A year ago, a friend of mine took a free online course in logic through Stanford University. The teacher was Michael Genesereth, an associate professor of computer science at Stanford. I was impressed with the robust simple clarity and authenticity of his approach, aimed at anyone with basic high school level math and some capacity to deal with simple concepts from set theory. I just signed up for the 2014 class, starting in September, regarding which he says
Logic is one of the oldest intellectual disciplines in human history. It dates back to the times of Aristotle; it has been studied through the centuries; and it is still a subject of active investigation today.
This course is a basic introduction to Logic. It shows how to formalize information in form of logical sentences. It shows how to reason systematically with this information to produce all logical conclusions and only logical conclusions. And it examines logic technology and its applications - in mathematics, science, engineering, business, law, and so forth.
https://www.coursera.org/course/intrologic
I like his point regarding “all logical conclusions and only logical conclusions”. His breadth of application is also significant. He is not talking about a specialized subset of logic, or a kind of logic that only applies in particular contexts or under particular circumstances.
For me – this point must be placed squarely in the center of any persuasive argument regarding “embodied reason”.
I did watch the video suggested by John Bottoms on George Lakoff’s new theory -- https://www.youtube.com/watch?v=XWYaoAoijdQ – and the fuzzy feeling continues to grow in me – that this idea of “embodied reason” should, at the least, be challenged. One questioner at the end of the lecture asked about alternative neural pathways for similar reasoning expressed in different languages – and though I might have misunderstood, it felt to me like Lakoff ducked the question. For me, any notion of isomorphic mapping between neural pathways and logic pathways seems like mythology. I’m no expert, and I know a lot of progress has been made – but for me, these things appear to be statistical field effects, not isomorphic correlations, as Lakoff seems to be suggesting.
So – as I continue to frame my understanding of Lakoff’s approach – I am starting to get the idea that he is making a distinction between “correct logic” (that does, according to my view, have a disembodied ontological existence), and “the observed empirical logic of what people actually do” – which, probably unfortunately, tends to be somewhat aberrant, and involve distortions of “the pure form” that I understand professor Genesereth to be teaching.
So big surprise – people don’t think logically. This is revolutionary? This discovery changes cognitive science forever? On this grounds, we are expected to throw out the laws of logic? I’ve been involved with many groups trying to figure out what’s wrong with politics, and how the world could straighten itself out, and a huge theme is the tendency to logical distortion in political thinking due to who-knows-how-many “embodied” influences – like ideology – or culture -- or cognitive overload. Psychology professor Jonathan Haidt’s 2013 book “The Righteous Mind: Why Good People are Divided by Religion and Politics” has influenced the national conversation on this subject: http://righteousmind.com/
This kind of distortion is what emerges if we decide what we want to study is “what people actually do” (“empiricism”) – without asking the question – “does what they do make sense, is it correct – or is it an aberrant distortion due to xyz influence?” If you take the view that there is no guiding standard on this subject – a view I sometimes tend to see as too fashionable among academics – you do end up with a very confusing relativism, that I would suppose could be straightened out with a major jolt of Genesereth logic.
Since my instinct is – “let’s fix this place” – I am less interested in studying the myriad ways thinking can become confused and messy as I am in devising some way or method or heuristic that could help guide us all back towards a shared human clarity and common ground of reasoning – an objective Lakoff seems to regard as not only impossible, but also undesirable. Is the logic taught by professor Genesereth “a property of the universe”? Well, I don’t know, but my guess is “yes” – and the alternatives to me feel like StarTrek or the Twilight Zone…
***
6. The theory of prototypes was well established by Aristotle in
his biological writings. His logical writings were the source
of the theory of categories that Lakoff criticized. But in his
more voluminous biological writings, Aristotle argued for a
bottom-up theory of analysis based on *prototypes* rather than
top-down definitions. He explicitly said that any definition
of species or genera must be based on a detailed description
of a specimen, and that the definitions must *change* when
new discoveries are made. Kant and many others made similar
observations -- but with the term 'schema' rather than prototype.
For years, I believed in the power and potential of numerical taxonomy as propounded by Sokal and Sneath -- http://en.wikipedia.org/wiki/Numerical_taxonomy. I thought it could be perfected if we could only get the algebraic cascades defined the right way.
And I was fascinated by the quote from Linnaeus on the fundamentals of classification:
All the real knowledge which we possess depends on
methods by which we distinguish the similar from the
dissimilar. The greater the number of natural distinctions
this method comprehends the clearer becomes our idea of
things. The more numerous the objects which employ our
attention the more difficult it becomes to form such a
method, and the more necessary.
I saw this as the master-principle for dimension-based models of classification, and the key to defining the illusive concepts of “similarity” and “difference” – which, though this approach, can be assigned mathematical/algebraic values through cascaded dimensions.
But for a long time, I did not fully realize that this process can only be stipulative – and that ANY taxonomic classification is ASBOLUTELY subject to ad hoc transience, depending on choice of variables and local/immediate purposes. This fact of life, as I see it now, is another direct consequence of the Sowa principle: “reality is continuous, concepts are discrete”. Pick your variables, deal with the consequences…
So – what this means for the ontology of language is – all taxonomic systems and classifications are social conventions, chosen for convenience, and subject to continuing evolutionary transience. They must be constantly updated – and that process must be understood as converging towards a “central” statistical approximation (a common theme in prototype theory). The “empirical reality” of these taxonomic systems – reflects social convention. Yes, they are absolutely useful for statistical social processes. But they have no independent absolute meaning. They are an agreement among participants that it is currently convenient to see the world in these terms.
When this is clear, we can then look at Aristotle’s point, cited by John
Aristotle argued for a
bottom-up theory of analysis based on *prototypes* rather than
top-down definitions. He explicitly said that any definition
of species or genera must be based on a detailed description
of a specimen, and that the definitions must *change* when
new discoveries are made.
This is more or less what I just said, and maybe the essential point in any critique of hierarchical top-down methods.
And this statement points to “the revolution” that many of us – Lakoff certainly included – are reaching for.
The critique of the top-down taxonomic form – is that it is cast in stone – and inherently not responsive to transience (this is the kind of problem inherent in “the early Wittgenstein”). So, the early-stage revolutionaries, recognizing this problem, want to drive the process with bottom-up specifics, intended to exert transformative influence of the top-level categories. And that is, of course, part of what we need.
But the recognition that any taxonomic form – postulated or asserted from the top, informed from the bottom – is still transient – transient, local, and immediate – is an essential next step in liberating the power of top-down categorical models, freeing them from their cast-in-stone rigidity, and opening the way to a new cognitive science that does not need to reject universals – as I tend to understand Lakoff and many others to be doing.
The key is to define actual point-of-experience intended meaning as inherently and always stipulative in all its particulars. Yes, guide the process of communication from a shared pool of meanings drawn from social convention – but always remember that intended meaning is driven in every detail by the speaker. “Who is to be master?”, asked Humpty-Dumpty. The speaker. And if the speaker wants to be successful with the listener – he/she better have a pretty good idea of shared word meanings…
From my point of view – these principles begin to describe how the classical view can be rescued from its current level of disrespect, and put back at the top of the world’s understanding of logic. All these other methods are subsets of the classical method, when its rigidity is transformed into fluency through bottom-up information and the recognition that categories in actual usage are always ad hoc and context-specific.
***
And with all that said – a review of some of Lakoff’s fundamental points, taken from his 30-year-old book – most of which, as I understand it, he is still asserting today, though perhaps in slightly different terms.
John in his email from 7/22 cites these points from the .pdf of Women Fire and Dangerous Things, http://originresearch.com/docs/George-Lakoff-Women-Fire-and-Dangerous-Things.pdf - page 9
In these terms, Lakoff outlines what he considers to be the revolution he and his compatriots are bringing to cognitive science and the world.
Would Lakoff still assert these points today, in these same terms?
If what he is saying is – throw out rigid top-down categorical models, and replace them with fluent ones, Lakoff is absolutely right.
And regarding ways that science understands the world, Lakoff is absolutely right when he says that (those old ideas) “need to be replaced by ideas that are not only more accurate, but more humane.”
We do need a revolution in accuracy – and that revolution might offer real hope for a world view that is more humane…
The evidence we will be considering suggests a shift from classical categories
to prototype-based categories defined by cognitive models. It is a
change that implies other changes: changes in the concepts of truth,
knowledge, meaning, rationality, even grammar. A number of familiar
ideas will fall by the wayside. Here are some that will have to be left behind:
- Meaning is based on truth and reference; it concerns the relationship
between symbols and things in the world.
- Biological species are natural kinds, defined by common essential
properties.
- The mind is separate from, and independent of, the body.
- Emotion has no conceptual content.
- Grammar is a matter of pure form.
- Reason is transcendental, in that it transcends-goes beyond-the
way human beings, or any other kinds of beings, happen to think. It
concerns the inferential relationships among all possible concepts in
this universe or any other. Mathematics is a form of transcendental
reason.
- There is a correct, God's eye view of the world-a single correct way
of understanding what is and is not true.
- All people think using the same conceptual system.
These ideas have been part of the superstructure of Western intellectual
life for two thousand years. They are tied, in one way or another, to the
classical concept of a category. When that concept is left behind, the
others will be too. They need to be replaced by ideas that are not only
more accurate, but more humane.
Bruce Schuman
(805) 966-9515, PO Box 23346, Santa Barbara CA 93101
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
Sent: Tuesday, July 22, 2014 8:21 AM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] George Lakoff - Women, Fire, Dangerous Things - Embodied Reason
Bruce, Rich, and Chris,
Bruce
> It's a powerful sophisticated highly detailed and substantial book
> -- and the entire 631 pages are available in a pretty good .pdf...
Thanks for the URL. I agree that it's an important book. I bought it shortly after it came out, but I'm glad to have an electronic copy.
General observation about George Lakoff: I have a large overlap of agreement with most of his conclusions, especially on metaphors, word meanings, the relationships between syntax and semantics, and the nature of the embodied mind.
But his history of ideas is almost always *spectacularly* wrong. See the excerpt below from p. 9 of the book. I agree that every one of those points is false or at least misleading. But every one of them was debated and rejected by some Western philosophers since the Greeks.
Rich
> I haven’t yet read Lakoff [philosophy] in the flesh...
That's another good book that suffers from the same historical flaws.
I said that in my review: http://www.jfsowa.com/pubs/lakoff.htm
Chris
> the book makes a persuasive case that prototype theory is a good model
> for how humans categorize things in their world.
I agree. So did Wittgenstein. Lakoff cited Rosch, and he mentioned Wittgenstein. Rosch wrote her PhD dissertation on using Wittgenstein's theory of family resemblance. But related ideas were very widely proposed, analyzed, and debated since the ancient Greeks.
William Whewell made a strong case for prototypes in biology in 1858 (but he did not use the prefix 'proto'). Kant used the word 'schema', which was widely used in psychology by Selz, Piaget, Bartlett, etc.
Another term is Gestalt. Unfortunately, Lakoff's citation for 'schema'
is Rumelhart, 1975.
Peirce had read Whewell and Kant. He said that the notion of schema in Kant was his single most important notion, which Kant should have made the centerpiece of his Critiques. Otto Selz was a psychologist who did make the schema his central focus. Herb Simon cited Selz's notion of schematic anticipation as a predecessor and inspiration for his theory of chunks and pattern-directed search in AI.
Chris
> Current methods rely on domain experts or knowledge engineers
> abstracting a variety of observations into a system of axioms that can
> be used downstream for deductive reasoning. This can lead to rigidity,
> bottlenecks, etc.
I agree. Such methods are valuable for solving particular problems.
They correspond to the microtheories in Cyc. But they are far too limited and brittle to put in a top-level ontology. For citations and discussion, see http://www.jfsowa.com/pubs/cogcat.htm
Some corrections to Lakoff's history:
1. Pythagoras and Plato had a theory of a detached or at least
a detachable psyche. Pythagoras had a notion of migration of
souls (which he probably picked up from Eastern philosophy).
Both Heraclitus and Pythagoras lived in Anatolia, where they
undoubtedly got ideas from the gurus who traveled the silk road
from China to the Greek colonies.
2. But Aristotle had a hierarchy of *embodied* psyches, which were
not detachable. They ranged a from vegetative psyche for plants
to more complex psyches for animals from sponges, to worms, to
mammals, to humans. By the way, Aristotle was the first person
to recognize that sponges were animals, not plants.
3. The great Christian theologian Thomas Aquinas was a good
Aristotelian. He used Aristotle's theory as a basis for
explaining the dogma of the resurrection of the dead at the
end of the world: the human soul without a body is pale
shadow (as Homer said in his description of Hades) and the
soul requires the body to support all its faculties.
4. The Greek atomists, starting with Leucippus and Democritus, had
a different view, but it was also embodied. They assumed atoms
of different shapes for the four elements (earth, fire, air,
and water). They assumed that the psyche consisted of spherical
atoms, because they were more penetrating. The atoms of the
psyche swirled around and thereby directed the motions of the
other atoms of the body. (If you relate the psyche atoms to
modern theories of the electron, that's not a bad summary.)
5. The mind-body problem was invented by Descartes. It was a huge
source of confusion that the Greeks never suffered from. Many
philosophers, such as Peirce and Whitehead, had read Aristotle,
and they argued for a continuum of psychological (or mind-like)
phenomena from the lowest level to the human (and perhaps beyond).
6. The theory of prototypes was well established by Aristotle in
his biological writings. His logical writings were the source
of the theory of categories that Lakoff criticized. But in his
more voluminous biological writings, Aristole argued for a
bottom-up theory of analysis based on *prototypes* rather than
top-down definitions. He explicitly said that any definition
of species or genera must be based on a detailed description
of a specimen, and that the definitions must *change* when
new discoveries are made. Kant and many others made similar
observations -- but with the term 'schema' rather than prototype.
7. Lakoff's primary opponents are Descartes and Chomsky (who wrote
a book with the title _Cartesian Linguistics_). Many logicians,
such as Frege and Russell, were guilty of the errors cited below.
But Peirce, Whitehead, and others were not. In fact, Whitehead
explicitly disavowed the introduction that Russell had written
in the 1925 revision of the _Principia Mathematica_. ANW wrote
a letter to _Mind_ saying that he had no part in the revision,
and he did not want to have his name associated with it.
If Lakoff had focused his attack on Chomsky, I wouldn't complain.
Marvin Minsky said something similar: Chomsky's contributions from the mid 1950s to mid 1960s were extremely valuable. But linguistics would have progressed much better if Chomsky had stuck with politics instead of returning to linguistics after the Vietnam War.
John
_____________________________________________________________________
> A number of familiar ideas will fall by the wayside. Here are some
> that will have to be left behind:
>
> - Meaning is based on truth and reference; it concerns the relationship
> between symbols and things in the world.
> - Biological species are natural kinds, defined by common essential
> properties.
> - The mind is separate from, and independent of, the body.
> - Emotion has no conceptual content.
> - Grammar is a matter of pure form.
> - Reason is transcendental, in that it transcends-goes beyond-the
> way human beings, or any other kinds of beings, happen to think.
> It concerns the inferential relationships among all possible concepts
> in this universe or any other. Mathematics is a form of transcendental
> reason.
> - There is a correct, God's eye view of the world-a single correct way
> of understanding what is and is not true.
> - All people think using the same conceptual system.
>
> These ideas have been part of the superstructure of Western
> intellectual life for two thousand years. They are tied, in one way or
> another, to the classical concept of a category. When that concept is
> left behind, the others will be too. They need to be replaced by ideas
> that are not only more accurate, but more humane.
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