TPF : Immaterial ideas : Potential & Infinite

[Gnomon]

Empiricism, potentiality, and the infinite
https://thephilosophyforum.com/discussi ... ent/934741

I'm no mathmatician, but it seems to me that in a practical sense we need at least the mathematical ideas of infinity and continuums. I'm not seeing a similar need for potency. ___Wonderer1

Well, the concept of potential is used all the time in practical matters, e.g. the counterfactual analysis that makes up a great bulk of the work done in the sciences, engineering problems, "potential energy," potential growth in economics, attracting "potential mates" in biology, etc.
It's really more in the realm of metaphysics or something like the amorphous "metaphysics of science" that the prohibition on talking about potentialities seems to hold. — Count Timothy von Icarus

I think you have hit upon the prohibitive problem with the word "potential" : Metaphysics. It implies the future creation of something new that does not yet exist in physical form : Counterfactual.

As you noted, materialistic Science is OK with the notion of Potential in cases where the before & after can be measured, in theory. For example, a AA battery is rated for 1.5 volts, but that future current is imaginary in the sense that it cannot be measured until a hypothetical circuit is completed by some external Cause. So, what is rated is unreal Potential*1 instead of real Actual voltage.

Ironically, the Potential of a physical battery refers to something physically non-existent, hence literally Metaphysical : knowable only by Reason, not by Senses*2. When defined mathematically, as in Quantum Field Energy*3, it's a statistical scientific notion. Although the storage medium (empty space) is immaterial, the math makes sense. But when defined philosophically, it's a taboo religious concept, in which the storage medium is presumed to be supernatural.


1. Potential :
Unrealized or unmanifest creative power. For example the Voltage of an electric battery is its potential for future current flow measured in Amps. Potential voltage is inert until actualized by some causal trigger.
https://blog-glossary.enformationism.info/page16.html

2. Metaphysical :
an idea, doctrine, or posited reality outside of human sense perception. In modern philosophical terminology, metaphysics refers to the studies of what cannot be reached through objective studies of material reality. . . . Thus, metaphysical claims stand today between the absolutist claims of science (scientism) and the complete relativism of postmodernism and deconstructionism.
http://www.pbs.org/faithandreason/gengl ... -body.html

*3. Quantum potential energy and non-locality :
It is a form of energy which cannot be localized in space. It represent the energy associated with the spatial curvature of the square-root . . . . The quantum potential energy has the units of energy but it does not share the characteristic properties of neither potential nor kinetic energies as understood in classical physics.
https://hal.science › file › quantumpotentialenergy

[Gnomon]

I have observed more than a few people argue that potency/potential is best left out of natural philosophy because it is, in principle, not empirically observable. Only act can be observable, hence, being good modern empiricists, we have no need for potency. — Count Timothy von Icarus

I'm no mathmatician, but it seems to me that in a practical sense we need at least the mathematical ideas of infinity and continuums. I'm not seeing a similar need for potency. — wonderer1

As you said, "only acts can be observed", but Potential for a future Act can be imagined, and even calculated mathematically. Ironically, Wonderer1 sees no need for spooky spiritual Potency, because he has a Mathematical term for the before/after relationship of Causation : Difference*1. He seems to think that mathematics is empirical, hence more real than metaphysical Potential. So, he asserts that Voltage can exist in the absence of Current flow*2. Which is true in the metaphysical sense of a calculated, but not measured, Difference. In Aristotelian terms, Voltage is a Formal (theoretical) Cause, not a Material (empirical) Cause*3.

In a storage battery the Voltage is not measured empirically, but calculated mathematically*2. You can hold a AA battery in your hand without getting shocked, because your skin is too resistive for such a small Potential to flow*2. Hence, you can have Potential (metaphysical ; ideal) Voltage without any (physical ; real) current flow. Voltage, as a mathematical definition, is a theoretical Cause without material Effect.

In what sense does Potential exist : space-time or infinity ; reality or ideality ; actual or theoretical? In what sense does Mathematics exist : material or metaphysical?*4


*1. How to find voltage without current?
How to Calculate Voltage Across a Resistor (with Pictures)
With basic algebra, we can change Ohm's Law to solve for voltage instead of current: I = V / IR = VR / IR = V.
https://www.wikihow.com/Calculate-Volta ... a-Resistor

*2. Voltage without Current :
Voltage can exist without current, as it is the cause of flowing charge. Current does not exist without voltage, as voltage is the main cause to flow current except theoretical superconductor.
https://www.toppr.com/guides/physics/di ... d-current/

*3. What is a voltage source with no current?
Voltage sources provide an almost-constant output voltage as long as the current drawn from the source is within the source's capabilities. An ideal voltage source loaded by an open circuit (i.e., an infinite impedance) will provide no current (and hence no power).
https://en.wikipedia.org/wiki/Current_source

*4. Mathematics is Metaphysics :
Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case for the objects that are studied in mathematics.
https://plato.stanford.edu/entries/phil ... thematics/