# Hegel and Infinite Series

Connected to the last post about comprehending how 1=0.99(9), here is what Hegel (§ 561 , The Science of Logic read at own risk) has to say about the issue of infinite series (in his own specific way):

Thus the usually so-called sum, the 2/7 or 1/(1 – a) is in fact a ratio; and this so-called finite expression is the truly infinite expression. The infinite series, on the other hand, is in truth a sum; its purpose is to represent in the form of a sum what is in itself a ratio, and the existing terms of the series are not terms of a ratio but of an aggregate.
Furthermore, the series is in fact the finite expression; for it is the incomplete aggregate and remains essentially deficient. According to what is really present in it, it is a specific quantum, but at the same time it is less than what it ought to be; and then, too, what it lacks is itself a specific quantum; this missing part is in fact that which is called infinite in the series, from the merely formal point of view that it is something lacking, a non-being; with respect to its content it is a finite quantum. Only what is actually present in the series, plus what is lacking, together constitute the amount of the fraction, the specific quantum which the series also ought to be but is not capable of being. The word infinite, even as used in infinite series, is commonly fancied to be something lofty and exalted; this is a kind of superstition, the superstition of the understanding; we have seen how, on the contrary, it indicates only a deficiency.

Let me try to explain previous quote with an example:

We say that 1+a+a2+…=1/(1-a) for a<1. But how to understand that addition of infinite number of terms? We can add as much terms as we like, but the sum will never be equal to the ratio. What does this equation say then?

If we subtract 1 from the  ratio (which is supposed to be sum of the infinite series) we have:
1/(1-a) – 1 = (1-1+a)/(1-a) = a·[1/(1-a)]  or by moving the 1 to the right side…
1/(1-a) = 1 + a·[1/(1-a)]

So, now we got to a recursive formula of the form
A = 1 + a·A  , where A is 1/(1-a)

And by iterating we get:
A = 1 + a·A
, then by changing second A with the whole right side we get…
A = 1 + a·(1 + a·A) = 1 + a + a2·A
, we change again, and we get…
A = 1 + a + a2·(1 + a·A) = 1 + a + a2 + a3·A
and so on, and so on ad infinitum.

We see that the sequence in the series can be generated from the ratio by recursive process, but it can never end, we can generate as much terms as we like, there will always be a certain left over (an·A), which also needs to be expressed through new terms.

So Hegel is saying that while we can represent what is specified by the ratio through infinite series, the series will be a “deficient” representation of what is clearly contained in the ratio itself.

Technorati Tags: , , ,

# Comprehending 1=0.99(9)

On first look it is weird when they tell you that 1 equals 0.999(9) where 9 is repeating.
Or, which is the same thing – that 3 * 0.333(3) , equals both 0.999(9) and 1.

I know I searched once on web for the explanation of why is it so – an explanation I could easily grasp/comprehend,  as intuitively it seems there is something wrong – our intuition tells us – “As much nines are repeating there, they won’t add-up to 1”. All I found is proofs that it is so, but from the philosophical point (well from common-sense point even) we can’t be happy (me at least) just with symbolic proofs, we need to comprehend the equality. So here goes the easy explanation…

When we have integer, let’s say four, we can say that we have a quantum of four things, a quantum which can be divided to four ones. Say you have four apples. You can divide them to four people – each person will get one apple.
Decimal numbers can be comprehended in similar way, just that if we add decimal fractions, we need to imagine that even the ones are further dividable – that they are made from parts. We need to imagine each one as made from ten parts, and each of those ten parts as made from even smaller ten parts, and so on…

In such way 1 would mean the item, 0.1 would mean one of the ten parts of the item (1), 0.01 would mean one of the ten part of the 0.1 part, and so on…

Now, let’s try to divide one item to three people. Because the item consist of ten parts, we will give three parts to each person, and we will be left with one of those ten parts that we need to divide:

1/3= 0.3 + 0.1/3

This 0.1 is again consisting of ten parts and we will likewise divide it between those three people – three parts to each, but we will be left again with one (now ten times smaller) part to divide further…

1/3= 0.3 + 0.03 + 0.01/3 , and dividing further…
1/3 = 0.3 + 0.03 + 0.003 + 0.001/3 , and so on..

Or if we sum the parts which are already divided we get

1/3 = 0.3 + 0.1/3
1/3 = 0.33 + 0.01/3
1/3 = 0.333 + 0.001/3 etc…

We see that this adding of cipher 3 to infinity, is not consequence of the part which is already divided, but of the part (left-over) which is left to be divided. As many threes are generated there will be still a part to be divided which would generate new threes. We can now say the following… the infinity in the never-ending repeating cipher 3, is not about the infinity of how much ciphers 3 are generated, but about the impossibility to finish the dividing process.

So, it is the wrong comprehension of what 0.333(3) means, that is causing the intuition against 1 being equal to 0.333(3) * 3. If we imagine 0.33(3) vaguely as some never ending string of cipher 3 – a decimal number in decimal notation that just has infinity of ciphers, our intuition tells you that however far you multiply with 3, you will only get 0.999(9), and however far you go, it won’t be 1.
But comprehending 0.33(3) in that way, is ignoring the reason of that infinity, for example in the given process – ignoring the left over which is still to be divided that causes us to add new and new ciphers 3, and which will never end. So, we need to see repeating cipher as a new notation added to the decimal system, which tell us about that impossibility to finish the description in the normal decimal notation, and not a shortcut for normal decimal notation, in which we could write the cipher 3 infinite number of times.

By the way we can divide 1 in similar way to get 0.99(9) directly…
We divide 10 of the parts (0.1) to 10 people, so that we divide 9 or those parts to 10 people, and leave one more to divide; and that we repeat that:
1/10=0.9/10+0.1/10=0.9/10 + 0.09/10 + 0.01/10, etc…
We will get 1 = 0.99(9), again this repeating 9 signifying the impossibility to finish the process.

* It isn’t really necessary for each part consist of 10 parts. What we need is just that each part can be divided to 10 parts, and if it can, we can treat it as consisting of 10 parts. For example if we don’t have quantum, but a continuous magnitude, it can be divided in any number of parts we want, hence to 10 also.

# Are things and states of affairs ruled by laws of logic?

I posted a comment at Postmodernism and Reality post at withallyourmind.net.
As I what said there connects nicely to previous post Existence and Transcendence, I will also post the comment here:

If we imagine reality as a state of affairs (or even “dynamics of affairs”), really one can’t see what it would mean for the rules of logic to be applied to it. State of affairs is merely that – state of affairs.
Laws of logic on other side are something that is connected to propositions, and propositions consist of objective meanings which while might be about the real world, are made possible only for a conscious being which first abstracts – breaks apart the state of affairs to some entities (which of course are not real – the entities can’t exist as abstract entities), and then tries to synthesize back the “situation” by putting those abstractions in some kind of objective relations or assigns objective properties to those entities.

So, it is not that the state of affairs somehow is “ruled” by the rules of logic. It is that if we imagine (factual) state (or dynamics) of affairs, it can’t be that both proposition A, and its negation for example can be true about it.

–end of what I commented there–

The rules and propositions are always about abstractions. The abstractions are based on the existing/concrete, but existing/concrete doesn’t exist qua abstraction. And because abstractions are based on existing/concrete, their truth comes from the existing/concrete they cover (actually or potentially). For more discussion of how abstractions can be related actually or potentially, and still be based on concrete, see the posts on the Post Threads page, under “Abstraction and Given” column.

This post talks about logical laws, but I believe that it is the same with all laws which can be based on abstractions – like mathematical laws. For example there might be state of affairs, and we abstract from it that it is “three apples”. But on the same state of affairs we can abstract two apples and one other apple. But that doesn’t mean that things and states (dynamic) of affairs are ruled by laws of math (e.g If you add one apple to two apples you will get three apples).

I would go as far as to say that I believe that physical laws (as necessary and transcendental) to be of same nature, but I won’t :)

# Are hedgehogs small spiny animals?

Consider those four sentences:

1. Hedgehogs don’t have spines.

There are (at least) three different things which can be meant by this sentence. One possible meaning is that hedgehogs were small animals which had spines, but which lost their spines. If someone is to say to me -Look, hedgehogs don’t have spines! it is most likely that she is using the sentence in this meaning.
Also, this sentence can mean that what we thought were spines, were in fact something else; it might be that, for example, biologically spines have some precise definition, and what we call “spines” in hedgehogs don’t fall into that category.
The third meaning is the one in which I want to consider the sentence, where the person uttering it is claiming that the hedgehogs are and were animals which don’t have spines.

2. Hedgehogs are enormous.

As in the previous case, there are at least three things which can be meant by this sentence. One is where the sentence is meant to inform us that hedgehogs have grown enormous. Or, someone can consider the issue of size of the hedgehogs relatively to the size of the atoms for example, and utter this sentence in that meaning. The third kind of meaning of this sentence is where the writer claims that hedgehogs are and were enormous animals. I take it here in this third meaning.

3. Hedgehogs are not animals, but like rabbits (in Putnam, Is Semantic Possible) they are robots controlled by Martians.

4. Hedgehogs are not material things, but they are massive hallucination induced by Martians.

First notice that all of those sentences speak of the same thing – they speak about hedgehogs. The sentences assume that people who read them will understand what is meant by that word and that by those sentences it is posited that those same things (hedgehogs) happen to be respectively: without spines; enormous; robots controlled by Martians; or massive hallucination induced by Martians.

Now let’s consider how we, the readers of those sentences, can understand them, if we are supposed to believe that the sentences are true. I will in this post analyze the first two sentences, and analyze the later ones, well… later.

In the first case, if someone utters the sentence “Hedgehogs don’t have spines” there are two possibilities me as listener I can conceive of (ignoring the alternative meanings which were discussed): either it can mean that what I thought were hedgehogs are not called hedgehogs; or that the person is using word “hedgehogs” to refer to some other things, which are not hedgehogs.
And the second sentence brings the same possibilities. If someone is to say to me that “Hedgehogs are enormous”, it is either that what I thought were hedgehogs are not in fact hedgehogs, or that person is using the word “hedgehogs” to refer to different things.

So, in the sentences (1) and (2), we see that one can acknowledge actually just one possibility, and that is that the person is not talking about things we think about when we mention hedgehogs. Or, from other point of view we can formulate this as a principle:
There can be sentences about specific word, that show clearly that the person which claims that those sentences are true, is not talking about the same concept we mean by that word.
This gives us possibility to notice a misunderstanding.
Consider this conversation:

A: My mother cooked two hedgehogs for dinner today, and whole family had very good dinner.
B: Wait, your mother cooked hedgehogs? Are we talking about same animals, the small spiny ones?
A: Oh, no, no… Hedgehogs… You know those big, flying animals.

So, let’s go back a little, and try to check once more what happens here.
A person utters the sentence “hedgehogs don’t have spines”.
We believe that person is saying the truth and we try to make sense of the sentence.
With additional questions we figure out that the person doesn’t mean to say that hedgehogs have lost their spines, or that things on hedgehogs that we call spines don’t satisfy some biological definition of spines.
After the person negatively answers those attempts from our side to make alternative sense of the sentence, we are left with not much choice. We have to conclude that the person is not talking about the animals we call hedgehogs. By the word “hedgehogs” the person is referring to different concept.

If “doesn’t have spines” (in its specific meaning) is enough to figure out that the person is not talking about our concept of hedgehogs, we should be inclined to suppose that “having spines” belongs to the core of the “hedgehogs” concept . But on the other side, it is easy to give examples contrary to that conclusion. We can imagine a hedgehog without spines. In fact hedgehogs can loose their spines when under extreme stress or sickness. Enormous hedgehogs are also imaginable, like in Monty Python’s sketch about Piranha Brothers:

Interviewer: Was there anything unusual about him?
Gloria: I should say not. Except, that Dinsdale was convinced that he was being watched by a giant hedgehog whom he referred to as ‘Spiny Norman’.
Interviewer: How big was Norman supposed to be?
Gloria: Normally Spiny Norman was wont to be about twelve feet from snout to tail, but when Dinsdale was depressed Norman could be anything up to eight hundred yards long. When Norman was about, Dinsdale would go very quiet and start wobbling and his nose would swell up and his teeth would move about.”

But then, if something which is a hedgehog doesn’t have to be spiny or small, how can we know that the person from sentences (1) and (2) isn’t talking about what we mean by ‘hedgehog’, but rather something else entirely?

There is one distinction that should be noted, which might resolve this apparent contradiction… In the “classical theory” it is supposed that concepts can be defined through a set of necessary and sufficient attributes, in such way that everything that falls under the concept will have those necessary attributes.

But here the difference is that we are not talking about the examplars of the concepts, and the attributes are not talked about as connected to the singular case, or “a hedgehog”, but to the plural – “hedgehogs”; We are considering hedgehogs collectively.

And when we think of it, it is not very hard to note that there needs to be plurality of things for general terms to be held at all. If there was just one thing, then using a general term wouldn’t make any sense, so we could use the proper name instead.
So, we can say that the plurality is central for the meaning of general terms. It is about “hedgehogs”. “A hedgehog” is just any of them.
Also plurality by itself isn’t enough, this multitude of things needs to have something in common, they need to be recognizable as have something in common. If we can’t find anything common for a set of things, there can be no reason to see them as falling in into same concept.

I will analyze the next two sentences in the next post…

# Online videos of philosophical lectures

|Updated on May.03rd 2008|

Bored by movies, and don’t feel like reading a book? You can watch philosophical and other interesting videos on web.

 Young Philosophers Podcast And Few Older Ones
1. A Priori Skepticism – James Beebe
2. The Fine Tuning Argument for the Existence of God – James Beebe
3. Is Morality Real, or Do We Make It Up? – Joshua Thurow

Also…

1. Debbie in the comments pointed to this course on Death by Shelly Kagan
2. And a link to a Gresham College Lectures and Events, which Tjh recommended in the comments long time ago, but I never got to pick out the philosophically interesting ones. There are many lectures there on all kind of topics.
 Few Lectures Added on 24 March 2008
1. Flame0430 on YouTube has uploaded a bunch of very interesting videos. They include interview with John Searle on Wittgenstein, interview with Ayer on Frege and Russell, and interviews with Quine and Searle about their work. It seems that there will be more interviews coming. (via Methods of Projection)
2. On an episode from UC Berkley’s “Conversations with History”, Harry Kreisler interviews Hubert Dreyfus about Heidegger, M.Ponty, AI, and such things. Very interesting stuff. (via Continental Philosophy)
3. If you didn’t have enough of Searle, there is also his talk on Authors@Google series, where he talks about his book “Freedom and Neurobiology: Reflections on Free Will, Language, and Political Power.”, and explains in what way he thinks free will might be related to Quantum Mechanics. (BTW, I just noticed that there is one by Pinker from the same series, haven’t watched that one. It says that he talks about his book “The stuff of thought”)
4. Kit Fine on approach to philosophy on YouTube: here and here (via Plurality of Words)

 Pufendorf Lectures
• 2004 – David Armstrong: The Scope and Limits of Human Knowledge, In Defence of the Cognitivist Theory of Perception, Four Disputes about Properties, Predication and Necessity
• 2005 – Philip Pettit: The Rule of the Populace, The Rule of the People, The Rule of the Public, Integrating the Dimensions
• 2006 – John R. Searle: Consciousness, What is language?, The logical structure of self, Rationality and society
• 2007 – Patricia Churchland: What is Neurophilosophy; A perspective on Self, Agency and Free Will; Brain-based Values

 University of Michigan ‘Saturday Morning Physics’ lectures

Some of those are philosophically interesting:

1. The Philosophy of Time -Thomas Hofweber
2. The Arrow of Time in Physics -Tim McKay
3. , and maybe also:

4. The Future of Particle Physics – Dan Amidei

Or check the whole collection for more.

 TED Talks – How the Mind Works

TED talks site hosts bunch of videos related to philosophy of mind, featuring Dennet, Pinker, Ramachandran, Kurzweil and others. (ht: Readings in Analytic Philosophy)

 Other 07 Nov. update videos
1. Debate concerning the neural correlates of consciousness between Susan Greenfield and Cristof Koch (ht: Brain Hammer)
2. Stephen Stich: Moral Theory Meets Cognitive Science: How the Cognitive Science Can Transform Traditional Debates (ht: Experimental Philosophy)
3. Interview with Oliver Sacks
4. And another one with David Chalmers (ht: Neurophilosophy&Sociocognition for both)
5. Second Online Philosophy Conference had two keynote addresses by Jeff McMahan and Ernest Sosa, which are available for watching on the 2nd OLPC site

 Being No One

You can check the lecture “Being No One: Consciousness, The Phenomenal Self, and the First-Person Perspective” by Thomas Metzinger (1hr) presented at UC Berkeley.
If you are interested in that video, check PSYCHE symposia on Thomas Metzinger’s book Being No One. (via Fragments of Consciousness)

 Michael Tomasello

Great lectures by Tomasello from Jean-Nicod Lectures 2006:

You can check descriptions of the lectures and get the handouts here. If some of the links doesn’t work, check the list here

 Cognitive Computing Conference

On google video you can see the lectures from IBM Research’s Almaden Institute Conference on Cognitive Computing:

1. From Brain Dynamics to Consciousness , Gerald Edelman (1hr 30min)
2. The Emergence of Intelligence in the Neocortical Microcircuit, Henry Markram (1hr 10min.)
3. The Mechanism of Thought, Robert Hecht-Nielsen (1hr)
4. Hierarchical Temporal Memory: Theory and Implementation ,Jeff Hawkins (1hr)
5. How the brain works, what it computes… ,James Albus, Theodore Berger, Kwabena Boahen, Ralph Linsker, Jerry Swartz (2hr)
6. The Uniqueness of the Human Brain, V. S. Ramachandran (54 min)
7. Beyond Dualism, John Searle (1hr 20min)
8. Cortical Dynamics of Working Memory, Joaquin Fuster (1hr 10min)
9. A Quantitative Theory of Cortex, Leslie Valiant (1hr 10min)
10. The 4 C’s of Neuroinformation Theory, Toby Berger (50min)
11. Consciousness, Christof Koch (1hr 10min)
12. The Future of Cognitive Computing, William Pulleyblank (1hr 10min)
 Interviews

Then there are also Robert Wright’s interviews with Daniel Dennett (1hr 19min), Steven Pinker (1 hr) and others.

Or alternatively check the list at MeaningofLife.tv.

 UCTV

From the University of California TV (UCTV), you can see following lectures connected to philosophy of mind, cognitive science and neuroscience:

1. Hilary Putnam’s lecture The Depths and Shallows of Experience (87 min.)
2. Patricia Churchland talk on the Decisions, Responsibility and the Brain
(55 min), and Philosophy in the Age of Neuroscience(57 min)
3. Francis Crick – Consciousness Now!, Consciousness: New Ideas and Experiments, and an episode of UCSD Guestbook hosted by Nick Spitzer
4. Richard O. Brown – Nothing in Mind: The Neuroscience of Nothing (52 min)

And several more on issue of evolution:

1. Phillip Johnson – On Darwinism, (57 min), Darwinism On Trial (89 min), Darwinism: Science of Philosophy? (58 min), and with William Provine – Darwinism: Science or Philosophy (89 min)
2. Michael Denton – On Darwinism (58 min)
3. Dean Kenyon interview- Focus On Darwinism (59 min)
4. Fazale Rana – Convergent Evolution (56 min)
5. Richard Weikart – From Darwin to Hitler (58 min)
6. Michael Behe – Irreducible Complexity: The Biochemical Challenge to Darwinism (59 min), From the Big Bang to Irreducible Complexity (58 min)
7. Michael Ruse – Darwinism and Atheism: A Marriage Made in Heaven (113 min)
8. Ronald Numbers – Experiencing Evolution: Darwinism and the Diminution of Religious Belief (88 min)
9. Dr. Minnich – Paradigm of Design: The Bacterial Flagellum (83 min)
10. John Hedley Brooke – Darwin, Design and the Unification of Nature (118 min)

On language, semantics and language use:

1. Noam Chomsky – Language and the Mind Revisited – The Biolinguistic Turn (87 min), Language and the Rest of the World (76 min)
2. David Kaplan – The Meaning of “Ouch” and “Oops” (85 min)
3. George Lakoff – How Liberals and Conservatives Think (58 min)

List update from 22 Oct. 2006:

1. John McDowell – Intention in Action (1 hour)
2. Martin Sereno – The Origin of the Human Mind: Insights from Brain Imaging and Evolution (1 hour)
3. Aniruddh Patel – Music and the Mind (50 min)
4. Jeff Elman – Understanding Language (1 hour)
5. Uta Firth – How cognitive theories Can Help Us Explain Autism (45 min)

 Computing and Philosophy Conference

On  North American Computing and Philosophy 2005 Conference page you can view several presentations, including very interesting one on chimerical colors by Paul Churchland.
Their site includes also archives from the Computing and Philosophy conferences from 2001, 2002 and 2003

 Ethics

Ethics Updates hosts lot of philosophy lectures from different conferences on the topic of ethics, among which:

 USC – Closer To Truth

Research Channel hosts a number of different shows. From philosophical perspective Closer To Truth series is particularly interesting. Included are episodes on topic of philosophy of mind featuring Searle, Chalmers, Hameroff, Koch:

 Philosophy of Science

San Jose State University has a sequence of 15 streaming video lectures of their Philosophy of Science class. (presented by J.Stemwedel).

1. Introduction: “What is Science? 56k/Dsl
2. Logical Empiricism 56k/Dsl
3. Induction and Confirmation 56k/Dsl
4. Challenges in Theory Testing 56k/Dsl
5. Popper and Falsification 56k/Dsl
6. Kuhn: Paradigms and Normal Sciences 56k/Dsl
7. Kuhn: Crisis and Revolution 56k/Dsl
8. Kuhn: Crisis and Revolution 56k/Dsl
9. Alternatives to Kuhn 56k/Dsl
10. Sociology of Science 56k/Dsl
11. Feminist Critique of Science 56k/Dsl
12. Naturalism 56k/Dsl
13. Realism and Anti-Realism 56k/Dsl
14. Explanation 56k/Dsl
15. Wrap up: What is Science? 56k/Dsl

 MIT World

MIT World hosts streaming videos of public events at MIT. Here are some connected to philosophy, cogsci and neuroscience I could find:

1. The Blank Slate:The Modern Denial of Human Nature – Steven Pinker
2. Words and Rules: The Ingredients of Language – Steven Pinker
3. Pinker’s Farewell – Steven Pinker
4. The Future of Digital Commons – Nancy Kranich, Ann Wolpert, Steven Pinker
5. The Idea of Universality in Linguistics and Human Rights – Noam Chomsky, Elizabeth S. Spelke
6. Vision of the Future (Part 1) – Susumu Tonehawa, Syndey Brenner, Richard Axel
7. Vision of the Future (part 2) – Eric R. Kandel, James D. Watson
8. Expand Your Mind:Getting a Grasp On Consciousness – Christof Koch, Patricia Churchland
9. Neuroethics – Stephan Chorover, Mriganka Sur
10. The Brain And Mind – Mriganka Sur
11. Cognitive Control: Understanding the Brain’s Executive – Earl K. Miller
12. The Neurology of Vision – Nancy Kanwisher
13. Neurobiology of Memory: How do We Acquire, Consolidate and Recall Memory – Susumu Tonegawa
14. Architecture of the Brain – Elly Nedivi
15. The Changing Brain – Mark Bear
16. Vision: Challenges and Prospects – Pawan Sinha

 University of Cincinnati

Visit web page of University of Cincinnati philosophy faculty to watch three interviews.
One is with Prof. Christopher Gauker about his book Words without Meaning (MIT 2003), one other with Prof. John Bickle about his book, Philosophy and Neuroscience: A Ruthlessly Reductive Account (Kluwer 2003), and interview with Prof. Jenefer Robinson about her book, Deeper than Reason: Emotion and Its Role

 Stanford Humanities Center Events

Among videos at audio/video archive of the Stanford Humanities Center:

1. Analogy as the Core of Cognition, Douglas Hofstadter (02/06/2006)
2. The Humanities and Human Nature, Steven Pinker (11/10/2004)
3. The Ethics of Identity, Kwame Anthony Appiah (11/01/2004)

Check their archive for more.

 Counterbalance Interactive Library

There are videos on lot of topics, among which there are these sets…

1. Becoming Human: Brain, Mind and Emergence conference held at Stanford University in 2003.
2. Neuroscience, Religious Experience and the Self conference held at Montreal in 2001
3. Nancy Murphy’s presentation of a non-reductive physicalist account of human nature (you need to click through the parts of the lecture the right part of that webpage)

For more check all of content at Counterbalance library.

 Rick Grush’s Video Podcasts

Here. Includes 15 lectures from Philosophy 10, Introduction to Logic; Locating Subjects of Experience in the Natural Order (67 minutes) and other. (via Brain Hammer)

 The Origins and Nature of Computation
1. Martin Davis: The Church-Turing Thesis: Consensus and Opposition (53 min)
2. Saul Kripke: From Church’s Thesis to the First Order Algorithm Theorem (01h24min)
3. John McCarthy: Formalizing Common Sense Knowledge in Mathematical Logic (01h12min)

List also here(via Brains)

 Christof Koch’s CNS/Bi 120 Lectures

18 Video lectures of Christof Koch at Caltech (from 2003) on Neuronal Basis of Consciousness, are available here.
From the description at the site:
What are the correlates of consciousness in the brain? The course provides a framework for addressing these questions from a scientific point of view. The course will focus on the neuronal correlates of sensory consciousness.

 The Royal Society

Frejya in the comments has pointed to the webstreams at The Royal Society. Among those you can check:

1. Daniel Wolpert – The Puppet Master – How The Brain Controls The Body
2. Alan Cowey – Magnetic brain stimulation: what can it tell us about brain function?
3. Douwe Draaisma – Why life speeds up as you get older
4. Steve Jones – Why creationism is wrong and evolution is right
5. Sandu Popescu – What is quantum non-locality? (on very popular level)
6. David Attenborough – Perception, deception and reality

 Ernest Nagel Lectures in Philosophy and Science

Jeremy Shipley in the comments has pointed to two lectures at Carnegie Mellon Department of Philosophy, on the topic of highlighting the deep connection between philosophical reflection and scientific activity. One is by Bas van Fraassen [Part 1, Part 2, Part 3], and the other by Patrick Suppes [Part 1, Part 2, Part 3]

 Single Video Lectures
1. The Ph.D/MA Program in Philosophy at the City University of New York Graduate Center hosted a two day celebration of the work of Saul Kripke, and hosts a video of the lecture by Kripke, named “The First Person”
2. B. Alan Wallace seeking ways to integrate Buddhist contemplative practices and Western science to advance the study of the mind – Toward the First Revolution in the Mind Sciences
3. Richard Feynman is not a philosopher, but still you might still want to see this… The pleasure of finding things out
4. The Roots of the Matrix – documentary about the philosophy behind Matrix movies (1 hour) Dennett, Chalmers, Searle, Clark, Koch
5. Webcast of the “debate between David Gelerntner and Ray Kurzweil on machine consciousness and a talk by Jack Copeland on Turing’s contribution to codebreaking and to the development of AI (at about the 1 hour 45 minute mark)” (via Brains)
6. Putnam presenting the UCD Ulysses Medal Lecture titled “The Fact/Value Dichotomy and its critics” at UCD on 5th March 2007 (via oscillate it)

 Continental Philosophy

Instead of putting list of videos here, I will just point to the Continental Philosophy blog, which under the videos tag has a big collection of videos connected to continental philosophy.

# Distinguishing Transcendence and Existence in Frege/Husserl

As addition to what I’ve argued  in previous post (also see the connected thread on Abstraction and Given), here are quotes by but Frege and Husserl  arguing that objectivity doesn’t entail existence/actuality.

From The Frege Reader, Michael Beaney (ed.), p96 (about The Foundations of Arithmetic)

Frege distinguishes what is objective (objectiv) from what is actual (wirklich), the later being the handleable (handgreflich), or spatial (räumlich), such that what is actual is only part of what is objective. Both the axis of the Earth and the centre of mass of the solar system are objective, but they are not actual like the Earth itself.

And Husserl explains that just because we think of something, it doesn’t mean that we should think that what we think of, has some intra-mental existence.

To assume that the intentional object is act-immanent, that is actually contained in the intention and therefore in possession of the same mode of being as the experience itself, leads to a rejection of the categorical distinction between act and object. That such a distinction does exist is easy to illustrate. (Hua 19/385)…  (From Husserl’s Phenomenology, Dan Zahavi, p.15)

For what he means by “easy to illustrate”, see this post.

In this way Husserl shows that also we shouldn’t use the word “existence” for the objects of intention in some
different mode, e.g. “exist as thought”. That is… The thought about something exists, but the object of intention is not part of the thought.

# Existence and Transcendence

This post was inspired by the post over at Philosophy, et cetera discussing the question of what is that “fundamental existence” of which philosophers speak when they are arguing if chairs fundamentally exist or not. Thinking of what that existence might be, I ended up writing my thoughts on existence, which I think might clear up the issue, while I’m not sure if it has any value in the discussion opened there.

First, to raise the issue of existence, we necesseraly need to talk about some thing to start with. We always talk about existence of something.
When we say that “Santa doesn’t exist”, that doesn’t mean that there is such thing as Santa just because we mention Santa, and because we talk about Santa. But it is also true that Santa has to have objective meaning, it has to refer to something objective, as if it doesn’t the proposition “Santa doesn’t exist” can’t have truth value. So “objectivity” and “existence” should be distinguished. By objectivity I mean the kind of objectivity of the terms which is established through critiques of psychologism by Frege and Husserl. (In short the issue of objectivity, is issue of transcendence, and even intersubjective transcendence… i.e. – how come it is possible to think about same thing in different times, and even multiple people to think and talk about same thing?)

So, we can agree for example that numbers are objective/transcendental (and not psychological events of some kind) entities. Because numbers are objective, there are objective truths about numbers. “1+1=2” is objective truth, “there is no biggest integer” is objective truth, and so on…

But if we are raising the issue of existence, or non existence of the objective thing, it means that the existence doesn’t belong to that objective something of which we talk. Or, to say it differently, if there was some property of existence which would belong to those things, then their existence wouldn’t be issue. This is what I think Kant’s “existence isn’t predicate” refers to.

So, the objective/transcendental can’t exist qua objective. What exist is concrete, and when wondering about the existence of the objective, that is the issue at hand, if there is concrete such that it can be further determined as that objective.
So we could say that numbers don’t exist qua numbers, 9 don’t exist as 9, there is no concrete 9 qua 9, but there exist concrete number of planets in the Solar system, which can be determined to be 9. Blue doesn’t exist as blue, there is no concrete blue out there, but there exist concrete color of my shirt, which can be determined to be blue, etc…
So, while we can agree that numbers don’t exist as numbers (e.g. there is no number 9 that exists as number 9), that colors don’t exist qua colors (there is no blue color that exists as blue color); we can ask if there is such things which can be determined as certain number (number of planets in Solar system), and if there exist things which are blue.

This of course is more problematic to accept in case of names. Isn’t it weird to accept that “Nothing exist qua Earth, but there might be a concrete thing which can be determined as Earth”?. Doesn’t “Earth” mean that concrete thing? It does… it means that concrete thing which is determined as “Earth” ,and which we happen to believe that exist. But doesn’t mean the concrete thing exists qua Earth.
It is possible to say “Earth doesn’t exist”, and even imagine it to be true. Example would be the case in which Vogon spaceship destroyed the Earth to build a hyper-space bypass. Earth wouldn’t exist in such case, but proposition “Earth doesn’t exist” will be true. For the proposition to have truth value, “Earth” would still need to have objective meaning, and it is for sure the same meaning it had while the Earth existed. So meaning of “Earth” is not at all changed by the fact that some concrete object is destroyed.
If you think that this is merely temporal issue, we could imagine The Matrix scenario, placed on the planet Kagiroino-Oka. Within the Matrix we might live on planet Earth, however it would be true that Earth doesn’t exist. There is just virtual-Earth in the matrix. But if that scenario is the case, “Earth” would mean same thing that it means now. “Earth doesn’t exist” would refer to same Earth. So meaning of Earth is “untouched” by the issue of existence of thing which can be determined as Earth.

Additional argument that the concrete thing doesn’t exist qua Earth, even if we put aside the argument that existence doesn’t enter the meaning of Earth, is that there are much more truth about whatever is concrete thing which is Earth, then its being Earth. We can investigate Earth, we can measure it, and in general we can learn facts about it – about the concrete thing which is determined as Earth. If we learn new things, we can’t say that the meaning of Earth changes. So again, we see that the concrete thing, and what Earth means are separate.

To give proper account, we need to analyze this distinction of objective and existing, we need to see what constitutes objectivity (transcendence), and what is its relation to concrete, i.e. how is it possible for concrete to be objective – because while objective can’t exist qua objective, concrete can exist as being something objective (as rabbit, chair, Earth and so on).  Threads of posts in which I try to discuss those issues on this blog can be found here.

# Information and Meaning

Everybody knows that one part of the computer is its memory. It is made of small parts which can take one state or other (e.g. on and off), like switches, and we say that one such part can hold amount of information of one bit. If you get eight of them, you get amount of information of one byte, 1024 bytes make one kilobyte, and 1024 kilobytes make a megabyte, 1024 megabytes make gigabyte. So if you have 1 gigabyte of memory in your computer, you have 1024*1024*1024*8 of those bits, of those switches – around 9 billion of them. If you have started switching those switches from one state to other state, from the day you were born, 15 of them per second, it would take you over 30 years to finish.

Anyway, those switches happen to be of a very particular kind… when you put them in one state, they stay in that state until you change it again, and more importantly those switches don’t disappear.

So we can look at this kind of computer memory as based on switches that exist, and which you can set now to “On” state, and then later read that state. If the state of the switch isn’t stable, or if the switch disappears, this can’t be done. And what is called RAM memory in the computer keeps the state only while the computer is turned on; it needs electrical power to maintain the state. When you turn off the computer, and then turn it on again, the states of those switches in the RAM memory are random, so you can’t read what has been written to it before the restart. Of course, we use hard disk for keeping the state when there is no power; the state of the “switches” in the hard disk is maintained even there is no power.

But we can ignore the technical details of the switches, and how their state is set or changed. From our point of view… as long as those things don’t suddenly disappear, and they maintain their state through time (state that can be set, and read later), they are switches… Like those on the picture:

If I’m forgetting things, I can use those to store information. For example I ask my wife if she would like eggs tomorrow for breakfast or not, and she says yes. Instead of remembering that, I put the switch in on position if she does, and in off if she doesn’t. The next day, when I get up, I just take a look on the switch, and there… she did want eggs for breakfast. Of course if the switches were such that they disappear this wouldn’t be possible.

But wait, you say, what if you need to remember if she would like bacon, if you need to throw up the garbage, to go buy something, etc… You will switch all those switches to on and off, but then – you will need to remember which switch is for what!

OK, I must admit it would be impractical, especially that those switches are such that can’t be tagged or written on. But there are lots of ways in which those can be still useful. First I can learn once what switch is for, and then I can use the switches to hold information for each new day. Other thing is that I can use it to store bigger information if I take few consecutive switches to store it. E.g. I can store 4 states by using two switches. “Off”/”Off”, “Off”/”On”, “On”/”Off” and “On”/”On”. In that case, I need to remember just the starting switch, but I can remember which of the four things I had to remember. If it is 8 different states, then I will need three consecutive switches, four for 16 states, five for 32 (e.g. remembering a number between 1 and 32), etc… So those switches are usable, by remembering just the starting switch, we can remember very big things. The American mathematician and electrical engineer Claude Shannon is known as father of the information theory which deals with this kind of transfer of information; in our case it is transfer of information from past to future, from me today, to the me tomorrow, but usually the sender and receiver are abstract, and are seen in such way that it is not important if they are same or different person, where they are, or in what time they are.

I could even make codes for letters (or use standard ones like the ASCII codes, which connect each Latin letter to a number), so I use 5 of those switches to remember one letter. So if I use it like that, I can, kind of, write by switching those switches. For example I can write: EGGS (each letter being 5 switches) and then the next switch “On”/”Off”, then BACON, the next switch “On”/”Off” depending on what my wife says and so on. So we can see we can use those switches to store information, and that’s why they call it memory. Note though that I will still need a way to somehow understand what the states of particular switches mean, and that the information can’t mean anything by itself. If I’m to encounter in somebody’s front yard several switches in “On” position and others in “Off” position, there is no way I can figure out from the position of the switches alone what they mean. They might be encoding what somebody’s wife wanted for breakfast, or maybe a sequence of letters, or any information that can be reduced to certain amount of states. For example my wife could some day say… “Instead of telling you what I want for breakfast, I set the first switch myself”, and I would still miss information what does “On” mean, does it mean eggs, or no eggs?

So, those states can’t mean anything by themselves, even if we are smart enough to figure out that they are supposed to mean anything. After all maybe we are in switches factory. Shannon himself said: “Frequently the messages have meaning”… these semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages”. If you have millions of switches, and each of them is in some random state, Off/On, in Shannon’s terms, you will have system with lot of information. However if it has some meaning (e.g. somebody used it to communicate something), or not, is separate question.

To be continued…

Technorati Tags: , ,

# What I take to be the grounds of Philosophy

If one needs to point to a central issue in philosophy, if one needs to use just one word to say what philosophy is about, it has to be – comprehension. As, if one removes comprehension, the philosophical questions and philosophical answers, philosophical discussions and everything philosophical looses sense… The questions make sense just if comprehended, the answers are good only if comprehended, the philosophical method or inquiry also need to be understood and comprehended. (BTW, the way I use “comprehend” here is roughly synonymous with “understand”. No fancy theoretical accounts or meanings.)

The comprehension is important on two levels. First the comprehension of Other, comprehension of what are people, asking, saying or wondering. But that comprehension is seen just as a way to the overall-comprehension, some ideal of comprehending everything that needs to be comprehended by philosophy.

Having put the central issue of philosophy as comprehension, we can put limits on what philosophy can allow, and what should be marked as inappropriate to it.

As one, for something to be comprehended, it must be brought clearly in front of the awareness. In such way philosophy is intimately bounded to consciousness and to awareness, and to the issue of what we can be aware of.

Because of this, I think critical stance towards our mental powers of awareness is needed, questions like ‘what are types of things we can be aware of?’, ‘how do we become aware of things?’ need to be asked. Those issues should be first explored, so that we are sure that the tower which is built has stable basis.

I’m repeating I think the words of Kant, who was saying that the powers of the mind has to be critically assessed before any metaphysics is built, but in my own opinion Kant failed to be critical enough. He took the terms such as “mind”, “objects”, “reality” in their common-sense usage in the society in which he was raised, and worked with them, without getting into inquiry into what he means by those words.

Or to put it another away, so it connects to the start of this post, one must get to this question…

-What is that which I’m aware of, and to which those words I use relate?

That is the stance the philosophy must make. I have to become aware of what each of the words I use (to speak about philosophy) refers to, and there has to be this possibility of comprehension, as otherwise (if the meanings of the words are something which can’t be comprehended), the proper critique of the grounds of philosophy can’t be made. Even if what one says ostensibly makes sense, if such critique is not done first, the sense will be there limited by the society, in which one is born, or by the paradigm through which one have learned things.

Does this mean that we should avoid the words as they are connected to the paradigms/society? No! Philosophers can’t accept that. If one takes the meanings of the words to be based in the unconscious otherness, one gives up the philosophical work from very start.

We must assume that what the words relate to, what the words mean, is accessible to the consciousness, and even if the meaning is connected to the society or paradigm, it is the work of the philosopher to comprehend those meanings as such.

Such philosophy, as a comprehension, is in that way possible only under such conditions. Not accepting those conditions is not philosophy, it is giving up.

# Philosophy news

After programming professionally for years, somehow the love for the programming itself disappears in the routine of everyday work.

This last weekend I reminded myself of the original love I had, by looking into the ways one can play with blogs from java program. I was playing with things, and the result is this semi-finished aggregator. It aggregates the posts of the philosophy blogs. (I added some blogs I read, and some others I found for testing purposes).

I think I will play with it some more the next weekend… First, I need to do the updates automatic (on X hours). As it is now I have to push a button for the update to happen. As I can’t put java code on the server, that solution will have to suffice for now. Second, I will probably do the archive thing, so that “Past Days” part properly shows aggregation of posts for each past day.

And some time in the future, I want to look into possibilities for some kind of text mining… I know next to nothing of this field, but sounds like interesting play field. It would be interesting to see what kind of semantical information can be extracted from blogs.

Update: It seems I didn’t have as much time as I thought to work on this… I will put this thing aside for now. I will keep updated aggregate page on this blog, at the “Power Blogroll” page.

# Help for reading on-line (firefox)

Back when I used Internet Explorer, whenever I was reading some web page, I would triple-click the paragraph that I am reading. The triple-click selects the whole paragraph in IE, making the paragraph stand out from the other text, and who-knows-why I found that helping me in the reading (I guess something to do with easier focusing)…

Now, when I installed Firefox, I found out that it is missing the triple-click feature. Actually it has triple-click but it selects just a line, not the whole paragraph. But of course the beauty of Firefox is in the extensions, so I did a search.

Tripleselect extension adds to Firefox this functionality, so i can now triple-click to select a paragraph.
But, recently I stumbled across Paragrasp extension which seems even better. With this extension, I right click the text in the paragraph, and choose “Paragrasp Here” from the right click menu. The paragraph gets higlighted, but what is very nice is that then I can use ctrl+down-arrow and ctrl+up-arrow to highlight the next or previous paragraph.
For longer texts, I use ctrl+shift+A hotkey and then it works just by pressing the up and down arrow keys.

Let me also remind you that if you have Firefox, you can also annotate the paragraphs using a separate extension, which is neat for analyzing on-line texts. I wrote about that here. (If it is still invitation only, drop a comment, and I will be happy to invite you).

Technorati Tags: , , , , , ,

# Red Riding Hood in-the-world

Usually imagination is considered as ultimately subjective thing, that what is imagined doesn’t belong to the world, but exists just as some purely mental-thing.
But on other side imagination as the other mental acts shows as being towards transcendental objects – We can imagine same thing multiple times, or we can talk with other person about the same imaginary thing.

So what is imagined can’t be fully subjective.

To figure out how this can be, we might think of situations where the children are encountering (their) imagination, and in which might notice it as specific mental act (of imagination). I can think of few such scenarios possible in early years. Of course the list is not in any way systematic…

Expectation… this is the earliest type of imagination I can imagine (no pun intended)…
I see it in really early ages of kids, and makes it possible to
make them laugh doing silly things, like crouching behind the couch
hiding from their view, and then jumping. I guess they laugh at my
stupidity doing such meaningless acts. Expectation doesn’t require language. Of course, sometimes they want you to repeat the act, so they make some sounds… until you do it again… And again… And again… They are never satisfied. In the expectation, they see more in the situation then there is “physically“. E.g. they expect the jump – they wait for it. There in front of them, in the world.

Playing with toys… Seeing in the toys more then there is (physically). Pushing toy cars around, also hitting the ball. Those things are seen as part of the potential of the thing, the ball is hittable, the toy-car is pushable, etc.. This possibilities are there in the toys for the kid. This also doesn’t require language.

Stories… about what has happened, really or not. To me, to Little Red Riding Hood,  or to Harry Potter. This is as much about imagination as about language. Hard to divide. Language is not possible without imagination it seems, and stories without language. But in any case, the person who tells the story is in the world, and the words are in the world, the Little Red Riding Hood is also imagined in the world… noticing, moving, talking. Where can she watch, move, talk if not while (imagined as) being-in-the-world.

Promises… about what will happen.  To the kid if he does his homework. Or that he can play on the computer tomorrow. Again, not possible without language. Surely connected to expectations. They are also about the world. They happen or don’t in the world.