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Summary
Summary
Exclusion is an essential property of experience (an axiom) and, by inference, also an essential property of the substrate of consciousness (a postulate).
The axiom states that experience is definite: it is this whole. Formulated in physical terms, the postulate states that the cause–effect power of the substrate of consciousness must be definite: it must specify its cause–effect state as this whole set of units.
Exclusion Axiom
Exclusion Axiom
Experience is definite: it is this whole.
Experience is definite: it is this whole.
[This excerpt is taken from Tononi, G. (forthcoming). On Being.
Ch. 2: The axioms of phenomenal existence.]
Ch. 2: The axioms of phenomenal existence.]
For example, my experience contains the full visual field, neither less nor more. It contains all of it, its left and right side. It excludes my experiencing less—say, the left side only but not the right side—and it excludes my experiencing more—say, a periphery that extends to the back of my head [see figure]. In other words, it has a "border" (the solid blue line). Similarly, my experience contains the feeling of my fingers touching the keyboard and the pressure of the chair against my body. It excludes my experiencing less—say, the feeling of touch only but not of pressure—and it excludes my experiencing more—say, a feeling of oxygen concentration in my blood [1].
Exclusion is immediate, in the sense that I do not have to infer that experience includes what it includes rather than less or more. What it includes is right there, "in front of my eyes." Exclusion is irrefutable, in the sense that its negation is self-contradictory or absurd. I cannot meaningfully conceive of an indefinite experience—an experience that contained at once nothing, everything, and anything in between [2]. Furthermore, while I can conceive of an experience that contained less or more than my current experience—one that were not this whole, but a lesser or greater whole—it would remain true that when I experience it, it would contain exactly what it contains, neither less nor more. It would still be this whole, reaffirming the validity of the axiom. Finally, exclusion is true not just of the experience I am having, but it must be true of every conceivable experience, which means that it is an essential property of phenomenal existence.
Footnotes
[1] Note that what is axiomatic about exclusion is only that the experience I am having contains what it contains, neither less nor more. By contrast, the possibility that other experiences might exist that partially overlap with mine cannot be excluded axiomatically, because it is certainly conceivable that they might exist.Note also that if integration deals with the fact that experience is a whole above its parts, exclusion deals with the fact that the whole has a definite border. In other words, integration says that experience is “a whole,” and exclusion says that it is “this whole.” [2] Indefinite should not be understood as vague (in the sense of hazy) or vast (extended as far as the eye can see).
Exclusion Postulate
Exclusion Postulate
The cause–effect power of the substrate of consciousness must be definite: it must specify its cause–effect state as this whole set of units.
The cause–effect power of the substrate of consciousness must be definite: it must specify its cause–effect state as this whole set of units.
[This excerpt is taken from Tononi, G. (forthcoming). On Being.
Ch. 3: The postulates of physical existence I.]
Ch. 3: The postulates of physical existence I.]
Phenomenally, exclusion means that experience is definite: every experience is not only a whole, but this whole—neither a lesser nor a greater one. How can this essential phenomenal property be formulated in physical terms? Clearly, exclusion requires that the substrate of consciousness, too, must be definite—it must be this irreducible set of units—neither a lesser nor a greater set. In other words, the substrate of my experience cannot at once shrink down to nothing, spread out indiscriminately over the universe, or anything in between. Instead, it must be constituted of a definite set of units, excluding lesser or greater sets.
But what establishes the “border” of a substrate of consciousness—which set of units constitutes it? Phenomenology only says that what exists intrinsically—the experience I am having—exists with the border it has, rather than with different borders. Can anything similar be said in terms of cause–effect power? IIT’s formulation is based again on the principle of maximal existence [...]: among candidate substrates (characterized according to the previous postulates), the one that exists is the one that exists the most. By the integration postulate, a substrate’s existence as one entity is quantified by integrated information φs. Therefore, the substrate of consciousness must be the set of units having maximal integrated information—a substrate that is maximally irreducible. Overlapping substrates with lower φs are excluded from existence. In IIT, a substrate that is maximally irreducible is called a maximal substrate or complex.
As an illustration, consider a set of units in a state—here, i, A, b, c, d, and o [figure below]. Many candidate substrates, all taken with the maximal state they specify, might be irreducible, including Ab, bc, Abc, bcd, Abcd, iAbcdo, and so on. Of these candidates, the “winning” one—the one with maximal integrated information (indicated by φs*)—turns out to be Abcd. As the maximally irreducible substrate, it excludes any overlapping substrates of lower φs, such as its subset Abc and its superset iAbcdo ([...] indicated by the dashed gray lines on the brain and on the TPM). It also excludes any parasets, meaning sets with some units internal to Abcd and some external to it (e.g., iAb).
Note that so far, we have considered a substrate as constituted of a set of units without defining their grain [...]. Should the units be micro-units—”atoms” of cause–effect power—or macro-units aggregating many micro-units, such as molecules, organelles, cells, and so on? Should they be considered over micro-updates or macro-updates (aggregating many micro-updates), such as milliseconds, seconds, minutes, and so on? Based on the exclusion postulate, the units that constitute the maximally irreducible substrate must also be definite in the sense of having a definite grain. Once again, the grain is defined by the principle of maximal existence: the “winning” grain is the one that ensures maximally irreducible existence to the substrate to which the units belong (marked in blue in the inset). On the other hand, units themselves must also be maximally irreducible, as measured by their φu value (u for units) [1]; otherwise, they would not be units but “disintegrate” into their constituents [2].
Footnotes
[1] [This is expressed more precisely in Marshall et al. 2024: “a macro unit needs to be a maximally irreducible constituent of a complex (‘maximally irreducible within’), rather than a complex itself (‘maximally irreducible within and without’).” In other words, “a macro unit need only have higher integrated information than any other system that could be constructed from its micro constituents.”][2] Extrinsically, of course, we can characterize the causal powers of any subset of units, whether or not they constitute a complex, as well as of any subset of micro-units (or -updates and -states), whether or not they constitute macro-units (or -updates and -states). As an illustration, consider the example of atoms, molecules, cells, and organs, with the caveat that the example is extrinsic (extrinsically, one can always consider multiple levels at once).
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For the exclusion axiom, please cite Tononi, Giulio. Forthcoming. On Being. Chapter 2: The axioms of phenomenal existence.For the exclusion postulate, please cite Tononi, Giulio. Forthcoming. On Being. Chapter 3: The postulates of physical existence I.
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