Author: Richard Brown

The Design Argument for Simulation Hypothesis

Richard Brown 3 Comments

I have always felt that the Fine-Tuning argument was the most serious of the empirical arguments for God’s existence. It is not merely that there is tuning but there is exquisite fine-tuning. Of course anthropic concerns are relevant. It is obvious that we will only be around to observe universes that have the requisite fine-tuning so maybe we shouldn’t be that surprised. Still, it seems reasonable to ask how and why the universe is fine-tuned. If it is by chance then that is amazing! Of course if there is a multiverse then we have a pretty satisfying explanation for why there is a fine-tuned universe at all. But whether there is or isn’t a multiverse is highly controversial. Overall then it seems to me that fine-tuning presents some (small, defeasible) evidence for design in nature.

Philosophers have known for some time that all design arguments suffer from the same basic flaw and that is that one needs to do a lot more work to get from ‘there is evidence for design’ to ‘God as traditionally conceived is the designer’. It is quite fun to imagine the various other possibilities, and as Hume points out, the more seriously one takes the analogy between nature and man made machines the more one starts to think that the designer is not perfect.

For my money the most compelling argument that God as traditionally conceived could not be the designer is the argument from evil (the fact that we are not photosynthetic pretty much cinches the deal for me). Of course there are responses, the necessity of moral freedom and the possibility of transworld saints to the logical problem and unknown motivations/ends to the inductive problem). But just as in the fine-tuning case I think that overall it is reasonable to conclude that the problem of evil provides defeasible evidence that God as traditionally conceived could not be the designer of the universe.

One possibility that immediately comes to mind is that the universe is designed because it is simulated. Bostrom’s simulation argument is well known and interesting but I think there is an interesting argument for the simulation hypothesis that stems from the above considerations. One way that a less than perfect being could design a universe is through simulation. To the extent that we find design inferences plausible, and to the extent that we find the problem of evil problematic, we have reason take the simulation hypothesis seriously.

Pretend Numbers

Richard Brown 9 Comments

As part of my Cosmology, Consciousness, and Computation course I have lately been thinking a lot about Zeno’s paradoxes and the ‘standard solution’ to them that we get from calculus and thinking about motion as a ‘completed infinity’, limits, etc (next week we start quantum mechanics and I am starting to wonder about how Zeno’s paradoxes might relate or not to that, but one thing at a time!). Take the function g(x)=1/x, as x approaches zero the function trends towards infinity (both positive and negative infinity depending on the direction one is going in). We put this by saying that the function’s limit is ∞ (in both directions), but ‘infinity’ is not a real number. So a different way of putting this point would be to say that there is no real number that is the limit of this function.

This got me to thinking. There may be no real number but does that mean that there is no number at all? Suppose that we introduced them on the lines of imaginary numbers. In homage to this let us call them ‘pretend numbers’. 1/0 will then be equal to some pretend number. I will use ‘Þ’ for pretend numbers, so ‘pretend one’ will be ‘Þ1‘. What is Þ1? It is the pretend number that when multiplied by real 0 will give you real 1. We can then define n/0 as follows:

where N≠0,

N⁄0=Þn,

N⁄Þn=0,

Þnx0=N.

These numbers are not on the real number line, or on the imaginary extension of that line. They are on a further pretend extension. Admittedly 0/0 is still tricky and I am not sure what to say about it but putting that to one side, do pretend numbers exist?

The Nature of Consciousness

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A couple of exciting developments today. First, over at Brains the symposium on Paul Churchland’s Matter and Consciousness 3rd edition is underway. It features commentary by Amy Kind, Pete Mandik, and William Ramsey. It will run through mid-Setember so be sure to check it out and get involved in the discussion!

In other news, today is the 5th anniversary of my dissertation defense. It’s kind of hard to believe that it has already been five years but there it is. Does this mean that I am not a junior faculty member anymore? That would be nice. Anyway, this time last year I gave the opening talk at the Graduate Center’s philosophy colloquium (see here for the post I wrote on it afterwards). Since then I have been very very busy but I have recently got back to writing up the paper which that talk was based on. It is still very much a rough draft but as usual feedback is appreciated!

Introspection, Acquaintance, and Higher-Order Representations

Richard Brown 4 Comments

Over at Brains Wayne Wu has been posting about, among other things, introspection and attention. One of the interesting things to come out of the discussion was the notion of ‘cognitive attention’ which consists in directing one’s thoughts. If this is truly a kind of attention then perhaps we can see higher-order thought and AIR theories as invoking different kinds of attention while both accept the transitivity principle. I hope to come back to this issue because I think it is time to start thinking about the connections between these two theories (and especially how we might experimentally differentiate them) but I will have to put that off. In this post I want to argue that higher-order theories are compatible with the acquaintance approach (see Brie Gertler’s comment for some links to some papers on this).

Before we begin we should note a potential confound here that may result in people talking past one another. Typically introspection is thought of as producing thoughts of the form ‘I am in pain now’ or ‘pain is instantiated in me now’ (see Brie Gertler’s paper in the link above for instance). And, of course, it is exactly these kinds of thoughts that higher-orer thought theories invoke to explain phenomenal consciousness in the first place. But of course by ‘pain’ the opponent to higher-order theories simply means what we would call ‘conscious pain’ and so we should reinterpret the above introspective claims as ‘I am in conscious pain now’ or ‘conscious pain is instantiated in me now’. They take the ‘conscious pain’ bit to actually be the phenomenal property of pain itself. A large art of the project that I have been engaged in recently has been to show that there is a way of thinking of higher-order thought theory that lets us, if we want, keep all of the benefits of the first-order theorist. On this view phenomenal consciousness consists in instantiating the right kind of higher-order representation. In particular one that attributes mental states and properties to the subject of the experience. This is what I have called the HOROR theory of phenomenal consciousness and it is metaphysically neutral.

In fact it looks like Dave endorses a non-physical version of this kind of theory in his response to Benj Hellie that he mentions in the discussion. There he says,

In effect, our phenomenology involves both a foreground awareness of redness and a background acquaintance with our awareness of redness. I think the most plausible line here is that phenomenal awareness is an acquaintance-involving relation by its very nature: in virtue of the nature of awareness, to be aware of x entails being acquainted with one’s awareness of x

and in the footnote he continues,

This is a relative of higher-order representation theories of consciousness, and especially of the Brentano-style self-representational views of consciousness that have become popular in recent years (see e.g. Kriegel and Williford 20xx). Some differences: the background awareness should be understood as Russellian instance-acquaintance rather than as a standard form of representation (this immediately avoids all objections from higher-order misrepresentation as well as from oversophistication), and the view does not lend any support to reductive views of consciousness. The awareness relation that the view appeals to is irreducibly a phenomenal relation. Of course someone might attempt to turn this into a reductive theory by identifying the awareness relation by a relation understood in functional terms, say. But just as in the case of first-order representationalism (discussed in chapter 8 of TCC), this move requires an additional and independent functionalism about the phenomenal, a view that is no more plausible here than elsewhere, and which leads to an explanatory gap that is as wide as ever.

Now here he is talking about phenomenal consciousness and not introspection and I am not sure whether the view is that this entire complex gets embedded in an introspective judgement or whether introspecting involves the background awareness coming to the foreground but either way is compatible with the HOROR theory. So, consider the way that Gertler lays out the Acquaintance Approach. She sums it up in the following three theses,

[Acquaintance Approach] Some introspective knowledge consists in judgments that
(1) are directly tied to their truthmakers;
(2) depend, for their justification, only on the subject’s conscious states at the time of the judgment; and
(3) are more strongly justified than any empirical judgments that do not meet conditions (1) and (2).

To be ‘directly tied’ on her account involves demonstrative attention and though that is not a requirement of the view I am happy enough with it. So, on the HOROR theory what will be required is that we deploy demonstrative attention to the proper higher-order representation and is compatible with (1). The term ‘conscious state’ in (2) should be interpreted as the appropriate higher-order representation and so the claim is just that some introspective judgements are justified solely by certain higher-order representations, which is compatible with HOROR theory and because of (1) and (2) these judgments are more strongly justified than other that don’t meet (1) and (2).

So not only is the HOROR theory compatible with introspective acquaintance it is also compatible with ‘same-order’ acquaintance.

The Argument from Photosynthesis

Richard Brown 10 Comments

Though I very much enjoy the taste of food I have always thought that the actual act of eating is very primitive and mildly repulsive. Described abstractly eating involves the mastication of organic substances which are then broken down in digestive acids to produce sugars that are then used to fuel metabolic activity. The mastication process involves mechanically breaking down the organic substances and mixing them with saliva and in the process the organic substance is rubbed over the taste buds in our tongues and released gasses interact with the olfactory receptors via the nasal passages.

Now compare this process with the process of photosynthesis. In photosynthesis light energy is converted to sugar with oxygen as a waste product. This process is more elegant and much cleaner than eating (eating/digestion has excrement as its waste product versus oxygen for photosynthesis). However, the naturally evolved photosynthesis we find here on Earth is not very efficient (it captures somewhere in the area of 3-6% of the energy available in sunlight) and as a result we do not find vertebrates that use photosynthesis, though there is recent evidence that salamanders have photosynthetic cells and we might have an invertebrate or two that uses it.

So is it possible that humans might be able to someday use photosynthesis? Some have recently argued that we have a moral obligation to get rid of meat eating animals and replace them with herbivores. But herbivores are carnivores as well in the strict sense. While I don’t think that eating plants is as morally problematic as eating animals I still think it would be nice to free ourselves from eating all together. At least I would like to be able to do so for myself. So might I ever be able to? As it stands it looks like it would be difficult to do because extant photosynthetic processes are relatively inefficient and so even if we did successfully integrate photosynthetic cells over the entire area of our skin we would need to be exposed to dangerous amounts of radiation to meet our energy demands. Still it is certainly possible to improve photosynthesis and in fact scientists are working on it now and so while it doesn’t seem likely to happen anytime soon it certainly seems possible that there could be photosynthetic humans at some point in the future. We might not be able to quit eating all together, we might still do it for pleasurable experiences of taste etc or we might have to eat some limited amount to supplement the energy from photosynthetic process, but still it is not physically impossible that this could happen and it does seem morally and aesthetically preferable to what we have now.

Aside from this bioethical issue I think this raises issues for those who think that there is evidence for design in the human body and it also puts new light on the problem of evil. Certainly if it is conceivable that we could produce a photosynthetic animal, human or not, then it must be possible for God to have created such a creature. But if so then why aren’t we photosynthetic? I mean God could have made it so that we run on solar energy, and even had the pleasurable taste and ‘mouthfeel’ experiences that makes eating enjoyable (perhaps different wavelengths and/or frequencies of light would produce different gustatory experiences). Doing this 1.) seems like a much better design. It is simpler and more elegant than eating is and 2.) seems much more humane. The sheer amount of suffering produced by eating meat over the course of evolution is nearly unimaginable. It seems to me that this argument from photosynthesis is as decisive as one can get in this area and I wonder why it has not received more attention…or maybe it has and I just haven’t found it yet?

Consciousness and its Place in Physical Reality

Richard Brown 1 Comment

In the Spring 2013 semester I initiated a new course at LaGuardia that had the theme Cosmology, Consciousness, and Computation. The basic idea was to explore issues relating to physicalism. Intuitively, physicalism is the view that everything that exists is physical but what is the nature of physical reality? The idea I had was to have the couse divided into three sections. In the first section we would do a conceptual physics course talking about the development of physics from the ancient world to the present day. Then we would turn to issues about consciousness and mind and where they fit in the physical picture we have so far developed. After that we turn to issues about computation; Is the universe computable? Or perhaps does it instantiate some computation? Is consciousness computational? Are we living in a simulation? Is the universe a hologram?

In my quest to have low cost book options for students I have adopted the Terminator book I co-edited and have supplemented that with readings from the Stanford Encyclopedia of Philosophy and other online material. The reception to the course was very good and I am really looking forward to doing it a second time in Fall 2013. I have updated the syllabus and, as usual, would welcome any suggestions or feedback.

Week I: Introduction
• →Richard Brown on What is Philosophy? – http://www.youtube.com/watch?v=ySS0bNeWZOg

Week 2: Early Attempts to Understand Mind and Physical Reality
• →Terminator Ch 10: The Nature of Time and the Universe
• Time- http://plato.stanford.edu/entries/time/
• Richard Brown on Pre-Socratic Philosophy- http://www.youtube.com/watch?v=zfLgRotdcKI&list=PLfR0qhtOKP6eYkUoW7DH8qdjwEyQnsbPJ&index=2
• Pre-Socratic Philosophy- http://plato.stanford.edu/entries/presocratics/
• Ancient Theories of the Soul- http://plato.stanford.edu/entries/ancient-soul/
• Parmenides- http://plato.stanford.edu/entries/parmenides/
• Zeno’s Paradoxes- http://plato.stanford.edu/entries/paradox-zeno/
• Ancient Atomism- http://plato.stanford.edu/entries/atomism-ancient/
• Democritus- http://plato.stanford.edu/entries/democritus/
• Intentionality in Ancient Philosophy- http://plato.stanford.edu/entries/intentionality-ancient/
• Time- http://plato.stanford.edu/entries/time/

Week 3: Modern Philosophy and Modern Science
• →Terminator Ch 2 –Animal consciousness, Descartes, and Emotions
• Descartes’ Physics- http://plato.stanford.edu/entries/descartes-physics/
• Descartes’ Epistemology- http://plato.stanford.edu/entries/descartes-epistemology/
• Descartes’ Theory of Ideas- http://plato.stanford.edu/entries/descartes-ideas/
• Other Minds- http://plato.stanford.edu/entries/other-minds/
• Animal Consciousness- http://plato.stanford.edu/entries/consciousness-animal/
• Locke on Real Essence- http://plato.stanford.edu/entries/real-essence/
• Locke’s Philosophy of Science- http://plato.stanford.edu/entries/locke-philosophy-science/
• Newton’s Philosophy- http://plato.stanford.edu/entries/newton-philosophy/
• Isaac Newton- http://plato.stanford.edu/entries/newton/
• Newton’s Views on Space, Time, and Motion- http://plato.stanford.edu/entries/newton-stm/
• The Contents of Perception- http://plato.stanford.edu/entries/perception-contents/
• The Problem of Perception- http://plato.stanford.edu/entries/perception-problem/

Week 4: Relativity Physics
• →Terminator Ch 8: paradoxes of time travel
• Einstein for Everyone: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/index.html
• Brian Greene’s The Elegant Universe on NOVA- http://www.pbs.org/wgbh/nova/physics/elegant-universe.html#elegant-universe-einstein.html
• Time Travel and Modern Physics- http://plato.stanford.edu/entries/time-travel-phys/
• Time Machines- http://plato.stanford.edu/entries/time-machine/
• The Equivalence of Mass and Energy- http://plato.stanford.edu/entries/equivME/
• The Hole Argument- http://plato.stanford.edu/entries/spacetime-holearg/
• David Lewis’ The Paradoxes of Time Travel- http://www.csus.edu/indiv/m/merlinos/Paradoxes%20of%20Time%20Travel.pdf

Week 5: Quantum Mechanics
• Brian Greene’s The Fabric of the Cosmos on NOVA- http://www.pbs.org/wgbh/nova/physics/fabric-of-cosmos.html
• Copenhagen Interpretation of Quantum Mechanics: http://plato.stanford.edu/entries/qm-copenhagen/
• Many Worlds Interpretation of Quantum Mechanics- http://plato.stanford.edu/entries/qm-manyworlds/
• The Uncertainty Principle: http://plato.stanford.edu/entries/qt-uncertainty/
• Quantum Entanglement and Information: http://plato.stanford.edu/entries/qt-entangle/
• The Einstein-Podolsky-Rosen Argument in Quantum Theory- http://plato.stanford.edu/entries/qt-epr/
• Measurement in Quantum Theory: http://plato.stanford.edu/entries/qt-measurement/
• Quantum Mechanics- http://plato.stanford.edu/entries/qm/
• Richard Feynman on Double Slit Experiment- http://www.youtube.com/watch?v=hUJfjRoxCbk&list=PLfR0qhtOKP6eYkUoW7DH8qdjwEyQnsbPJ&index=3

Week 6: The Nature and Origin of the Universe
• →The Scale of the Universe- http://htwins.net/scale2/
• Hubble Deep Field: http://hubblesite.org/hubble_discoveries/hubble_deep_field/
• Cosmology and Theology- http://plato.stanford.edu/entries/cosmology-theology/
• Atheism and Agnosticism- http://plato.stanford.edu/entries/atheism-agnosticism/
• Religion and Science- http://plato.stanford.edu/entries/religion-science/
• Teleological Arguments for God’s Existence- http://plato.stanford.edu/entries/teleological-arguments/
• Cosmological Argument- http://plato.stanford.edu/entries/cosmological-argument/
• The Possible Parallel Universe of Dark Matter- http://discovermagazine.com/2013/julyaug/21-the-possible-parallel-universe-of-dark-matter#.UhDhPRbtaz6

Week 7: The Possibility of Life Beyond Earth
• Life- http://plato.stanford.edu/entries/life/
• Molecular Biology- http://plato.stanford.edu/entries/molecular-biology/
• Finding Life Beyond Earth- http://www.youtube.com/watch?v=FVzmGaGCqP8

Week 8: Consciousness in the Physical World?
• Consciousness- http://plato.stanford.edu/entries/consciousness/
• Representational Theories of Consciousness- http://plato.stanford.edu/entries/consciousness-representational/
• Functionalism- http://plato.stanford.edu/entries/functionalism/
• The Mind/Brain Identity Theory- http://plato.stanford.edu/entries/mind-identity/
• Dualism- http://plato.stanford.edu/entries/dualism/
• Zombies- http://plato.stanford.edu/entries/zombies/

Week 9: Beyond Physicalism?
• Eliminative Materialism- http://plato.stanford.edu/entries/materialism-eliminative/
• Folk Psychology as a Theory- http://plato.stanford.edu/entries/folkpsych-theory/
• The Philosophy of Neuroscience- http://plato.stanford.edu/entries/neuroscience/
• Panpsychism- http://plato.stanford.edu/entries/panpsychism/

Week 10: Transhumanism
• →Terminator Ch 4: Extended Mind, Transhumanism
• A History of Transhumanist Thought- http://www.fhi.ox.ac.uk/documents/journal_publications/al/nick_bostrom
• Biohackers: A Journey into Cyborg America- http://www.youtube.com/watch?v=K0WIgU7LRcI&list=PLfR0qhtOKP6eYkUoW7DH8qdjwEyQnsbPJ&index=48
• Tim Cannon on Potential Benefits of Sensory Augmentation- http://www.youtube.com/watch?v=KZ1KCpSL51E&list=PLfR0qhtOKP6eYkUoW7DH8qdjwEyQnsbPJ&index=46
• Aubrey de Grey on Defeating Aging- http://www.youtube.com/watch?v=d1FBJGl2c-Y&list=PLfR0qhtOKP6eYkUoW7DH8qdjwEyQnsbPJ&index=17

Week 11: A.I. and The Singularity
• →Terminator Ch 1: A.I., Chinese Room, Transhumanism
• →Terminator Ch 3: Why always with the killing?
• The Chinese Room Argument- http://plato.stanford.edu/entries/chinese-room/
• The Turing Test- http://plato.stanford.edu/entries/turing-test/
• The Frame Problem- http://plato.stanford.edu/entries/frame-problem/
• David Chalmers’ The Singularity: A Philosophical Analysis- http://consc.net/papers/singularity.pdf
• David Chalmers on Simulation and Singularity- http://www.youtube.com/watch?v=FafHdF_D8gA&list=PLfR0qhtOKP6eYkUoW7DH8qdjwEyQnsbPJ&index=13

Week 12: The Simulation Argument & The Holographic Hypothesis
• Nick Bostrom’s Simulation Argument Website- http://www.simulation-argument.com
• Nick Bostrom on The Simulation Argument- http://www.youtube.com/watch?v=nnl6nY8YKHs&list=PLfR0qhtOKP6eYkUoW7DH8qdjwEyQnsbPJ&index=24
• David Chalmers’ The Matrix as Metaphysics- http://consc.net/papers/matrix.html
• Leonard Susskind on The World as a Hologram- http://www.youtube.com/watch?v=2DIl3Hfh9tY&list=PLfR0qhtOKP6eYkUoW7DH8qdjwEyQnsbPJ&index=16

The Phenomenology of HOT

Richard Brown 1 Comment

I am happy to announce that Pete Mandik and I have finished our co-authored paper on higher-order thought theories of consciousness and cognitive phenomenology, which is forthcoming in the issue of Philosophical Topics that features participants from the 4th Online Consciousness Conference. Check it out!

Consciousness Without First-Order Representations

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I am getting ready to head out to San Diego for the Association for the Scientific Study of Consciousness 17th Annual meeting. I have organized a symposium on the Role of the Prefrontal Cortex in Conscious Experience which will feature talks by Rafi Malach, Joe Levine, Doby Rahnev, and me! A rehearsal of my talk is below. As usual any feedback appreciated.

Also relevant are the following papers:

1.(Lau & Brown) The Emperor’s New Phenomenology? The Empirical Case for Conscious Experience without First-Order Representations

2. (Brown 2012) The Brain and its States

The ASSC Students have also set up the following online debate forum: http://theasscforum.blogspot.com/2013/06/symposium-1-prefrontal-cortex.html

A longer video explaining the Rahnev results can be found here: http://www.youtube.com/watch?v=_gQYdGRbkpE

Lot’s of ways to get involved in the discussion!

[cross-posted at Brains]

Recent Events

Richard Brown Leave a comment

Well, the semester at LaGuardia is finally coming to a close (our schedule is out of step with the rest of CUNY). A lot has been going on and I have barely had time to do anything but since today is our reading day and I have a brief break before final exams come in, I thought I would quickly talk about what has been going on.

My new course, Cosmology, Consciousness, and Computation was a huge success and the students really seemed to enjoy the chance to take these kinds of questions seriously. The basic idea behind the course is to explore issues related to physicalism but after a grounding in the actual physics. My experiment to use the Stanford Encyclopedia as a primary text seemed to work ok as well. Some of the readings are fairly technical but I gave students the choice of which to read and which to write a one page summary/reaction to. They also seemed to like the Terminator book, which was nice. This is the first time I have used it in a class. I am toying with the idea of maybe recording the lectures for this course over the summer as I prepare to teach it again next semester (but I am also teaching philosophy of religion and ethics over the summer and I am tempted to record my philosophy of religion as well…they do overlap a bit so maybe I’ll do both!). For those interested, here is the syllabus. As with any new class I expect to update a lot of it in light of what happened this semester and any feedback would be appreciated.

All of that will have to wait until later in July, though, since I am currently getting ready for my trip to San Diego for the 17th meeting of the Association for the Scientific Study of Consciousness (ASSC). This year I have organized a symposium on the Role of the Prefrontal Cortex in Conscious Experience. The speakers are Rafi Malach, Joe Levine, Doby Rahnev, and myself. I am really looking forward to it, as well as to the rest of the program! I am hoping to post a video of my talk in the nearish future.

I have also been working on a new paper, which came out of discussion at the 5th Online Consciousness Conference. It is entitled Consciousness is (Probably) a Biological Phenomenon. Those who know me know that I am attracted to an identity theory when it comes to consciousness and that I harbor the suspicion that consciousness is a uniquely biological phenomenon. This paper is my first attempt to spell out an answer to Chalmers’ fading and dancing qualia arguments using empirical results (in particular the partial report results that have figured in the overflow debate (see here and here)). It is extremely drafty (I have been working on it an hour here and hour there for the last few weeks) and any feedback would be much appreciated.

In addition to all of this I have just returned from my trip to the Omaha Kripke Conference (during which I was also on my first dissertation committee at the Grad Center, which was very much fun but then I also had to read and think about a dissertation!), which was a really rewarding experience. Omaha is a wonderful town and the conference itself was excellent, if exhausting. Three days of excellent papers and excellent discussion, and it was very cool to see Saul so active and engaging with the material. Unfortunately, due to bad weather, he came late and so he missed my talk but there was none the less a lot of very helpful discussion. The main objection was Dan Shargel’s ‘hierarchy objection’ which he presented at Tucson last year (the basic idea is that we can move the argument up to the level of appearance and imagine that we have that appearance without the neural state, etc). I have got to get better at explaining what my answer to that objection is. After the discussion at the conference I have come to think that the main problem is that we are using ‘how pain appears to me’ as a way to pick out two different states, one a psychological state and the other a neural state. On the one hand we use it to pick out the pain sensations, that is the first-order sensing of bodily damage. But we can also use it to pick out the neural state that the appearance is identical to (note: not the neural state that the sensation is identical to, but the neural state that is identical to the awful painfulness appearance. We can use the appearance property as a way to pick out that state itself). It is in that second sense that we avoid the charge of regress. This takes some spelling out to make sense of it and I am hoping to write something more detailed on it in the nearish future (hopefully before I head out to the ASSC).

During and after one of the other sessions I had the chance to talk to Saul about his 1963 paper Semantical Considerations on Modal Logic, which I have discussed previously on the blog. When I suggested that it was a cost to one’s theory to give up logical constants in your quantified modal logic he insisted that it was not. This was because for any sentence with a logical constant in it we could translate it into a sentence without the constant without loss of meaning using Quine’s trick of inventing a predicate. This led me to wonder whether this made it the case that we could reformulate the bothersome proofs using translated sentences. At the time I wasn’t able to come with a way to do this but once I got home I thought about it a bit more and came up with the following.

In the original reductio we used this sentences ☐∃x(x=k), where this is read as ‘there exists an x such that x is identical to Saul Kripke’. How would we translate this sentence to get rid of the constant? We would replace the constant with a predicate, say ‘K’ (‘the Kripisizer’) and thus we would get ☐∃x(x=Ky) but this has a free variable in it so we would have to take it as asserting the ‘closed’ version, so we get ∀y☐∃x(x=Ky). We can then proceed to prove this in the same way as before using a reductio

1. ~∀y☐∃x(x=Ky) -assumption for reductio
2. ∃y~☐∃x(x=Ky) -1, quantifier exchange
3. ∃y◊~∃x(x=Ky) -2, definition of ☐
4. ∃y◊∀x~(x=Ky) -3, quantifier exchange
5. ∃y◊~(Ky=Ky) -Universal instantiation on 4
6. ∀y☐(Ky=Ky) -instance of axiom of identity
7. ~∃y~☐(Ky=Ky) -6, quantifier exchange
8. ~∃y◊~(Ky=Ky) -7, definition of ☐
9. ∃y◊~(Ky=Ky) & ~∃y◊~(Ky=Ky) -4,8 -conjunction introduction
10. ∀y☐∃x(x=Ky) -1-9 reduction

I think the main issue with this reformulated proof is line 5 when I use ‘Ky’ as an instance of x in 4. It seems to me that this move should be allowed, though. This is because part of the whole point of the 1963 paper was that we could block these kinds of proofs and still keep our traditional quantification theory. So we should be able to use UI, but if we are not allowed the use of constants then we will have to use predicates, which is what I did. Also, the variable in 5 is not free and is bound by the existential quantifier. So all in all I think this reformulated proof works but I really haven’t had the time to think about it very carefully.

Well that is enough for now…time to head over to Brains to read some of the commentaries in the Symposium on Louise Richardson’s “Flavor, Taste and Smell”.

Pain, Painfulness, and Kripke’s Modal Argument

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I am getting ready to head out to Omaha for a conference on the work of Saul Kripke at the University of Nebraska Omaha. My talk is on Monday the 20 but for those that can’t make it I have recorded the below rehearsal. It should be a really fun conference. I have never been to the ‘midwest’ before so I am looking forward to finally setting foot in a flyover state. As for the talk, the content is stuff people familiar with my work might recognize but I think I am getting better at expressing it. As usual, any comments or feedback is welcome.