What is an electron? How do we answer such questions? If we try to explain it in more fundamental terms, we have to ask what is that and keeps going. So, my question is should we take things like electron, quarks, space, time, consciousness as undefineable quantities which just exist?
So electron is something that exists and has such and such properties. Same for other quantities. It's like how we define a set in math. We don't define it per se but give it lots of properties (axioms).
1.) Before answering a ‚What is?‘-question it may help to clarify:
Which type of statement would I accept as a satisfying answer?
We are not familiar with objects like electrons, protons, positrons, photons, quarks etc. These entities belong to a domain where our senses do not have access to. We cannot define electrons by classifying them according to one of our familiar classfications from everyday experience.
2.) We observe physical phenomena which can be explained best by the hypothesis of entities with properties described by a corresponding theory:
3.) Answers like these are far away from Aristole’s approach to determine objects by giving their essence, not to mention his doctrine of the four causes.
4.) Summing up: 'Electron' is a technical term from a physical theory. Within the theory an electron is characterized by a set of properties. The theory makes predictions about some related, observable phenomena. In this sense the theory explains what an electron is.
When trying to answer a why question, no matter how many intermediate logical steps are explained there may always arise a new why question. So generally we accept a logical consequence of one thing to another and even if we go deeper in examining the whys at some point we find a logical bond between two states in order to proceed forward.
For example if we dedicate a computer in finding all the digits of pi it would work forever calculating more and more digits. So, in fact we calculate so many digits as to how accurate we want to make a specific calculation.
In the same sense we stop asking when we have sufficent information to go on.
In this case if you really want to answer the question "what is it" you would go on forever until everything that has ever happened and thought of, is integrated back to a single entity (god) and because of this unity, every question would be meaningless!
Well, three ways philosophers usually answer the question of 'what is it' are names, definitions and descriptions, and explanations with the first being the briefest and the last being subject to a lifetime of study.
The question of 'what is it' falls under the domain of ontology. For thousands of years, philosophers have wrestled with the way to answer this question, but generally, most times when the question is asked, one is most interested in identity. It is the trivial case. What is it? A book. What is it? The tangent squared. What is it? I don't know what it's called; and generally we can tell the difference between things using Leibniz's Law. Of course, philosophical identity can get tricky, such as with both the sorites paradox and Ship of Theseus thought-experiment.
But after moving beyond simple questions of identity and identifiers which was a topic of interest often explored with the terms sense and reference, the next step is usually a brief description called a definition. Of course, there are many types of definitions: ostensitive, intensional, extensional, circular, genus-species, precising, and so on. What is it? ~Points to the flowers.~ What is it? The class of all featherless bipbeds. What is it? The set of 24 dishes: 8 cups, 8 saucers, 8 bowls. What is it? The class of persons born on October 23rd, 1999 who currently resides in the boundaries of the city of New York with a height under 6' who owns a dog. Often times, the use of sufficient and necessary conditions can be used, but that sort of definition often leads to loopholes due to the ambiguity which inheres in natural language. Another type of definition is the prototype definition. Descriptions are essentially detailed narration that go above and beyond the succinctness of a definition.
Lastly, (and my favorite, much to the chagrin of my wife) one has explanation which many people characterize with different methodologies and definitions. For instance, there is theological explanation, explanatory myths, lay-person explanations, metaphysical explanation (SEP) and scientific explanation (SEP). And naturally, among each category, one finds various methodologies. See Which Question Is Right for Functional Analysis? (PhilSE) for a brief discussion of one form of scientific explanation.
So, my question is should we take things like electron, quarks, space, time, consciousness as undefinable quantities which just exist?
Well, that depends on your metaphysical preferences. Kant defined space and time as forms that concepts take that inhere to the property of the mind. A scientist will tell you an electron fundamentally exists within a standard model or system of particles. It's up to you to decide what requires explanation and description and which is brute fact. What you should do with philosophy, in fact, is a normative question studied in metaphilosophy.
