1. A physical and mathematical approach to Metaphysics
by Andrés Martínez de Azagra Paredes
ETSIIAA – University of Valladolid
What is an idea?
Which are its quantities?
How many dimensions does it have?
How can we measure an idea?
Presentation to the X International Ontology Congress
San Sebastián (Spain) – October 2, 2012
I will try to answer these and other related questions in a few minutes. 1

2. Introduction
Classical physicists claim that all phenomena of the world can be measured. And that is what they do: Metrology, base and derived quantities, units of measurement, systems of units, measuring instruments, standards, …
Can we really measure everything?
Physicists have concluded that it is possible to measure what is big and medium sized but not (entirely) that which is very small. The Uncertainty Principle of Quantum Mechanics.
On the other hand, and since long ago, physicists dream of the possibility of merging Theory of Relativity and Quantum Theory, and arrive at a theory that would explain it all: the Theory of Everything.
Everything? - Isn’t that a bit much?
All political systems, all societies and cultures are smug and brag about their successes, exaggerating them. Our adorable culture seems to stick to this rule.
Do we really know so much?
If so, it should be easy for us to answer the following important question: 2

3. Central Question
What is an idea, and which are its quantities, dimensions and units?
Physics and its metrology seem to have some difficulty in answering this simple question: because an idea cannot weight 5 kg, have an extension of 50 ha, an electric current of 17 A, a luminous intensity of 10 cd nor an amount of 33 mol of thinking matter.
► Therefore and through a reductio ad absurdum, we may conclude that ideas are unitary spiritual entities.
When trying to answer the above question, it becomes necessary to add to the seven fundamental quantities physicists work with today (i.e. mass, length, time, temperature, electric current, luminous intensity and amount of substance) another seven metaphysical quantities.
► The following table shows our proposition: seven base metaphysical quantities and their corresponding units of measurement: the Descartes (De), the Socrates (So), the second (s), the Galen (Ga), the Ortega y Gasset (Or), the Kirchhoff (Ki) and the Leibniz (Le). 3

4. The Essential Answer
Correspondence between the physical and the spiritual world
Physics
Equivalent
Metaphysics
Mass {m; kg}

Conscience {cg; De}
Length {x; m}
Knowledge {co; So}
Time {t; s}
Temperature {T; K}
Empathy {em; Ga}
Electric current {i; A}
Mood {an; Or}
Luminous intensity {L; cd}
Transcendence {; Ki}
Amount of substance {n; mol}
Amount of spirit {ne; Le}
Quantity {quantity symbol; unit symbol}
Authors: Martínez de Azagra Paredes, Del Río San José & Pando Fernández (2008)

5. Our symmetry: a reasoned conjecture
Making Metaphysics Mathematical
Our symmetry: a reasoned conjecture
We are probably symmetrical. (¿¡!?)
Do we have the seven base physical quantities? - Of course we do!
Then we ought to have the corresponding number of fundamental metaphysical quantities as well!
Therefore, following the hypothesis of simmetry, we can deduce that we possess 14 base dimensions (or quantities); 7 are physical and 7 metaphysical.
Let us try to identify the latter ones:
They have to appear in language.
They must be familiar to us.
They must concur with our life experience.

6. Three metaphysical base quantities
Mathematical Metaphysics
Three metaphysical base quantities
 Time {t; s} is a physical and metaphysical quantity. In fact, life is the intersection of the physical with the metaphysical world, an intersection that occurs during a certain period of time t. Time is the main axis of symmetry of our entire existence t  t
 Conscience {cg; De} is the spiritual mass of the brain. It assesses the number of neurons which are awake (active and connected) at a given moment. We could define conscience as the neural attention level of the brain. According to the axiom of the reasoned conjectures, it corresponds to the number of transformers (or perspective changers) active in the brain at a given moment. m  cg
 The third fundamental spiritual quantity is knowledge {co; So}. It is the mental path (or route) the brain has followed; its course. Therefore, by analogy, its equivalent in the physical world is length {x} x  co

7. The four other base quantities
Mathematical Metaphysics
The four other base quantities
 Empathy {em; Ga} refers to the warmth or coldness with which we act; it assesses how we relate to others. It is the equivalent of temperature in the physical world. T  em
 Mood {an; Or}, i.e. the inner happiness or sadness of a being, its joy or its disappointment with life, is yet another base quantity of metaphysics. In physics, its equivalent is the electric current. i  an
 It is easy to establish the next equivalent, for it often appears in language and literature: there is a clear path leading from light to the sixth fundamental quantity of metaphysics: transcendence {; Ki}. L  
 The last base quantity we are searching for is the amount of spiritual matter {ne; Le}; the number of monads contained in a soul (to express it in Leibniz’ terms) n  ne

8. Making Metaphysics Mathemathical
Once we have worked out the table and accepted its equivalents, it is easy to develop a quite solid mathematical Metaphysics.
We just have to transpose, with the help of the established analogies, the basic laws of physics to the world of metaphysics.
It is interesting to interpret these laws and, in a near future, it may help to make philosophy more precise and mathematical.
► Law of universal gravitation
► Newton’s second law of motion
► The principles of thermodynamics
► Ohm’s law (electrical resistance)
► Faraday’s law of electromagnetic induction
► Wien’s displacement law
► Stefan & Boltzmann law ►

9. Conclusions  Ideas and thoughts are more than mere physics.
 We will be only able to measure ideas if we define additional metaphysical quantities, independent from those of the International System of Units (S.I.).
 The hypothesis that there are as many metaphysical as physical base quantities, and the establishement of equivalents and analogies between both types of quantities, allow us to obtain a grounded number of base metaphysical quantities.
 With the aid of the established equivalents the fundamental laws of physics can be transposed into metaphysics.
 The interpretation of the (thus obtained) laws of metaphysics is interesting and could be useful, among other fields, in philosophy, psychology or neurology, etc. (once they have been validated and calibrated)

10. Related bibliography
▪ Buckingham, E. (1914): “On physically similar systems. Illustrations of the use of dimensional equations”. Physical Review, nº 4: 345 – 376
▪ Martínez de Azagra Paredes, A. (2012): Una aproximación físico –matemática a la Metafísica. Revista de Microfilosofía (on line).
▪ Martínez de Azagra Paredes, A.; Pando Fernández, V. & del Río San José, J. (2007): “Generalizaciones al teorema  de Buckingham con algunas aplicaciones”. In
▪ Martínez de Azagra Paredes, A., del Río San José, J. & Pando Fernández, V. (2008): “Introducción a la Física inmaterial". Número de Asiento Registral 00 / 2009 / 3240 (solicitud P-45-08) del Registro General de la Propiedad Intelectual de España
▪ Martínez de Azagra Paredes, A.; Pando Fernández, V. & del Río San José, J. (2010): “Del teorema  al axioma de las conjeturas razonadas”. Boletín de la Sociedad Puig Adam de Profesores de Matemáticas, 86: 55 – 73
▪ Vaschy, A. (1892): “Sur les lois de similitude en physique”. Annales Télégraphiques, 19: 25 – 28

11. Thank you very much for your attention!
Andrés Martínez de Azagra Paredes correo: Dr. Ingeniero de Montes Catedrático de Hidráulica e Hidrología Universidad de Valladolid