Hi mihai-qa
Thank you for your extensive response.
You tell me that I am "stuck in updating the definitions." I understand what you say because, by questioning that traditional formula for assessing occupational risk, I have limited myself in this forum to talk about definitions and meanings of the concepts contemplated in that formula. - I'm somewhat hinting at the potential to go past a formula and discuss in depth about the necessity of defining risk through mathematical means and if there's such a need.
You say: "Risk is such a subjective term that I don't see how a definition will add objectivity." I have thought to write “you are right”, but I immediately gave up because in English that expression has a different meaning than in Spanish. I have been told on the forum that in English the expression "you are right" means "that you say is correct", but in Spanish this expression means "I agree with what you say; I have the same opinion”. I think the same as you “in general”, but there are cases where a good definition describes the direct causes of a fact and, better still, can mathematically assess that fact if the definition can be written in mathematical form. This is what happens, for example, with the definition of gravitation, with the definition of kinetic energy, etc. - Science defines objectivity as a typically something akin to "independent of the observer". Meaning, any individual following the same procedure should reach the same conclusion. In complex areas such as risk analysis, research requires expert judgment, but judgement nontheless (Fischhoff et al 1984).
In my theory, the definition of risk is not invented by applying empirical intuition, but is objectively demonstrated because it derives from the occupational risk theorem. This happens with all the key concepts of my theory. Moreover, in my theory I do not apply my personal approach interpreting the facts that exist or happen in a work system, because the theory applies mathematical logic from the beginning to a repertoire of only five empirical axioms”. All theorems that arise from the concurrence of axioms are typical or essential causes that have existed, exist and will exist at all risk, and I call "canonical causes of risk/contingency". - Let's please stay with this thought for a minute. Based on this assertion, you should have already a formula able to convert "typical or essential" causes into a measurable result. What are those 5 empirical axioms you're referring to? Sorry if you've mentioned it previously but I haven't seen them mentioned.
I call all other causes that exist only in certain particular cases "casuistry" (particular causes of the specific case) or "causal noise". I add the term "contingency" (accident or pathology) to canonical causes because the equation of risk and contingency is the same. The only difference is that an incident has not occurred in the risk, while in the contingency it has occurred. In my theory, the incident is defined as "physical/psychic contact between an employee and a harmful agent/factor", making an abstraction of its possible harmful effect because it is something that goes beyond the mere incident. - Your definition of an incident requires the presence of a human (employee) in that equation, which is not always the case. You could argue that unkept machinery still depend on the human element, as well as software and IoT, but I don't think that's what you are referring to. I would like to see this into practice, if you have converted your thoughts into an excel or some form of paperwork, perhaps it will clear some things.
You say: "We have many methods to assess risk." I have verified that most of these methods do not assess risk, but rather certain "causes of risk": harmful capacity of the labor system (which in my theory is the canonical cause of risk/contingency that I call "damageness of a labor system"), causes of technical failures and human (in my theory it is the canonical cause of risk/contingency that I call "incidentality" of the labor system). In my theory, to evaluate the risk, it is based on its mathematical definition, which expresses its necessary and sufficient causes (excluding the "causal noise", different in each risk): risk/contingency = incidentality · axiom of harmful action · axiom of causal execution ("ejecutividad" in spanish). - Let's try to clarify the "damageness of a labour system" first as I'm not sure what you mean by it (harmful capacity of a labour system)- is this referring to the text of Law? "Incidentality of the Labour System" you seem to use for technical/human factors. So, if I understood correctly: Risk/Contingency=incidentalidad (or probability of an incident occuring)*axiom of harmful action (what are you referring to here? Tech/Human?)*Causal Execution (Ejecutividad - or Enforceability - relating to the legal aspect and the feasability of enforcing it? I guess this is similar to reasonable practicability?)
The incidentality variable includes the damage to the labor system and the two intermediate (indirect) causes "employee vulnerability" and "system threat" (on an employee). - This somewhat answers a bit my previous question but how will you mathematically assess these 2 causes and again, what are you referring to by "damage to the labor system"?
The incidentality cause includes the possibility of an incident at its beginning, progress and consummation. - This could be rephrased as chance of occurence? Frequency? Are we looking at a specific job life cycle, project phases or machinery? I do hope this does not refer to the human factor as we already have plenty of "theories" quick to blame the worker.
The "axiom of harmful action" assesses the susceptibility of the employee considered to a certain harmful agent/factor. - Now I'm intrigued. How will you/we individually assess the susceptability of employees? I work on a somewhat smaller site now but we still have close to 600 employees. Previous project we had 4000 workers for a 6 year phase. There is no generic employee that we can apply mathematical certainties even when using emiprical data. We are far too complex and ever shifting for this to be a valid approach. Maybe I'm misreading it, please correct me if I'm wrong.
The "axiom of harmful causal enforceability" assesses the effectiveness of intrinsic safety against harmful action and, failing that, the effectiveness of the safety measure against harmful action, during an eventual (risk) or actual (contingency) physical/psychic contact between an employee and a harmful agent/factor. - I go back to my previous statement: this sounds incredibly close to reasonable practicability but in an attempt to somehow quantify the term or give it measurable meaning. Although I must admit, when you mention instrinsically safety, I'm not sure exactly what you're pointing to. Is it the machinery, tools, work method, system? Harmful action vs intrinsical safety - do you mean a capacity (i hate this word) to fail safe?
These brief ideas are but a brushstroke of my theory, which has about 400 pages. - I've said it before, romance languages tend to flow and embelish texts. Cut those 400 pages or split them into manageable, bite size pieces of information and we might be able to talk a bit more in detail. From what I can gather, some concepts you're referring to are already available while others seem a bit abstract at face value. I believe OHS is cumbersome and bureaucratic as it is and the next big "thing" will come not from the academics but from the shop floor. Barring the extensive use of computation software, I fail to see how you could possibly quanitfy "incidentalidad" or incidentality, but I would love to be proven wrong...maybe I'm missing something.