What is a Planet?

March 1, 2026 – 2:01 pm

The dispute over the criteria used for the categorization of celestial bodies as planets reveals either a confusion concerning the reason for a definition, or an unhappy compromise between independent reasons. The criteria adopted by the International Astronomical Union (IAU) are that the body

  1. is in orbit around the Sun,
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape), and
  3. has “cleared the neighbourhood” around its orbit.

These criteria are clearly intended to include the classical planets while excluding most of the new and unfamiliar bodies from the Kuiper belt (and beyond,) without simply naming them as such. Controversy over the exclusion of Pluto means the second option would probably have been preferable, but that would not have looked like a scientifically defensible definition.

A really scientific definition, of course, would attempt to determine some sort of Natural Kind amongst such bodies. In this respect, a pretty standard view is that Natural kinds are the classes of real objects that fill the positions of variables or class names in the best scientific theories relating to the relevant domain. (For a very relevant example, when Copernicus determined/theorized that the Moon differed from all the other planets in the traditional system according to its orbital character, he removed it from the category of planets.) In that case, the class of planets should be a class of astronomical bodies that relatively narrowly includes the classical planets and that features in theories of stellar formation, solar system dynamics and development, and so on. Such a class would not obviously be required to regard either condition 1 or 3 of the IAU definition. A better definition would simply require that a planet be any body that:

  1. is not massive enough to produce fusion reactions, and
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape)

The IAU itself accepts that their condition 1 should be generalised to say that the body is in orbit about a host star. This would still, however, exclude interstellar objects from the class and invalidate the term ‘rogue planet.’ It isn’t clear why this should be necessary: if we desired to speak of only such objects in orbit about a star we could simply talk of the star’s planetary system. (For convenience the planetary system of Tau Ceti, for example, would be the ‘Tau Ceti system.’) The fact that planets that we know of are generally in orbit about a star is a fact about that class but not a definitive one. (That most Zebras live in Africa is a fact about them, a consequence of their origin and history, but it is not definitive.)

Given that the requirement of IAU condition 1 can be discounted, we might further be relieved of the necessity of distinguishing planets from satellites in those cases where two bodies that both satisfy the other criteria for a planet orbit each other. Previously, we might have achieved this by declaring that where the barycentre of the system lay within one of a pair of bodies, that one would be the planet and the other would be the satellite; or we could have insisted that the secondary body has to be significantly smaller than the primary. A reasonable limit for the second would perhaps be a mass ratio greater than 10:1 given that the Pluto-Charon mass ratio of about 1:8 is enough for some – but not for everyone – to describe it as a double planet. It might be more convenient now to speak rather of a planetary sub-system, and, in the case that one of the bodies is clearly the primary, to speak of that planet’s subsystem. We could unambiguously speak, for example, of the ‘Jovian sub-system,’ or even of the ‘Terran sub-system.’

We might, however, need to modify the conditions in order to exclude neutron stars and white dwarfs from the planet class, because they are not massive enough to produce fusion reactions in their matter, as required by condition 1, and yet they are clearly not of the same natural kind as what we intend to refer to as ‘planets.’ We might achieve this by requiring that the body be composed of non-degenerate matter, but that doesn’t really get to the heart of the problem. In fact, this indicates that purely observational criteria are not adequate for distinguishing the class of planets, because we would insist that any body which had been a star in the past, but through natural processes had become non-fusing should not be in that class – regardless of mass or composition or shape. Natural kinds, so many theorists insist, have historical depth or causal boundaries. (A painted horse does not become a zebra.)

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The Sun Simile

February 28, 2026 – 11:43 pm

Plato’s simile in Republic 508-9 can be summarised as follows:

The Form of the Good The Sun
Intelligible world Visible world
Source of Truth or Reality(508e)
Yields (508e)
1.       Truth or reality to intelligibilia
2.       Power of knowing to mind
Thus (508e)
1.       Not knowing but cause of knowing
2.       Known by the knowing it causes
Source of light (508a)
Yields
1.       Visibility to sensibilia (507e)
2.       Power of seeing to eye (508b)
Thus (508b)
1.       Not seeing but cause of seeing

2.       Seen by the seeing it causes
Causes reality of objects of knowing
But is not that reality (509b)
Causes processes of growth
But is not such a process (509b)
Deprivation results in (508d)
1.       No truth or reality (= change/decay)
2.       Poor intelligence (= opinion)
Deprivation results in
1.       No light (508c)
2.       Poor sight (508d)

In the simile, note two stumbles.

  1. If light yields visibility to visible things, then it would be more natural to say that the Good is responsible for the intelligibility of the intelligible, rather than the truth or reality of those things.
  2. The claim that the Sun is the source of light and the Sun causes the processes (genesis) of growth is not a match to the claim that the Good is the source of Reality and the Good causes the reality of knowable things. The ‘coming into being’ of natural things is not like the unchanging being of the knowable things.

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The Divided Line

February 28, 2026 – 6:30 pm

Plato’s analogy in Republic 509d-511e can be summarised as follows.

Line segments A B C D
Realm Intelligible (νοητος) (509d) Visible (ορατος) (509d)
Objects Forms (511c) – considered in their relationship to the Good.
The First Principle of things. (511a, b)
The unassumed.
Forms – NOT considered in their relationship to the Good

Assumptions, mathematical postulates. (510c-511b)

Living beings, plants, artificial things. (510a, e)
Models, drawings of geometrical figures (510d, e)
‘Images’ of objects in C. Shadows, reflections, etc. (510a)
Operations a. Derive First Principle from conclusions in B (511a, b)

b. From First Principle, draw conclusions for objects in B

a. Draw conclusions from assumptions (to be applied to objects of C?)

b. Assumptions are taken for granted

c. Appeals made to sensibilia (in C)

Operators Philosophers Mathematicians and other masters of τεχναι [Scientists] Sophists, poets, artists
Mental States Intelligence
(νοησις/νους)
(Intelligence)
(511a, b)
Thinking
(διανοια) (Reason)
(511a, b, d)
Perceptual Assurance
(πιστις)
(Belief)
(511d, e)
Conjecture
(εικασια)
(Illusion)
(511d, e)
Status Knowledge (επιστημη) Opinion (δοξα)

Just as the Line Segments are related A:B::C:D::A+B:C+D wrt length,
so are the associated Objects related wrt ‘genuineness’/’reality’ (αληθεια)
and the Mental States (παθηματα) wrt ‘clarity’ (σαφηνεια)

Note that whereas the construction Plato gives actually forces B=C, he makes no reference to that and we must assume that it is irrelevant to the analogy.

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Planetary Categorization

February 27, 2026 – 8:47 pm

The explosion in exoplanet discoveries has revealed that the Solar System is very far from a typical stellar system, and a need has arisen for a categorization of planetary types that includes far more than the kinds of planets found orbiting the Sun. To form these classification appeal has been made to a range of characteristics that are at least observable. The principal such characteristics are

  • r = Radius (rE)
  • m = Mass (mE)
  • D = Density (x H2O)
  • T = Temperature (eq. to 1AU from Sun) – referring to the irradiation of the planet
  • a = Atmospheric composition (n)
    • n = 0: No atmosphere (P < 0.001b,)
    • else: n = mean molecular mass of atmospheric gases.

Together with a few other observables these can be used to produce the following table of categorizations.

  • Common            
    • Orbital focus
      • Rogue                   Not orbiting a star
      • Circumbinary     Orbiting a binary star
      • Circumtriple        Orbiting a triple star
    • Orbital character
      • Eccentric              Highly eccentric orbit
      • Double                  Two planets orbiting each other
      • Trojan                   Co-orbiting with another planet
  • Solid                                           r < 1.7                    m < 6                                   D ≈ 5
    • Structure
      • Coreless               No metallic core, thus essentially all mantle
    • Composition
      • Carbon                 Iron core w/ carbon-based mantle
      • Iron                        Iron core w/ minimal mantle
      • Ocean (1)              Significant hydrosphere around core/mantle       
      • Silicate                  Iron core w/ silicone-based mantle
    • History
      • Chthonian           Close to star. Ex-fluid with envelope stripped away
    • Surface
      • Desert                   Dry desert (Arid, Dune)
      • Hycean                 Ocean w/ Hydrogen envelope
      • Ice                          Frozen volatiles (eg. water, ammonia, methane)
      • Lava                      Lava
      • Ocean (2)             Liquid (usually H2O.) Oceans may be sub-surface
    • Habitability
      • Goldilocks            T ≈ 1
    • Size
      • Sub-Earth            r < 0.8                   m < 0.5
      • Earth(-sized)       0.8 < r < 1.7        0.5 < m < 6
      • Super-Earth                                         6 < m < 10
      • Mega-Earth                                        10 < m
  • Fluid                                           1.7 < r,                   6 < m                                  D << 5  
    • Irradiation
      • Hot–                       T >> 1
      • Cold-                      T << 1
    • Size
      • Super-Earth (Gas Dwarf)               6 < m < 10
      • Mini-Neptune     1.7 < r < 3.9           6 < m < 20 (sic) 
      • Sub-Neptune       1.7 < r < 3              m < 10
      • Neptunian            3 < r < 5                10 < m < 20
      • Super-Puff           4 < r                       m < 4                                  D < 0.8
      • Super-Neptune    5 < r < 7                20 < m < 80
      • Jovian                   7 < r < 10              80 < m < 400
      • Puff planet                                          80 < m < 400                    D < 0.8
      • Super-Jupiter     10 < r                     400 < m < 4000
    • Composition
      • Gas Giant            0 < a < 4
      • Helium                  a ≈ 4
      • Ice Giant              4 < a                      

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The Music of the Scop

February 27, 2026 – 12:56 pm

According to the poetic corpus itself, poems such as Beowulf were typically performed in front of the lord in his feasting hall by a scop, roughly equivalent to the ON skald. There are those who doubt the reality outside literature of this class of persons, but the evidence of all other Germanic and Northern barbarian traditions makes that doubt unreasonable. Moreover, again on the evidence of the literature and cognate traditions, there is no doubt that the scop’s performance of the poem. was typically accompanied by what the Anglo-Saxons called a hearpe but which we think of as a round lyre rather than a ‘harp’ as the OE term would suggest. (This is the case even if Pope’s theory concerning the use of the hearpe to determine metre is rejected.) A number of examples of these instruments have been found, most notably in the Sutton Hoo ship burial, which is dated to the 6th or 7th C – about the accepted time of the composition of the poem. A reconstruction of the instrument is shown.

We note that the instrument has 6 strings, which strongly suggests a pentatonic scale (the 6th string being the ‘octave’ of the first.) Though there are many possibe pentatonic scales it is likely that the Anglo-Saxons used the series C E♭ F G B♭ because it is the scale used in early English folk song and it is reasonable to assume some continuity in the musical tradition.

Finally, the textual evidence indicates that the hearpe when used by a scop to accompany a recitation was not played just by the ‘block and strum’ method, nor yet by providing a simple drone, though these techniques were doubtless available for variety. Descriptions of the hearpe’s use indicate that at least on occasion music and voice were linked, though on other occasions the action of the hearpe was relatively independent of the scop’s voice, and that it could be played loudly and with a rapid flow of notes. [1]

Perhaps a good example of what this sounded like is to be found in Beowulf: The Epic in Performance – Benjamin Bagby, voice and medieval harp. This performance looks and sounds much more like how I imagine a scop’s performance than the poetry readings generally performed. Note, in particular, the use of the hearpe and the division into air and recitative (and the fact that the hearpe is not just strummed, but his fingers fly as the records show they did.) 

[1] Beowulf: 1063-5, Widsith: 103-4, The Gifts of Men: 49-50, The Fortunes of Men: 77-84

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Remnant Auras of Absent Terms

February 27, 2026 – 9:44 am

In discussion, a friend proposed that the use of the via negativa might be defended even if it lacks logical or rational justification by supposing that there is an ‘aura’ that is associated with certain words and which remains when they have been definitionally negated in pursuit of some ‘deeper’ understanding, or in recognition that no finite understanding is possible. I thought that was an interesting idea but wasn’t quite sure what this ‘aura’ could be.

The previous discussion had covered the fact that the Greek aura or aurh was a breeze, esp. a cool breeze from water, cognate with ahr, meaning air or a morning mist, and by ways that are not too clear came to mean an emanation of some subtle fluid from a body, and then the subtle substance surrounding a body. Comparisons had been made with the idea of a halo in Classical and Christian iconography, by which the spiritual worth of a hero is displayed. In that case the power of the saint is imagined as flowing out of him and surrounding him, but more like light from a flame than like air from a lake. The same concept is found in the Persian farr (khvareneh) (‘glory’) and the Mesopotamian melam(mu) and doubtless in other places. None of this, however, provides any clue how to go beyond the level of metaphor.

I suggested that the aura desired might be understood as one of the several semantic (?) properties that Frege identified as contributing to the meaning, broadly understood, of terms. The clearest explanation of these can be found  in Dummett’s Frege. Unfortunately, Frege wasn’t particularly interested in making these peripheral issues altogether coherent, so there’s quite a bit of confusion concerning terminology. The general idea is clear enough though. On p. 2 of that text Dummett says

Frege distinguished two elements in the meaning of a sentence or expression, for one of which he reserved the word ‘sense’ (‘Sinn’), and for the other of which we might use the word ‘tone’ (‘illumination’ [‘Beleuchtung’] and ‘colouring’ [‘Färbung’] being the words Frege himself used for this latter). He explained the difference in this way: to the sense of a sentence belongs only that which is relevant to determining its truth or falsity; any feature of its meaning which cannot affect its truth or falsity belongs to its tone. Likewise, to the sense of an expression belongs only that which may be relevant to the truth or falsity of a sentence in which it might occur; and element of its meaning not so relevant is part of its tone.

And on p 85 he says

[Frege] accounts for tone as a matter of the association with a word or expression of certain ‘ideas’ (Vorstellung), by which he means mental images.

That idea won’t fly for reasons Dummett goes through. For example, Frege says that ‘dead’ and ‘deceased’ differ only in tone, but it’s hard to believe that there are associated mental images which distinguish them. Worse, the terms ‘and’ and ‘but’ supposedly differ in tone and/but it’s hard to imagine that there even are associated mental images.

On the other hand, supposing that ‘dead’ and ‘deceased’ differ in the expectations of context of occurrence or in their associated (non-imagistic) ideas might very well work. Those expectations and associations might also be able to do the work that we want the ‘aura’ to do for terms such as ‘God’ which are semantically eviscerated on the via negativa . (Now there’s a mental image to savour.)

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Crossing the Via Negativa

February 26, 2026 – 11:03 pm

We do not generally think that it is acceptable to discuss a thing only in terms of what that thing is not, or in terms of what qualities may not be used to characterize it. Nor do we typically think it reasonable to declare that comprehension of some important concept is in principle impossible and we shouldn’t even try. Apophatic theology, however, takes exactly that approach in treating of the nature God and we should wonder why this is the case.

The standard justification is just that God’s qualities are by definition infinite and therefore beyond the power of positive comprehension by the finite human brain, and therefore the only possible approach is to limit ourselves to the sorts of finitely comprehensible predications involved in saying only what is not the case. By this means we can suggest the qualities of God, without committing ourselves to any positive claims concerning God’s qualities.

I’m not so sure about that: it seems to me that there are plenty of such concepts, like the concept of infinity itself, that are perfectly comprehensible to our finite minds. Cantor showed that even if we cannot hold an infinity in our minds, we can define it positively, describe its characteristics, distinguish its kinds, and generally manipulate it in all the ways that we would need to be able to in order to say that we understand it. Moreover, to say that God lacks the quality X, where X is a finite concept, may very well be making a claim of infinite possibilities un-foreclosed, which means that to understand it would require understanding an infinity; while saying that God lacks some infinite quality would require an understanding of that quality in order to understand the thought that God did not have X. In either case, being able to comprehend the negative thought involves comprehending an infinite concept, and that justification for the via negative fails.

A less charitable proposal is that the impossibility of describing or thinking of God at the same time positively and coherently is a consequence of the fact that the very concept of God is not well-formed. The problem seems to be that it began as a positively defined concept within comprehensible limits but been subsequently expanded into incoherence by the necessities of philosophical argument – in particular, philosophical arguments for His very existence. One can give a Just-So story: primitive man wanted to explain how the world came into being; he looked at examples of things coming into being that he could understand, like his making a flint tool, and analogised a world-knapper. The world-knapper was just like him but bigger, distant, more powerful, wiser. More than that though, the world-knapper became, as devotion and reverence demanded, not just bigger but as big as possible, and so on, and thus we arrived at the qualities of omniscience, omnipotence, omni-benevolence, as well as ineffability, eternality, ubiquity, etc. These unlimiting concepts are, however, both difficult to directly comprehend and collectively incoherent. The puzzles that arise are well-known. Can God make 2+2=5? Can He make a rock He can’t move? Can He do wrong? Can there be evil in the world He made? And so on. The ultimate point of this is that the seeming necessity of the via negative should be taken not as a sign of the transcendence of God, but as a sign of the ill-discipline of thought about God.

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Unspeakable God

February 26, 2026 – 11:00 pm

Hilary Putnam claimed as a consequence of the causal-descriptive semantic theory, that if you were a brain in a vat then you could never think that you were a brain in a vat, let alone say it, because the terms would fail to be properly causally connected to the things they were supposed to reference. (The brain in a vat would not have thoughts of vats created by the right sorts of sensory connections to real vats – only to mad-scientist-illusions of vats.) Similarly, if God exists outside of and independent of the causally structured universe – which He created – then we could not conceive of or even speak of Him.

There might be a couple of ways around this. Firstly, His incarnation as Christ might be a way for us to speak of a part of God – though not all of Him, naturally – since that part of Him does actually exist in the right causal relationships to us; though that brings up a further problem about how the ‘identity’ of the three parts can account for our different possibilities of reference. Secondly, God might have the same status as such fictional creatures as unicorns or dragons, in which the reference to non-causally-active entities (non-existent, in their cases) is constructed from other successfully referring terms. I have no idea how that could be achieved; and even if it was, would believers in God be satisfied with this status for God (or for their beliefs?)

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Zombie Iconography in a Portrait of St Catherine

February 21, 2026 – 12:00 am

A post on the Althouse blog discussing the Vogue cover of ‘Dr’ Jill Biden compared it to the figure of Catherine in a painting by Raphael.

She commented that

Catherine’s hands do not hang limply at her sides. They are expressive of ecstasy and placed in locations that would seem truly odd on a modern-day politico. Unlike Jill, she’s got her weight shifted to one side, and also unlike Jill, she’s leaning on what we know to be the device used to torture-murder-martyr her. 

The hands of Raphael’s Catherine seem oddly positioned because they’re misplaced. Catherine is in the pose for nude females known as venus pudica, and her hands are supposed to be covering her modesty – in this variant both the breasts and the pudendum. Raphael has modified the lower hand so that it is holding her clothing, but the upper hand is doing nothing useful.

Statues in this pose and with a pronounced twist to the body (contrapposto) often have some kind of an elaboration which can be used to give the statue extra support. (Even drapery would work in marble.) I notice that in the painting she’s leaning on her wheel, and I would guess that Raphael just thought that some such elaboration was a necessary part of the figure.

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Information Flow

February 18, 2026 – 9:18 pm

There is a fundamental sociological interest in the infrastructure or social conditions that facilitate the distribution of information in a society. Unfortunately, treatments of the ‘Flow of Information’ in the context of sociological or organizational theory typically refer to the ‘information channels’ that play that role with minimal if any definition or consideration of the criteria that need to be met in order for anything to play that role, while treatments in the context of Network Theory or in the domain of Logic, Language, and Computation offer only definitions that are irrelevant to the sociological context.

Begin with the necessary relevant agent interactions with information.

  1. Insertion

For some proposition p, agent x∈X, ax ∈ αx considered as a state transformation such that ax(σ1) = σ2 is an Insertion of p into σ1 iff

  1. (∃y∈X)[ (∃{xi:i = 0, …, n}⊂ X) (∃<axi ∈αxi: i = 0, …, n>) [ axi(σ1+i) = σ2+i & ax0 = ax ] &
    p ∈ Ivy,σ(2+n) \Ivy,σ1 ]
  2. Bx [ ‘i.’ ] ∈ qx
  3. Dx [ ‘i.’ ] ∈ qx

» An insertion is the deliberate addition to a state of affairs of an item of information that can be made available to some agent by some sequence of state-transforming actions by other agents.

  • Write Ins(ax, p, σ1).
  • We can also say that x Inserts p into σ1 by ax and write In(x, p, σ1, ax)
  • The restriction to available information is justified by the fact that information that is not available to any agent is sociologically inert.
  • The agent making the insertion must be supposed to be intending (desiring and believing) that the information will be sociologically active or else there is no sociological import to the insertion.
  • Note that in the case that n = 0, condition (i) is equivalent to
    • (∃y∈X) GenIv(ax, σ1, p, y) or
    • (∃y∈X)[ p ∈ genIv(ax, σ1, y) ]
  • Refinements to this definition are possible to account for situations in which condition (i) fails, or in which conditions (ii) and (iii) are not required to hold at the time of the action. For example, to take an extreme case, the Voyager spacecraft plaques would not qualify under this definition. Whether these possibilities should be considered need not delay us here.

Define an Information Insertion Point as a state of affairs, σ1 such that

  1. (∃p∈ℙ) (∃x∈X) (∃ax∈αx) [ ax(σ1) = σ2 &
  2. (∃y∈X)[ (∃{xi:i = 0, …, n} ⊂ X) (∃<axi ∈axi: i = 0, …, n>) [ axi(σ1+i) = σ2+i & ax0 = ax ] &
    p ∈ Ivy,σ(2+n) \Ivy,σ1 ] &
  3. Bx [ ‘ii.’ ] ∈ qx ]

» An information insertion point is a state of affairs to which some agent correctly believes he may add an item of information that can be made available to some agent by some sequence of state-transforming actions by other agents.

  • Write IIP(s1)

We shall also define the Information Insertion Point for p or P as an insertion point defined for a particular proposition p or class of propositions P as a state of affairs, σ1 such that

  1. (∀p∈ℙ) (∃x∈X) (∃ax∈αx) [ ax(σ1) = σ2 &
  2. (∃y∈X)[ (∃{xi:i = 0, …, n} ⊂ X) (∃<axi ∈axi: i = 0, …, n>) [ axi(σ1+i) = σ2+i & ax0 = ax ] &
    p ∈ Ivy,σ(2+n) \Ivy,σ1 ] &
  3. Bx [ ‘ii.’ ] ∈ qx ]

» An information insertion point for p/P is a state of affairs such that for every proposition of a certain kind some agent correctly believes he may insert that proposition as an item of information that can be made available to some agent by some sequence of state-transforming actions by other agents.

  • Without danger of ambiguity, we may write IIP(σ1, p) when referring to the case for single propositions or IIP(σ1, P) for the case of classes of propositions, and say that σ1 is an information insertion point for p or P.
  1. Extraction

For some proposition p, agent x∈X, state of affairs σ, ax ∈ αx is an Extraction of p from σ iff

(∃ω)(∃h)[ Mot(ω, x, h, σ, ax) &

» Some question ω motivates x to apply some supposed adduction h on σ using ax

Add(ax, h, σ) & h(σ) = p) ]

» which actually is an adducement applying the adduction h to σ, yielding p.

  • Write Ext(ax, p, σ) and say that ax is an extraction of p from σ.
  • We can also say that x Extracts p from σ by ax and write Ex(x, p, σ, ax)
  • The agent making the extraction must be supposed to be intending (desiring and believing) the action to adduce information, otherwise the retrieval of information is merely an accidental effect of the action and cannot be part of a sociologically significant process.

Define an Information Extraction Point as a state of affairs, σ such that

(∃p∈ℙ) (∃x∈X) (∃ax∈ax) [ (∃ω)(∃h)[ Mot(ω, x, h, σ, ax) & Add(ax, h, σ)
⇒ h(σ) = p]

» An information extraction point is a state of affairs from which some agent correctly believes he may extract an item of information that he is motivated to discover that is available to some agent.

  • Write IEP(σ)

We shall also define the Information Extraction Point for p or P as an insertion point defined for a particular proposition p or class of propositions P as a state of affairs, σ such that

(∀p∈ℙ) (∃x∈X) (∃ax∈ax) [ (∃ω)(∃h)[ Mot(ω, x, h, σ, ax) & Add(ax, h, σ)
⇒ h(σ) = p]

» An information extraction point for p/P is a state of affairs such that for every proposition of a certain kind some agent correctly believes he may extract that proposition as an item of information that he is motivated to discover that is available to some agent.

  • Without danger of ambiguity, we may write IEP(σ, p) when referring to the case for single propositions or IEP(σ, P) for the case of classes of propositions, and say that σ is an information extraction point for p or P.
  1. Transmission

Let p be a proposition, σ1 a state of affairs, such that IIP(σ1, p)

σ = (σ1, …, σn+2) is an Information Arc for p if

(∃<τi: i = 0, …, n >)[ τi(σ1+i) = σ2+i &
(∃x∈X) (∃ax∈αx)[ In(x, p, σ1, ax) & τ0 = ax &
~IEP(σ1, p) &
IEP(σ2+n, p) &
(~Ins(ax, p, σ1) ⇒ ~IEP(σ2+n, p)) ]]

» An information arc for a proposition is a sequence of states of affairs produced by state transformations of an information insertion point at which that proposition has been inserted that ends in an information extraction point for it.

  • Write IA(σ, p)
  • Note that n = 0 is possible, in which case we can talk of a Null Information Arc for p.

Define an Information Channel as a state of affairs χ, such that

(∃P⊂ℙ) (∀p∈P) (∃σ) [ IA(σ, p) &
(∀σi∈σ) [χ ⊂ σi & (~(χ ⊂ σi) ⇒ ~IIP(σi, p) & ~IEP(σi, p)) ]]

» An information channel is a stable state of affairs that facilitates information arcs for a class of propositions as items of information.

  • Write IC(χ)
  • We can call P⊂ℙ that appears in the definition above the Matter of χ, and write that M(χ)=P

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