expand_less ItContemporary is[[http://en.wikipedia.org/wiki/Theory_of_everything|Theories of Everythng]] a(ToEs) bitare surprisingnot thatbased contemporaryon [[http://en.wikipedia.org/wiki/Theory_of_everything|Theories of Everythng]]semiotics (ToEs)and almostdo nevernot addressconsider the ontic status of signs.signs.   IIdeas wouldlike citeTegmark's this[[http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis|mathematical universe hypothesis]] asmight thebe centralbetter problemunderstood with Tegmark'sa [[http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis|mathematical universe hypothesis]]foundation.  It'sof atriadic blindspotsigns.  Carlo Roveli speaks of "relational quantum mechanics" in mostwhich thinkingit aboutmight ToEs.be best to think of the elemental relations as completely constructed of signs.
The way that Feynman diagrams are always constructed of three legs per node is just like Peirce writing that signs need three parts and no more because you can construct higher degree relations from triads, but you can't get a triad from a diad. Of course, each leg of the diagram is a sign, and just like semiosis that constructs meanings from constellations of signs, quantum scientists construct constellations of individual Feynman diagrams that are used to calculate observational expectations.
Physicists characteristically claim what is essentially philisophical territory as their own, often stating that, "Finding a ToE is one of the major major [[http://en.wikipedia.org/wiki/Unsolved_problems_in_physics|Unsolved problems in physics]]".  The modest version of this project is about integrating theories of the large and small, of gravity and quantum mechanics, and that work is clearly within the bounds of physics.  When we get into questions of what really is so in the world, what is real vs. ideal, permanent vs. dynamic or emergent, we are no longer doing physics.  These philisophical arguments often concern the "status of un-observables" in the theory.  These are objects that appear in the mathematical theory to signify elements of the theory that may be only indirectly observable.  The observables are calculated from mathematical analysis of models in terms of idealized objects from the theory, but if the measurements closely match the calculated predictions we say the theory is (relatively) accurate.
 That's what Tegmark's hypothesis is about, assigning reality to ideal objects in the theory.theory and that's why he need signs to ground his ideas. In other words, a comprehensive (mathematical) theory of signs could provide a metaphysics that gives reality to the simulations. Only when you grant ontological status to signs can you claim the simulation has reality. It is precisely the grounding of all of this in embodied experience that grants real status to the abstract entities of science. Roveli's description of properties and observations only being meaningful in relations between interacting systems is a way to say that such interactions are "sign systems" from bottom to top. This is about supporting strong emergence, turtles all the way down. Semiosis of signs vs. elementary partical interactions are just different descriptions, so that complex systems are grounded in the standard model without needing to connect the dots. The emergent properties of higher levels of organization will be better described by sign systems developed by investigators looking at that level. Signs, much in the forms of language including mathematics, are the way all the layers of the analysis are linked such that the realities of each and the whole itself are enacted and experienced.
Peirce is precient in his turn towards a much deeper analysis of signs, and I consider his work to be foundational to current and future work on these problems of logic and meaning.  What all of these myopic theories have in common is that they never consider the reality of the theories themselves and the signs they contain.  They are only concerned about the reality of the objects that the signs in question signify as if semiotic action were not part of the real world.  Sucinctly, the real clearly includes ideas (signs, meanings) and their beingness, their ontology, is something that must be addressed in a true ToE.  Peirce has this to say about the importance of semiotics:

{{The Importance of Semiotics}}

When we pull thinking back from some meta-world into reality, the importance of his project becomebecomse clear.  He is working to bring scientific and philisophical productions into the world and subject it to a rigorous treatment.  Arguments about [[http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences|the unreasonable success]] of mathematical science aren't careful to distinguish between the [[http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems|limits of mathematics]] and the reality of a complete and absolute mathematics.  To be sure, there is a large measure of faith involved in the leaps necessary to get from our necessarily limited experience and semiotic capacities to any ToE.  We could take Gödel'stake Gödel's theorem to suggest that mathematical refers only to this limited space of incompleteness but I see no reason we cannot consider the existence of a complete mathematics, God's math, absolute, complete and consistent.  Consider the related [[http://en.wikipedia.org/wiki/Halting_problem|Halting problem]] which concerns the completeness of sequential computing.  With infinite time or some sort of magic parallelism in an infinite computational capacity, there is a concrete, finite answer to all instances of the halting problem where the answer is "yes, it does halt after N steps".  Nothing says the world, or God cannot do infinite calculations, if our theory claims that this is impossible, we have to say why not.
When we considers his [[http://plato.stanford.edu/entries/peirce-semiotics/#DivInt|final interpretant]], we see a description of the computation of thought and the production of true theories.  The construction of final theories by logical progression according to a rule governed process.  Pierce wouldn't have had Gödel's theorems to challenge his thinking on this, so he seems to project somethng like logical positivism in a not completely analyzed projection that the process is effective, that it will inevitably lead to a complete understanding.  It would have been interesting to see how he responds to these discoveries and the projects in fields like cognitive science to understand intelligence and thinking.  He was so far ahead of his time in so many ways, it would not be surprising if he did develop related ideas, but it also isn't a weakness in his work, just a place he didn't get to yet.
In [[Autopoiesis of Signs and Systems]], the scope of semiotics is expanded to the point it is almost a ToE in its own right.  Although Peirce make use of his semiotics in all analytic projects as described in the quote above, I can't really find any direct evidence that he makes a similar leap.  In all cases, the semiosis is happening in the mind of a thinking being, a human being as the only true example of this, and the signifying is about the systems under inquiry and the interpretants have the character of human thought.  The claim here is that the reality of signs and signifying goes much deeper, that we can model many systems better if we can consider the semiosis in terms of any (sub)systems that have internal organizations and internal states that can be interpretants in a sign process.  In Peirce, chains of interpretants (i.e. where one interpretant is the sign for further interpretation) only lead to more interpretations.  The interpreters are not just symbol processors, they are also objects in the world and the result of many interpretants won't be yet another sign, but an action that responds to the signs present.
In the end, none of this is really a limitation in Peirce, but a reflection of his focus on the history of argument and the logic of thought.  My claim is that his work on signs is a missing element in much current work.  Some of his ideas have infiltrated science through the back door.  Few attribute Peirce as the source of their thinking, but would do well to reframe their work on his foundations.  It seems like some cyberneticists and biologists have come to related insights along their own paths, but unfortunately this foundational work isn't fully integrated with later developments.  Much current thinking denies the reality of subjective experience and splits the world into the experimenter (observer) and the experiment (world) without any thought to their relationship.  In Peirce, the scientist is in the world and does his work of thinking (semiosis) in the world, about the world.
Development of the theory signs will require the inclusion of the context of interpretation.  Where does the interpretant reside?  Scientific theories are not the possession of individual minds, they contain only what can be the shared understanding of a community.  Peirce is exploring how to think correctly, how to make valid arguments and draw confident conclusions.  He isn't as much concerned with all the automatic things that happen with perception and experience, but where the semiotic approach would be very useful.  When we recognize a face, we are involking an entire evolutionary history where a person's face is their sign in social interactions.  Emotions are expressed and read from facial expressions.  Much of this is measurably independent of culture and training, which demonstrates the instinctiual nature of it.  When the perceptual system recognizes "predetor", the organism goes into evolved automated responses.  These responses can be shared across related groups of organisms, and even share the same signalling systems, specific hormones or neurotransmitters.  The point is that all of this is best analyzed as interactions based on signs, but they aren't anything like the signs and symbols of conscious thought and shared understandings.  For a T-cell in the immune system of an organism, the proteins on the outside of cells and viruses are the signals that they extract the signs of "self" or "alien" (or "self-gone-bad" as in cancer cells).  These signs are interpreted by other immune cells to mount an immune response and defend the system.