requires a common context.
For example we both have a proximal existence within the physical universe, we have a communication channel, we both understand English, and we both understand basic arithmetic. These types of common contexts allow us make some very practical and reasonable assumptions about what the other person means.
Common contexts allow us to agree on the consequences of arithmetic.
The short summary is that meaning/existence is formed by contexts of evaluation, and common contexts allow us to communicate. These processes explain your observations and operate entirely within the physical universe. The concept of metaphysical existence is not needed.
I think your argument involves reflection somewhere. The desk calculator agrees that 2+2=4, and it’s not reflective. Putting two pebbles next to two pebbles also agrees.
Look at the discussion under this comment; I maintain that cognitive agents converge, even if their only common context is modus ponens—and that this implies there is something to be converged upon. At the least, it is ‘true’ that that-which-cognitive-agents-converge-on takes the value that it does (rather than any other value, like “1=0”).
Mathematical realism also explains my observations and operates entirely within the mathematical universe; the concept of physical existence is not needed. The ‘physical existence hypothesis’ has the burdensome detail that extant physical reality follows mathematical laws; I do not see a corresponding burdensome detail on the ‘mathematical realism hypothesis’. Thus by Occam, I conclude mathematical realism and no physical existence.
I am not sure I have answered your objections because I am not sure I understand them; if I do not, then I plead merely that it’s 8AM, I’ve been up all night, and I need some sleep :(
Agreement with statements such as 2+2=4 is not a function that desk calculators perform. It is not the function performed when you place two pebbles next to two pebbles.
Agreement is an evaluation performed by your mind from its unique position in the universe.
The conclusion that convergence has occurred must be made from a context of evaluation. You make observations and derive a conclusion of convergence from them. Convergence is a state of your map, not a state of the territory.
Mathematical realism appears to confuse the map for the territory—as does scientific realism, as does physical realism.
When I refer to physical reality or existence I am only referring to a convenient level of abstraction. Space, time, electrons, arithmetic, these all are interpretations formed from different contexts of evaluation. We form networks of maps to describe our universe, but these maps are not the territory.
Gottlob Frege coined the term context principle in his Foundations of Arithmetic, 1884 (translated). He stated it as “We must never try to define the meaning of a word in isolation, but only as it is used in the context of a proposition.”
I am saying that we must never try to identify meaning or existence in isolation, but only as they are formed by a context of evaluation.
When you state:
I look for the context of evaluation that produces this result—and I recognize that the pebbles and agreement are states formed within your mind as you interact with the universe. To believe that these states exist in the universe you are interacting with is a mind projection fallacy.