NOTE-700: Floridi — The Method of Levels of Abstraction

Contribution

Floridi separates four kinds of “levelism” (epistemological, ontological, methodological, and the Oppenheim–Putnam amalgam). He concedes the ontological kind to Heil and Schaffer, and rebuilds the epistemological kind as a method with definitions borrowed from formal methods in computer science (typed variables, Z-style predicates, simulation between levels). What is new after it is a single citable statement of the method, with its claimed consequences for ontological commitment, relativism and realism. Before this, the method lived inside Floridi & Sanders 2004 (LIT-898) and their Yearbook chapter. The paper does not prove anything about the formalism. It defines it, illustrates it, and positions it.

Key insight

A question about a system has no answer until the observables are fixed, and fixing them is a choice made for a purpose. Many philosophical disputes, Kant’s antinomies being the model case, come from asking about “the system in itself” while silently shifting between LoAs. “Trying to overstep the limits set by the LoA leads to a conceptual mess” (p. 23). The LoA is an interface, “the place at which (diverse) independent systems meet and act on or communicate with each other” (p. 30). It is not a layer of the world: “Nature does not know about LoAs either” (p. 35).

Assumptions

• Knowledge of systems is indirect, mediated by an LoA. Direct knowledge is taken to be only knowledge of one’s own mental states (fn. 9, p. 18).
• Systems may be empirical or “purely semantic”, that is, domains of discourse (p. 6). The method is meant to apply to both.
• Naive set theory, and well-typed variables. Type-free systems, and the antinomies a typed theory exists to exclude, are outside its scope (pp. 7, 36–37). “Its limitations are those of any typed theory” (p. 36).
• GoAs are finite sets of LoAs, and only discrete systems are handled; the infinite case is said to apply to analogue systems and is not considered (fn. 7, p. 14).
• The interpretation that makes a typed variable an observable is left informal, by design (p. 33).
• Ontological levelism is “probably untenable” (pp. 3–4). This is taken from Heil 2003 and Schaffer 2003, not argued here.

Key results

The paper’s results are definitions (§2) and arguments about them (§§3–4).

• Typed variable (p. 5): a uniquely named variable with a type, the set of its possible values, written x:X. An observable (p. 6) is an interpreted typed variable: a typed variable plus a statement of what feature of the system it represents. It is discrete if its type is finite, else analogue. Equality of observables requires equal typed variables, the same feature, and co-variation (Peter’s height in feet and Ann’s in metres are the same typed variable but different observables, p. 7).
• LoA (p. 10): “a finite but non-empty set of observables”, unordered; discrete, analogue or hybrid. Examples: tasting, purchasing and cellaring LoAs for wine.
• Behaviour and moderated LoA (p. 11): a behaviour at an LoA is a predicate whose free variables are its observables; the satisfying assignments are the system behaviours; a moderated LoA is an LoA with a behaviour (height: 0 < h < 9).
• Translation (p. 13): a relation R ⊆ A × C translates a predicate p on A to P_R(p)(c) = ∃a:A R(a,c) ∧ p(a).
• GoA (p. 14, “the main definition of the paper”): a finite set {Lᵢ | 0 ≤ i < n} of moderated LoAs with relations Rᵢ,ⱼ ⊆ Lᵢ × Lⱼ (i ≠ j) such that (1) Rᵢ,ⱼ is the reverse of Rⱼ,ᵢ, and (2) the behaviour at Lⱼ is at least as strong as the translated behaviour, pⱼ ⇒ P_Rᵢ,ⱼ(pᵢ) (eq. 1); and, for each related pair of observables x:X and y:Y, a relation R_xy ⊂ X × Y between their types (added at Hughes’s suggestion, fn. 8). The defining property is taken from simulation in computer science, “the conformity of behaviour between levels of abstraction” (p. 5). A one-element GoA is an LoA.
• Disjoint and nested GoAs (p. 15): disjoint if the LoAs share no observable and all relations are empty; nested if the only non-empty relations are between Lᵢ and Lᵢ₊₁ and the reverse of each Rᵢ,ᵢ₊₁ is a surjective function from the observables of Lᵢ₊₁ to those of Lᵢ. So every abstract observation has a concrete counterpart, and one abstract observable may be refined by many concrete ones (p. 16). Example: a traffic light’s colour:{red, amber, green} refined to a wavelength wl with behaviour (λ_red ≤ wl ≤ λ_red′) ∨ … and colour = c ↔ λ_c ≤ wl ≤ λ_c′ (p. 17).
• Interconvertibility (p. 18): disjoint and nested GoAs are said to be “interchangeable, at least theoretically”, by passing between A, B and A ∪ B. See Limitations: the argument works for sets but not for the paper’s definition of a nested GoA.
• Four advantages (pp. 18–19): an LoA specifies “indirect knowledge”; it fixes the questions that “(a) can be meaningfully asked and (b) are answerable in principle”; it guards against level-shifting fallacies (metabasis, category mistakes, antinomies); and it makes ontological commitment explicit.
• SLMS scheme and commitment (pp. 19–21): system, analysed at an LoA, generates a model, which identifies a structure. The LoA is “O-committing” (types: a three-colour LoA commits one to a Roman, not an Oxford, traffic light) and the model “O-committed” (tokens).
• Kant’s antinomies (§3): antinomies 1–2 (finitude, divisibility) mistake features of the interface for features of the system, so neither thesis nor antithesis holds. Antinomies 3–4 (freedom, necessary being) “come close to” a disjoint GoA, so both may hold (pp. 22–23). The method is “Kantian” and “transcendental” without Kant’s mentalism, and “anti-metaphysical”: “metaphysics is that LoA-free zone where anyone can say anything without fear of ever being proved wrong” (p. 24). Its realism is “liminal realism”, between internal and external realism (p. 22).
• Levels of organisation and explanation (§4.1): LoOs are ontological (a hierarchy in the system de re); LoEs are pragmatic and epistemic; LoAs “provide a foundation for both” (p. 26). Marr, Pylyshyn and Dennett each give “GoAs with three LoAs”, do not distinguish LoO, LoE and LoA, and, because they privilege explanation, their “ontological commitment is embedded and hence concealed” (pp. 27–28).
• Conceptual schemes (§4.2): LoAs differ from Davidson’s schemes in being networks of observables usable by non-human “agents” (p. 29), and in standing to their systems by design, not discovery or invention (p. 29). Agents can change and expand their LoAs, but two LoAs can still be untranslatable, so agents “may inhabit only some types of information spaces in principle” (p. 31; Nagel’s bat). Davidson’s argument assumes a linguistic, representationalist view that LoAs do not share, so “Incommensurable and untranslatable LoAs are perfectly possible” (p. 31). Histories of science are comparable at some LoA: “do not ask absolute questions, for they just create an absolute mess” (p. 32).
• Pluralism without relativism (§4.3, one paragraph): LoAs are “mutually comparable and assessable, in terms of inter-LoA coherence, of their capacity to take full advantage of the same data and of their degree of fulfilment of the explanatory and predictive requirements laid down by the level of explanation” (pp. 32–33).
• Realism without descriptivism (§4.4): no circularity in defining “realistic” observables, by analogy with Tarski’s truth definition; a regress arises only if a complete characterisation is sought (pp. 33–34). A GoA is judged by validation (external adequacy) and verification (internal coherence), like “a multidimensional crossword puzzle”. GoAs “do not describe, portray, or uncover the intrinsic nature of the systems they analyse … Adequacy and coherence are the most we can hope for” (p. 34).

Claims

id	claim	strength	support
C1	Ontological levelism is probably untenable	weak	deferred to Heil 2003 and Schaffer 2003 (pp. 3–4); not argued here
C2	Epistemological levelism, as the method of LoAs, is a fundamental and, for discrete systems, indispensable method of conceptual analysis	weak	the four advantages (§2.7) and the analogy that the method does “for discrete systems what differential calculus has traditionally done for analogue systems” (p. 12). “Indispensable” is asserted (p. 36)
C3	Fixing an LoA fixes which questions about a system are meaningful and answerable, and the amount of information a model can contain	moderate for the first half, weak for the second	the first follows from the definitions. “A quantified commitment to the kind and amount of information” (p. 19) has no measure behind it: information is not quantified anywhere in the paper
C4	Adopting an LoA commits a theory to types and endorsing its model commits it to tokens	moderate	the SLMS scheme and the traffic-light example (pp. 19–21); a clean distinction, though stated rather than defended
C5	Kant’s first two antinomies come from treating features of an LoA as features of the system; the last two resemble a disjoint GoA	weak	an illustration by analogy, “assuming for the sake of simplicity that a LoA is comparable to an interface” (p. 23); no antinomy is formalised as a GoA
C6	Marr’s, Pylyshyn’s and Dennett’s three-level schemes conflate LoO, LoE and LoA and so conceal their ontological commitment	moderate	the diagnosis is argued from their own statements (pp. 26–28). The claim that each is “readily formalised” as a three-LoA GoA is asserted, not carried out
C7	Davidson’s argument against conceptual schemes does not touch LoAs, and untranslatable LoAs are possible	weak	argued by contrasting four features (pp. 28–31). The one example of untranslatability, tasting versus purchasing wine, shows two LoAs that do not overlap, not two that cannot be translated
C8	Making the LoA explicit gives pluralism without relativism	weak	one paragraph listing ranking criteria (pp. 32–33). Each criterion is relative to “the level of explanation”, so LoAs are ranked given a purpose, not across purposes
C9	Defining realistic observables involves no vicious circularity or regress, and the method supports realism without naive realism	moderate	the analogy with Tarski’s truth definition and the validation/verification account (pp. 33–34)
C10	The method has settled problems elsewhere (the Gettier problem is unsolvable, zombies, structural realism, telepresence, the value of informational objects)	assertion	referred to other papers (p. 35)

Concepts

• observable: an interpreted typed variable, which need not come from measurement or perception (p. 6).
• level of abstraction (LoA): a finite non-empty set of observables; the interface at which a system is accessed (pp. 10, 30).
• behaviour / moderated LoA: a predicate over an LoA’s observables, and an LoA paired with one (p. 11).
• gradient of abstractions (GoA): moderated LoAs related so that each level’s behaviour is consistent with its neighbours’ (p. 14); disjoint views are complementary, nested views successively more informative (p. 15).
• method of abstraction: making the commitment to an LoA or GoA explicit before elaborating a theory (p. 18).
• SLMS scheme: system, LoA, model, structure; the LoA is O-committing and the model O-committed (pp. 19–21).
• level of organisation (LoO) and level of explanation (LoE): ontological and pragmatic levelisms respectively; an LoE is “an important kind of LoA” (p. 25).
• liminal realism: between internal realism and external or metaphysical realism (p. 22).
• information space: what an LoA generates and commits an agent to (p. 30).
• agent: used broadly and undefined in this paper. Agents are anything that “operate[s] and deal[s] with the world … at some LoAs”, including computers, animals, plants, scientific theories and measuring instruments (p. 29). A thermometer is an agent with “hardwired” LoAs (p. 30).

Connections

Floridi says the method was “forced” on him and Sanders by “the problem of defining the nature of agents (natural, human and artificial)” in Floridi & Sanders 2004 (LIT-898, read in NOTE-701) (p. 35). He calls Sanders someone who “should really be considered a co-author of this paper” (p. 37). Their joint “The Method of Abstraction” (Yearbook of the Artificial, 2004) is the earlier statement, and is not held. This paper generalises the method from defining agents to conceptual analysis at large, and refines the GoA definition by relating types as well as observables (fn. 8). The extends on the LIT records this. Floridi 2025 (LIT-897, read later in NOTE-702) compares kinds of agency by this method.

Informational structural realism. Floridi’s defence of ISR (LIT-152, read in NOTE-099) restates these definitions in its §2.2. This paper lists that work as an application, “to propose and defend an informational approach to structural realism that reconciles forms of ontological and epistemological structural realism” (p. 35, citing it as Floridi 2004b, the 2004 draft). NOTE-099’s judgement that “the LoA formalism is rigorous in isolation, but no result about it is used in the argument” holds here at the source too. No result about GoAs is used here either, and the definitions carry slips (see Limitations). NOTE-099’s gloss of an LoA as “a model-theoretic interface, not a metaphysical ‘level of being’” is this paper’s own position (pp. 30, 35). That confirms NOTE-096’s correction of Karpenko (LIT-215), who reads information as what has “the highest level of abstraction”: here LoAs are interfaces, and ontological levels are given up outright.

Personal identity. Floridi’s informational account of the self (LIT-136, read in NOTE-130) deflates diachronic identity to purpose-relative LoAs. It assumes the method from “Floridi 2008c”; I have not checked that LIT-136’s reference list resolves that to this paper. NOTE-130 grades its “this is not relativism: given a particular goal, one LoA is better than another” as a one-sentence assertion, and asks how goals are adjudicated. This paper’s §4.3 is where that sentence comes from, and it does not answer the question either. Its ranking criteria are all relative to “the level of explanation”, which is a purpose already fixed. NOTE-374 notes that the encyclopedia entry on personal identity (LIT-454) rejects the view that persistence is answerable by conceptual means, of which Floridi’s deflation is a version. That objection reaches the method, not only its use there.

Watson. NOTE-172 reads Watson (LIT-187) as building on “Floridi’s method of levels of abstraction (2008)”. That is very probably this paper; I have not checked it against Watson’s references.

Dennett. The paper compares GoAs to Dennett’s stances (p. 13) and formalises the intentional, design and physical stances as a three-LoA GoA (p. 27), citing “Intentional Systems” (LIT-440) and The Intentional Stance (LIT-430, unread). LIT-440’s reading (NOTE-350) makes being an intentional system relative to an observer’s predictive strategy. The method of abstraction generalises that relativity to any property, and objects only that Dennett privileges explanation and so hides his ontology (p. 28). Dennett’s “True Believers” (LIT-398) later withdraws that relativity, by LIT-440’s record; this paper does not engage the later view.

Other cited work the record holds. Nagel’s bat (LIT-096) is used for information spaces too far apart to translate (p. 31). Craver’s “forthcoming” Explaining the Brain (fn. 3; LIT-832, unread) is cited for ontological levelism in biology.

Bearing on the record

It carries nothing for machine-learning practice. It is held here as the source of a method the record’s Floridi readings (LIT-152, LIT-136, LIT-898, LIT-896, LIT-897) assume. I file no THEORY. The paper’s results are definitions and a stance, not a claim about the world with evidence, and NOTE-099 filed none for the ISR paper that uses the same machinery. THEORY-034, which places LIT-152, is not affected: this paper adds nothing on intrinsic natures beyond §4.4’s statement that GoAs “do not … uncover the intrinsic nature of the systems they analyse” (p. 34), which agrees with NOTE-099’s reading.

The agency line (my pairings; the paper cites none of these).

• QUESTION-009 (when does a pattern of coordination constitute an additional agent?). The method gives the form of an answer, not an answer: something is an agent at an LoA if its observables there satisfy some criteria. The criteria are Floridi & Sanders’s (LIT-898), not this paper’s. What this paper adds is the condition under which “additional agent” questions are well posed, namely an explicit LoA. It also adds the warning that an LoA-free version of the question is the “metaphysics” it dismisses (p. 24). It does nothing about the permissiveness objection (CLAIM-010, a thermostat has a will). The paper’s own usage is more permissive still: a thermometer and a scientific theory are “agents” that operate at LoAs (pp. 29–30).
• Two roles for an LoA. §4.2 uses “the agent’s LoA”, what an agent can itself observe (a thermometer’s hardwired LoA). Floridi & Sanders, and the later agency papers, use “the LoA at which a system is analysed”, the theorist’s interface. The paper does not separate the two. A claim that something is an agent “at a given LoA” needs to say which is meant, and a reading of LIT-897 should check.
• CLAIM-045 and CLAIM-110. The record’s correction at A10, that differences in explanatory emphasis between Brooks, Kelso and Levin do not imply competing ontologies, is this paper’s distinction between levels of explanation and levels of organisation (§4.1). “By structuring the explanandum, LoAs can reconcile the explanans” (p. 32). CLAIM-045’s “complementary components … each answering a different sub-question” is, in this vocabulary, a GoA whose LoAs are disjoint or partly overlapping, with the sub-questions as levels of explanation. The vocabulary could state CLAIM-045 more exactly, but it does not argue for it.

Nothing in the record cites this paper for something it does not say. NOTE-172’s line distinguishing it from LIT-152 is accurate. Now that the paper is held, that line could name LIT-900.

Limitations

• The interconvertibility argument fails under the paper’s own definitions (p. 18). Disjoint to nested: the inclusion of A in A ∪ B, reversed, is not total on A ∪ B, so it is not the surjective function nestedness requires (p. 15). Nested to disjoint: “if A and B are increasing sets with the former embedded in the latter, then A and the set difference A \ B are disjoint sets”. With A ⊆ B, A \ B is empty; the intended set is B \ A. The claim survives for sets of observables, not for GoAs as defined. The hedge “at least theoretically” does not cover this.
• Index and orientation slips in §2.6. “If one LoA Lᵢ extends another Lⱼ by adding new observables, then the relation Rᵢ,ⱼ is the inclusion of the observables of Lᵢ in those of Lⱼ” (p. 14) is consistent with the rest of the sentence only if Lⱼ extends Lᵢ. The nested definition says the only non-empty relations are the Rᵢ,ᵢ₊₁, but condition 1 makes each Rᵢ₊₁,ᵢ non-empty too. Figure 1 draws L₀ as the widest band, while the traffic-light example makes L₀ the coarser LoA, and the figure does not say what width means. Two different figures are both numbered “1” (pp. 16, 20). None of this damages the method. All of it is in the preprint, and I have not seen whether print corrects it.
• “Quantified commitment” without a quantity. The paper says an LoA gives “a quantified commitment to the kind and amount of information” extractable (p. 19), and that a lower LoA’s model “contains more information” (pp. 18–19). No measure is defined. It is resolution in the sense of a finer type, not Shannon information.
• Relativism is answered within a purpose, not across purposes. The §4.3 criteria rank LoAs relative to “the explanatory and predictive requirements laid down by the level of explanation”. So two parties with different purposes can each be right at their own LoA, which is the pluralism claimed. But nothing here says when a purpose is the wrong one. Every use of the method that deflates a question (identity in LIT-136, the antinomies here) inherits this gap.
• The tripartite formalisations are promised, not done. Marr’s, Pylyshyn’s and Dennett’s schemes are “readily formalised in terms of GoAs” (p. 27), but no relations or behaviours are written down. The claim that the formalism adds rigour to them is untested here.
• Scope, by the author’s own account (p. 36). The method is that of a typed theory. Floridi does not know whether every complex system can be approximated at finer LoAs, and allows that “the mind or society” may not be susceptible. He does not commit to exporting the method to ontological or methodological contexts.
• The interpretation of observables is informal (p. 33). The method’s claim to make ontological commitment explicit rests on a step it leaves unformalised.

Open questions

• Is there a principled way to rank purposes, or levels of explanation, that would make §4.3’s “pluralism without relativism” hold across purposes and not only within one? Without it, the deflationary uses (identity, agency) stay purpose-relative all the way down.
• Does the GoA consistency condition (eq. 1) do any work in the papers that cite the method? NOTE-099 found none in the ISR paper. A reading of the agency papers should check whether any argument there uses a relation between LoAs, or only the choice of one.
• Which LoA does an agency claim name: the system’s own (what it can observe) or the analyst’s (what it is observed by)? The two come apart for a thermostat or an LLM, and this paper uses both without marking the difference.
• Does the Springer version of record correct the §2.6 slips?