Aging is agings: towards a recursive definition of biological aging(s); part 4, Success criteria

In the first part of this study, Aging is agings: towards a recursive definition of biological aging(s); part 1, definition a new definition of biological aging(s) was introduced.

In the second part Aging is agings: towards a recursive definition of biological aging(s); part 2, Explication we argued why the ‘need and must’ to come up with a consensus definition and that there’s strong reasons it should be a so called explicative definition a la Carnap.

In the third part, Aging is agings: a recursive definition of biological aging(s); part 3, Recursion we explained what recursion means in the proposed definition and how it is structured further. Also we have added one modification to the proposed definitions, that is now the following:

‘Biological aging is agings underneath, the result of multiple, separate, diverse, interconnected, but malleable processes, eventually compromising normal functions of the organism at different rates and at all levels.’

Today we connect the second, explicative and third, recursive parts by going back to the 4 criteria Carnap lists for a  – good, or at least functional – scientific explicatum to meet: 

i., similarity to the explicandum, 

ii., exactness to introduce the explicatum ‘into a well-connected system of scientific concepts’,

iii., fruitfulness to be useful in formulating empirical laws or logical theorems, I take this feature roughly the same as scientific ‘utility’, ‘applicability’ or ‘productivity’,

iv., simplicity as simple as possible and allowed by the above 3 criteria.

In what follows I fill in the blanks in the separate rows of the success criteria column concerning the proposed recursive solution and will also add 2 additional criteria, that of flexibility and formal correctness.

1. Similarity

Here’s a more detailed and considerable relaxed version of this criterion by Carnap:

The explicatum is to be similar to the explicandum in such a way that, in most cases in which the explicandum has so far been used, the explicatum can be used; however, close similarity is not required, and considerable differences are permitted. 

This criterion makes a lot of sense if it refers to ordinary, common language examples Carnap is using for instance ‘heat sensation’, ‘warmer’, colder’. However it seems considerably unsubstantiated in case of more technical solutions where the explicandum is already a deeper concept that has been the result of scientific development and distinction. Such is the case for ‘biological aging’ as already asking about the disconnect between chronological and biological aging, requires a deeper understanding and formulation of the problems. 

Yet there’s still one derivative sense we can talk about ‘similarity’ that refers back to similarity to the original concept used in common language and here I have to offer one dimension of similarity my definition emphasises. In case of biological aging this root common concept is ‘aging’ in general, that is used in many different meanings in everyday conversations. In a separate post I argued for the the irreducible plurality of aging, and in the definition this plural agings aspect lies at the heart of the recursive definition calling a base case component of itself all the time to build other aging processes. This irreducibly plurality of biological aging is the dimension of similarity towards the common ‘aging’ concept of everyday conversations.

2. Exactness

According to Carnap, p7:

The characterization of the explicatum, that is, the rules of its use (for instance, in the form of a definition), is to be given in an exact form, so as to introduce the explicatum into a well-connected system of scientific concepts. 


The key element in our proposed definition is its reliance on the emerging consensus framework within aging research, the so called ‘Hallmarks’ framework. This is the current most mature framework out there to pull together the different strands of aging research. The very idea of the resursive definition came from the acknowledgment of this framework and trying to take its proposed internal structure seriously. This exhausts the criterion of introducing the explicate into a well-connected system of scientific concepts. 

3. Fruitfulness aka Utility

In Carnap’s original formulation fruitfulness is being useful in formulating empirical laws or logical theorems.

A scientific concept is the more fruitful the more it can be brought into connection with other concepts on the basis of observed facts; in other words, the more it can be used for the formulation of laws. 



3· The explicatum is to be a fruitful concept, that is, useful for the formulation of many universal statements (empirical laws in the case of a nonlogical concept, logical theorems in the case of a logical concept). 


for instance Carnap’s example (p14): ‘The quantitative concept Temperature has proved its great fruitfulness by the fact that it occurs in many important laws.’

Carnap hints at the generalisation of a scientific concept used as an explicatum by it being a component in formulation of further – compared to the state of science it was introduced – empirical laws. 

This criterion can only be assessed from retrospect it seems, after the new explicatum had been out there for a while having a chance to ‘prove itself’ fruitful or to be forgotten for good.

In the lack of a retrospective opportunity now, I will use the ‘fruitfulness’ criterion simply in the sense of ‘utility’, ‘usefulness’, ‘applicability’.

In the case of a biological concept applicable to humans, the concept’s medical usefulness is a straightforward application.

In the case of biological aging, the criterion takes the form of whether the concept can be used to start to look for biomarkers of aging to evaluate the aging status of an organism/individual and to design interventions to slow down, stop or rejuvenate the particular individual. In a less careful but more clinical, so medically more fitting, vocabulary we can say that if the concept helps diagnosis and treatment and leads to diagnostic tools and new therapeutic options, it is useful, its applicability is high. Putting aside the fairly complicated connection between biological aging and disease, please see my thought experiment indicating their unavoidable conceptual linking, the structure and content of the definition provides ample munition for both sides of the clinical equation. The 9 separate but interconnected hallmark processes serve as separate lines of research, both for delivering clinical aging biomarkers and to develop therapeutic interventions. What’s more, these interventions all can be delivered within the same time period to act upon all these processes which is the only ultimate guarantee of safe progress on the whole organism level, according to our current knowledge. This is the ultimate challenge of comprehensive rejuvenation and by making the Hallmarks framework’s proposed internal structure explicit via the recursive formulation the definition is trying to focus both on diagnosis and treatment options and their interplay. This is what I mean by utility, applicability or usefulness of the definition. 

The relation to the Hallmarks framework can be phrased also as another fruitful feature, the feature of the definition that helps to consolidate our current knowledge on biological aging and pull together the separate lines of investigation under one umbrella. This knowledge consolidating role the definition can play is in itself a fruitful feature.    

There’s one aspect, that will be discussed in the next post, and it belongs mainly into this criterion and potentially overlaps with the ‘exactness’ criterion is the quantitative nature of the definition.

4. Simplicity

Carnap is introducing this criterion as additional to fruitfulness acknowledging its derivative importance. He distinguishes 3 types of simplicity in the following paragraph: i., the form of the definition ii., the forms of the laws it is part of and iii., a comparative criterion picking the simpler one amongst competing definition candidates along the lines of the 2 former criteria.

In addition to fruitfulness, scientists appreciate simplicity in their concepts. The simplicity of a concept may be measured, in the first place, by the simplicity of the form of its definition and, second, by the simplicity of the forms of the laws connecting it with other concepts. This property, however, is only of secondary importance. Many complicated concepts are introduced by scientists and turn out to be very useful. In general, simplicity comes into consideration only in a case where there is a question of choice among several concepts which achieve about the same and seem to be equally fruitful; if these concepts show a marked difference in the degree of simplicity, the scientist will, as a rule, prefer the simplest of them. 

page 7

What we are looking at is a basic economic consideration, quite frequent amongst scientists and a favoured option amongst logical positivists. 

I’m not going to discuss the version of simplicity related to the form of the ‘empirical laws’ the definition play a part of. This formulation is focusing on physical concepts where the concept of the empirical laws is pretty well established and was the subject of intensive research within the classical philosophy of science. However the concept of what forms of scientific empirical laws exist in biology is not as clear, and I currently have a neutral position about them, open to any progress. Whether biological aging might represent anything resembling an empirical law is an investigation for another occasion.

In terms of the comparative criterion I’d like to invite everybody to go back to the definitions given in Part 2 and compare them and ask the question which has a simpler forms, or ask the questions which has any definite forms at all.

This leaves us with the option to look into the form of our proposed definition. Here we can say that the first, more informative and actionable part of the definition is the familiar recursive definition format:

‘Biological aging is agings underneath, the result of multiple, separate, diverse, interconnected, but malleable processes, 

and the second part introduces a crucial temporal element (‘at different rates’), and also a more complex spatiotemporal element, (‘at all levels’) and an unambiguous temporal directionality pointing towards complete collapse of an individual living organism/system amounting to death at the limit (‘at all levels’’, ’eventually’).

eventually compromising normal functions of the organism at different rates and at all levels.’

This is how simple the definition of this most complex phenomenon can get to me presently by not sacrificing the more important exactness and utility criteria.

This was also something Carnap did not notice, the dimension of complexity involved in the original concept for which the scientific definition is searched for. The original complexity is heavily relativising further the simplicity that can be reached. 

5. Elementary formal correctness 

Formal correctness of the suggested scientific explication is something Carnap did not consider, if am not mistaken, but certainly not as a criterion. This might be surprising considering Carnap’s knack for logic and formalism that lied at the core of his theories in other respects. But since his main examples were concepts from the natural sciences, physics in the first the place, perhaps the provided explications did not warrant a more formal treatment to him when considering inductive reasoning and probability. Who knows?

Formal correctness is not a too rigid feature in the sense I mean it here, more like a sanity check, hence am adding ‘elementary’ to it as a prefix, say that there is no infinite regress in the definition and the different parts of the definition cover their respective corners and do not overlap. 

In Part 3 on the recursion case I argued that it is a correct version that avoids infinite regress and that multiple bases cases are fine too. The rest is for you to assess.

There’s a more technical version of formal correctness, say when one defines a function in a programming language and it must be syntactically correct in order to complete the task it was designed to execute. I’m not touching this question here, but not because it’s not important, on the contrary, but it would lead to more technical waters, than this study can cater for.

6. Flexibility or Openness

Here is the criterion that Carnap clearly missed to include into his list, but which contributes to both the utility and the timeliness of the proposed definition. A good scientific definition should capture and consolidate not only the most relevant current knowledge but it should leave space for known unknowns. In brief, It should stay open in the sense to be able to incorporate new knowledge, at least within the framework it has arisen. I’m not talking about unknown unknowns here, things we don’t know we miss here that might be crucial about biological aging, as those are epistemologically inaccessible to us.

We don’t have any real guarantees that the current Hallmarks framework is comprehensive enough, we cannot be sure that there aren’t any more hallmark processes out there that will emerge only later backed by sufficient evidence. It might also be possible, though not too probable, that some of the current hallmark processes will turn out to be driven by deeper processes and hence there’s scientific rationale to merge them.

The proposed recursive definition is, by it being a recursive one, is flexible enough to enable both kind of modifications in the future: i., it can accommodate new hallmark processes and ii., it can reduce the number of hallmarks by merging some. It’s internal structure, with acknowledging multiple base cases and multiple derivative ones, can change in actual content but not in form. It’s the formal structure of such a recursive definition that is hard to challenge when it comes about consolidating existing knowledge and being open to incorporate new one. 

The next, probably concluding part will address some open problems related to the definition.