Levels

One of the first things you need to know to understand the world properly is that everything that exists, exists at some level in both space and time. Consider the world at the scale of individual human beings, trees, buildings, mushrooms, coffee mugs, and ants. These things all exist at roughly the same "level." They interact with each other, they are all roughly the same size, they exist for about the same length of time. When most people think about the inventory of the world they are thinking about things at this level.

Things that are much larger---or exist for much longer---than a person or a mushroom are things like a continent, a forest, a species, a society, a language, a solar system. What exists at this "higher" level are things composed out of the things from the lower level, but also make up something new. What exists at the higher level is distinct, and independent from a mere aggregate of lower level things. A forest isn't just "a bunch of trees" and a society isn't just "a bunch of people."

One way to understand the relationship between things at two different but adjacent levels is to think of a mosaic. Each small tile has a relationship to the tiles next to it that only makes sense in the context of the larger image the tiles produce. Any individual tile could be swapped out for a different one and the whole image remains the same, but change lots of tiles and the image changes.

Another way to think of the relationship is the pattern of iron filings under the influence of a magnetic field. The individual filings line up the way they do because of the presence of the field. All of the filings together mirror the shape of the field in space.

Likewise, we could "scale down" to smaller things, like cells or molecules to see how these things constitute the things at the higher level. Patterns that repeat at each level give rise to more complex structures, which themselves form repeating patterns. These patterns also subtly shift and mutate, which produces endless variation and change.

Part of the reason this is one of the first things to understand about the world is that it lets you see all of the things of which you are a part. This idea "de-individualizes" you---not in the sense of acknowledging that you have ancestors, or that you are a member of a culture or a species---but that your existence is constituted by these things at higher levels, just as much as cells make up (and are also made by) a body. Part of what a person is, is being a cell in a larger body called society. There are also social institutions that exist and have capacities to act in ways that are distinct and independent from their constituent parts.

One of the next things you need to know to understand the world properly is that these levels are fictions. "Higher" and "lower" are metaphors that we use to make sense of our embodiment relative to these other things, our power over them and theirs over us.

The systems that exist at each of these levels and the relationships between and among them are real, but the idea that distinct, clear-cut levels separate and organize them isn't. The levels themselves do not exist; there is no cut-off point where one level ends and another begins. Everything that exists is mutually reinforcing and interwoven, not hierarchical or discrete.

Of what use is philosophy?

When I started writing here I was a graduate student working towards a doctorate in philosophy. I was disaffected and disillusioned with the way academic institutions functioned, their priorities and incentives, who seemed to benefit, and why. But I still believed that philosophy was a worthwhile activity and that a life committed to philosophical work was a life well lived. What I believed then---and still believe---is that philosophical practice needs better institutions and that the means of producing "academic philosophy" belong in the hands of the people doing that labor. There is a great deal of artificial scarcity in philosophy that only serves elite institutions and their beneficiaries.

We also live in a time where almost all academic philosophy has very little value. It does not address the world that we actually inhabit, it is too self-regarding, and it fails to give us any insight into what matters. In the United States, philosophy is practiced by people who are almost entirely insulated from reality, whether by their identity, their acceptance of exceptionalist propaganda, or their social and institutional relations. Philosophy is supposed to be a liberatory force on our habits of reasoning. The academy, as an institution, will only ever seek to reinforce its own power.

There are plenty of polemics against institutional academic philosophy that you can read, but they are all carrying on the tradition of philosophy that is by and for institutional academic philosophers. They are also, mostly, by people like me who failed to "make it" in academic philosophy and who feel harmed by a social institution that let them down in some way. I'm not interested in polemics.

If you care about philosophy, if you have read some philosophy or want to pursue a more "philosophical" life, what should you do? What does it mean to "love wisdom" now, at this moment in history? I don't know the answers to these questions. I don't know if it is possible for me to either fully participate in, or fully break from, the patterns of academic philosophy that I tried for a long time to habituate myself to.

I think the use of philosophy, if there is any, is entirely found in doing it. I hope that if I start doing philosophy again, that it will be of some use.

Christine Ladd-Franklin

Christine Ladd-Franklin (1847-1930) was a philosopher, logician, and psychologist. A student of C. S. Peirce, she made numerous contributions to psychology and mathematical logic despite a tenuous attachment to professional academia. Misogyny being what it was (and is) in academic hiring, Ladd-Franklin never secured a reliable academic post:

Laurel Furumoto notes that "her inability to secure a regular academic position was a predictable consequence, in that time period, of her decision to marry" (Furumoto, 1994, p. 97). In light of the fact that "she never held a regular academic appointment" and therefore never secured solid academic affiliation, her active academic career was remarkable (Furumoto, 1994, p. 93). [source]

Plenty of interesting biographical work on Ladd-Franklin exists, though I somewhat recently got to hear Jessica Gordon-Roth speak on the implicit sexism involved in the (often lengthy) biographical preamble that precedes discussion of women in philosophy, so I won’t rehash Ladd-Franklin’s life story. Recently I read her paper “Epistemology for the Logician” [link]. In it she claims that philosophy, unlike science, does not make steady progress and her argument for why is that science, unlike philosophy, has a “common groundwork” (what she later calls explicit primitives) that command the assent of everyone involved. Here’s a reconstruction of the argument:

1. If X is a branch of knowledge, then the knowledge produced by X is cumulative.

2. If the knowledge produced by some branch of knowledge is cumulative, then there is some set of explicit primitives that are the common ground among practitioners of that branch.

3. So, either philosophy is not a branch of knowledge or there is a set of explicit primitives that are philosophy’s common ground.

Since she wants to reject the first disjunct of the conclusion, Ladd-Franklin sets out to describe what the set of explicit primitives must be like, assuming they exist. For now I’m less interested in the content of the common ground than I am in the claim that philosophy, or science for that matter, must have one.

It seems to me that Ladd-Franklin is on to the same thing expressed by Peter Spirtes, Clark Glymour, and Richard Scheines in Causation, Prediction and Search when they distinguish between Platonic and Euclidean analyses of causation:

One approach to clarifying the notion of causation—the philosophers’ approach ever since Plato—is to try to define “causation” in other terms, to provide necessary and sufficient and noncircular conditions for one thing, or feature or event or circumstance, to cause another, the way one can define “bachelor” as “unmarried adult male human.” Another approach to the same problem—the mathematician’s approach ever since Euclid—is to provide axioms that use the notion of causation without defining it, and to investigate the necessary consequences of those assumptions.

Ladd-Franklin is calling for a set of philosophical axioms or, at the very least, a set of methodological axioms for philosophy. It’s clear that Spirtes et al. heartily endorse the Euclidean approach over that of Plato. But if we understand logic, and philosophy more generally, as the normative study of methods—methods of inquiry, methods of political organization, methods of living—why expect that that study will have a static method? In particular, it seems like a fixed metaphilosophical (or metametaphilosophical, or…) method would be to already answer the questions posed by philosophy.

This isn’t to say that philosophical subfields ethics, or politics, or the metaphysics of causation, or whatever can’t do the thing Ladd-Franklin wants them to do. They clearly can! It’s just that taking Ladd-Franklin’s proposal to apply as a general aim for philosophy as such seems wrong to me.

Regarding the argument reconstruction above, I’d want to deny premise (1), though only on the grounds that I think the implied universal quantifier doesn’t scope over philosophy. Or, rather, that philosophy isn’t a branch of knowledge in the same way that physics, biology, or ethics are. Philosophy is the trunk. The evidence of its cumulative development of knowledge isn’t in the advancement of better theories or more accurate predictions, it is the proliferation of its branches.

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"If you're happy and you know it, clap your hands!"

How should we translate this into a logical sentence in order to capture everything that’s going on here?

First, we could just translate it as “P” but that seems way too easy. We can at least get the conditional and conjunction structure like this:

P = “You’re happy.” | Q = “You know it.” | R = “Clap your hands.”

(P ∧ Q) → R

So far so good. But there’s at least three things in those atoms that we ought to try and get some logical vocabulary for. First, let’s consider the epistemic modality. If X is true and S knows X, then we can introduce an epistemic modal operator, K, that we use to represent knowledge. We’re not going to worry about multi-agent modeling, so we just need one operator.

p = “You’re happy.” | Kp = “You know (that you’re happy).” | r = “Clap your hands.”

(p ∧ Kp) → r

We could also represent the relationship of the object (‘you’) and its states or properties (‘being happy’) with first-order predication.

y = you | H = “…is happy.” | Kϕ = “S knows that ϕ.” | r = “Clap your hands.”

(Hy ∧ KHy) → r

Okay, that’s two of the three features of the sentence that seem obviously worth capturing the logical structure of. Last, there’s the imperative: “Clap your hands.” We could just leave it as is and include an imperative operator (‘!’) to indicate that it’s a non-propositional subformula. It would be better, I think, to try and incorporate the first-order structure we have so far. In that case, we can think of imperatives as issuing to specific objects that are defined in our first order language. We might as well do the same for our epistemic modal operator:

y = you | H = “…is happy.” | Kˢϕ = “S knows that ϕ.” | !ˢϕ = “S, do ϕ!” | C = “Clap …’s hands.”

(Hy ∧ KʸHy) → !ʸCy

This is, I think, the best translation we can give without getting into worries about second-person indexical pronouns. It’s interesting to me that this sentence, which is ostensibly so simple that we teach children to sing it, requires a non-propositional, first-order epistemic modal logic in order to capture its structure.

♩♫ 𝅘𝅥𝅯 𝄽 ♬ 𝄽♪ 𝄽 ♫ 𝅘𝅥𝅯 ♪♬ 𝅘𝅥𝅯 ♬ ♪ ♫ ♩ ♪ ♫ ♬ ♫ 𝅘𝅥𝅯 ♪ 𝄽 ♬ 𝅘𝅥𝅯 ♬ ♪ ♫ ♫ 𝅘𝅥𝅯 𝄽 ♪♬ 𝅘𝅥𝅯 ♬ ♪ ♫

(Hy∧KʸHy) → !ʸCy, (Hy∧KʸHy) → !ʸCy, (Hy∧KʸHy) → Fy, (Hy∧KʸHy) → !ʸCy

(Hy∧KʸHy) → !ʸSy, (Hy∧KʸHy) → !ʸSy, (Hy∧KʸHy) → Fy, (Hy∧KʸHy) → !ʸSy

(Hy∧KʸHy) → !ʸRy, (Hy∧KʸHy) → !ʸRy, (Hy∧KʸHy) → Fy, (Hy∧KʸHy) → !ʸRy

(Hy∧KʸHy) → !ʸ(Cy∧Sy∧Ry), (Hy∧KʸHy) → !ʸ(Cy∧Sy∧Ry), (Hy∧KʸHy) → Fy,
(Hy∧KʸHy) → !ʸ(Cy∧Sy∧Ry)

♩♫ 𝅘𝅥𝅯 𝄽 ♬ 𝄽♪ 𝄽 ♫ 𝅘𝅥𝅯 ♪♬ 𝅘𝅥𝅯 ♬ ♪ ♫ ♩ ♪ ♫ ♬ ♫ 𝅘𝅥𝅯 ♪ 𝄽 ♬ 𝅘𝅥𝅯 ♬ ♪ ♫ ♫ 𝅘𝅥𝅯 𝄽 ♪♬ 𝅘𝅥𝅯 ♬ ♪ ♫

Designated Values

In logic a designated value is a valuation of sentences in the logic that is preserved by entailments. In other words, if we define a logic L=⟨P,F,⊢⟩ with atomic sentences in P and operations in F, then the entailment relation ⊢ takes (a set of) sentences to another (set of) sentence(s) in the language with the following condition: If the input sentences all have the designated value, then the output sentence will too. When the designated value isn’t “preserved” in this way, then the entailment relation doesn’t obtain between the sentences.

Typically, we think of the designated value as “Truth” and, in the case of bivalent logics with only two possible values, the other value is “Falsity.” Falsity is undesignated so it isn’t preserved by the entailment relation. But Truth isn’t the only thing that we might want to preserve across some entailment-like relation. There are a few ways we might extend this idea.

First, there might be other values that we could assign to sentences in our logic. If the sentences aren’t declaratives—but instead they’re imperatives or interrogatives—then we might preserve the force of the commands or the answerability(?) of the questions. Another way of taking this idea forward would be to preserve something other than, or in addition to, truth in declarative sentences. Truth might not be the only valuation we can give to declarative sentences and other valuations might have their own structure. We could preserve their (pragmatic or evidential) assertability. Or we could preserve their believability or justifiedness. Other than broadly epistemic values, we might care about preserving the beauty or pith or pragmatic value of some sentences. We could restrict our attention to only sentences of a certain kind, such as descriptions of moves in a game, and identify those sets that preserve the possibility of a win.

One question about this extension is whether entailments can mix. If we have two orthogonal valuations with two designated values, then do we need distinct entailment relations for each designated value? Could these mix in interesting (i.e. non-additive) ways?

A problem with this approach, however, is that identifying alternative valuations and designated values may be a different way into creating a kind of modal logic. We could just as well introduce a “believable” modal operator and then assert something like ‘◻P’ means that it is true that P is believable. All these other modalities and moods can just collapse back into a single designated value: Truth.

A second extension we could try is to assign a gradient of distinct measures of a single value to sentences in our logic. If invent multiple possible valuations and we think that each of the values are all measuring the same thing, then we’re faced with a decision. Should we assign a threshold value such that that value and the ones ‘above’ it in some sense are designated or should we treat designation (and entailment) as something that comes in degrees? Both directions make sacrifices. The former essentially reproduces the same division between Truth and Falsity but with extra steps. Furthermore, it permits us to treat a relation between sentences that is ‘lossy’ as if it were an entailment. This might be a desirable property for a logic of a process that is lossy in this sense; perhaps we can never be certain of X, so any inference to X (even from X itself) will only entail an ‘above-the-threshold’ valuation.

The latter approach is more suggestive, although it’s hard to see how to designation and entailment could come in degrees. It could be that under certain conditions the entailment relation returns an output that is no less designated than the least designated input. This would be some kind of deductive or super-deductive entailment relation, in the sense that we could actually improve the level of designation that we started with. Or we could have entailment that returns the mean or some other function of the designations of the inputs. Perhaps instead the entailment relation returns an output that is at best the level of the highest designated input. This looks more inductive. In any case, what entailment preserves on this approach is less clear. The point of the entailment relation seems to be that it functions as a guarantee: if you put good things in and play by the rules, then good things will come out. But weakening entailment this way results in an entailment relation that only guarantees the result is ‘minimally bad’ in some way, rather than really preserving the designated value.

The last thing to consider about how we could extend designated values and entailment relations is other contexts in which we care about preserving values across some operation or relation. Take cooking, for example. Abstracted from any specific content we can think of cooking as just “Take some ingredients, apply some operations to them, produce some food.” Not only is “edibility” preserved across (some) cooking relations, but another valuation of food that we care about—tastiness—should increase when the relation successfully obtains. This is a limitation on the classical entailment relation: the output can never be any better than the inputs. There are lots of cases of practical reasoning—morality, economic or political strategy—where we want inference relations of this sort to be ampliative, that is, to improve upon or go beyond their inputs. Whatever alternative valuations we can imagine it seems to me that ampliative inferences, while valuable, are much more context-dependent. Whether so much so that they no longer merit the term “logical,” I’m not sure.

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