Tuesday, 18 August 2015

Holisms (3) – Definitional Holism


One

A definition isn't just an appendage to the word under scrutiny. The word would have no meaning if it weren't for the definitions we supply in order to facilitate understanding.

A word isn't atomic in nature. We can't say, for instance, that the word ‘freedom’ means, well, freedom and leave it there. Neither can we accept (on a naturalistic reading) some kind of abstract and non-individuated meaning or proposition which would allow us to escape from our linguistic system. Even if we were to allow for abstract and non-spatiotemporal meanings or propositions, they would still become material or concrete (as it were) as soon as they were expressed and communicated – which would need to be done, evidently, in some natural language or other.

Two

It seems counterintuitive, at least initially, to think that the primary relation is not between words and things, but between words and other words. This isn't so surprising when, for example, we think of the classic example of defining ‘bachelor’ as ‘unmarried man’. However, these words are taken to be synonyms. But try explaining or defining a word like ‘freedom’ again. This certainly doesn't have a reference in a strict sense of the term. Thus we are moved on, immediately, to words like ‘liberty’, ‘choice’, ‘will’ and so on. And try getting further without bringing in terms which are themselves as much in need of defining or explaining as the original word ‘freedom’. Of course it may be the case that we arrive back at the word ‘freedom’ or use this term as part of some of the other definitions.

This word isn't as problematic as words like ‘thing’ and ‘experience’. Try defining those words without reference to things or experience.

It may follow, then, that if a word has a definition which includes terms themselves not defined (or even if we provide simple synonyms for the definiendum) then the speakers may not fully understand the word’s meaning. They may not even understand their own usages of the word in question because any full meaning (or full understanding) can only belong to the linguistic system itself. Any definition or explication of a word's meaning must reach an arbitrary finishing point if the game of understanding is to begin in the first place. And that stopping place will be contingent, if not exactly arbitrary.

Three

Words are defined by other words, which are themselves defined by other words. No word, concept or thing is ever captured in a “finite web” of meaning. This is Karl Popper on this problem:

The derivation [of a term] shifts the problem of truth back to the premises, the definition shifts the problem of meaning back to the defining terms (i.e., the terms that make up the defining formula). But these, for many reasons, are likely to be just as vague and confusing as the terms we started with, and in any case, we should have to go on to define them in turn; which leads to new terms which too must be defined. And so on, to infinity.”

That must surely be the problem with definitions: they too will contain terms which themselves will need defining.

A similar problem is apparent when it comes to a logical argument and the premises on which it is based. That is, the premises of any argument may themselves depend on further premises and conclusions that may act as justifications for the validity or truth of the initial premise. Thus we have on our hands a regress of justification. However, the game can't go on forever.

This is why we must, at some point, simply accept premises, arguments or definitions if we're to get going on our philosophical or logical enterprise. The premises that we accept, however, needn't be seen as being “self-evident”, “indubitable” or anything like that. They simply need to be the starting points of reasoning if we are to avoid an infinite regress.

In a sense, it's precisely because definitions depend on their own un-defined terms that all words (or nearly all words) are inherently somewhat vague. That's because the meaning of a single word can be said to depend upon all the meanings of all the words in the symbol-system to which it belongs. We can't have a precise definition if the definiendum itself contains terms that aren't themselves defined. Though even if we do in fact define the terms in the definition, these definitions will themselves require elaboration and definition. And so on indefinitely.

The holist position on this problem will be that we must take into account the symbol-system to which the words under definition belong. But this too is problematic. How can we really take on board an entire symbol-system each time we want to define a term? Does this mean going on an infinite regress? Or if not an infinite regress, does it mean taking on board all the other words in a symbol-system? (Or perhaps a large sub-system of the larger system?) So, in that respect, the regress won't be infinite: it will be circular. This essentially means that we will arrive back at some of the terms which we actually started with.

This means that there are jut as many problems with holism (or coherentism) as there are with atomism.

Similar points to those above were raised by, amongst others, Bradley in the 19th century. Because of the problem of holism, Bradley concluded that no statement could be entirely/absolutely true. Similarly, we may now say that no definition is ever free from vagueness precisely because of its containment within a larger symbol-system.

Thursday, 13 August 2015

Susan Greenfield & John Searle on Artificial Consciousness


 

Let's start off with a longish quote from the neuroscientist, writer and broadcaster Susan Greenfield:

The idea [of a conscious robot] is ridiculous. Consciousness entails an interaction between the brain and the body, trafficking a myriad of chemicals between the two. To reproduce that, you would have to build a body with a whole range of chemicals, and the three-dimensionality of the brain would have to be preserved to the very last connection.” 

Susan Greenfield puts what can be called the case for biologism when it comes to consciousness. The way Greenfield expresses this position seems to make her an even stronger proponent of biologism than John Searle (who'll be discussed in a moment).

Her argument appears to be excruciatingly simple. It's this:

In order to create artificial consciousness we would need to build a biological brain and a biological body.

Or less extremely:

In order to create artificial consciousness one would need to replicate a biological brain and a biological body.

Or even more simply:

In order to replicate x, one would need to replicate everything of x (which has y) – down to its material constitution.

You could ask what would be the point of replicating biological brains and biological bodies when we already have them. (Though the replication of brains and bodies - regardless of consciousness - would be an incredible thing.) This would be equivalent to a scientific model that literally replicated every aspect of that which it is modelling.

Another way of putting this is to say that Susan Greenfield's position is the exact opposite of functionalism. That is, it's not functions (or computations, algorithms, etc.) which matter to consciousness: it's the material constitution (or "substrate") which underpins it.

Isn't that why Greenfield talks in terms of “trafficking a myriad of chemicals between” the brain and body and then goes on to say that “to build a body with a whole range of chemicals, and the three-dimensionality of the brain would have to be preserved to the very last connection”?

Here Greenfield goes beyond material constitution (which would include biochemicals) to stressing the “three-dimensionality of the brain”. Thus we've moved beyond material constitution to the shape/dimensionality of the brain. (In any case, three-dimensionality - at least in the abstract - would be easy to replicate.)

Again it would seem that the replication of consciousness would require the replication of both the brain and body in their entirety. That would be a pointless act of replication in terms of replicating consciousness. Though in terms of creating artificial-life-with-consciousness it would be earth-shattering.

Despite all that, the Chalmers, Penroses and dualists among us may still ask Susan Greenfield and others the following question:

What if we carried out this act of perfect replication (of both brains and bodies) and it still turned out that the replica didn't have consciousness?

Even though that's a subject for another day, I suspect that some philosophers would discount this possibility in an a priori manner.

John Searle



Many philosophers and scientists have called John Searle a dualist. He, in return, says that those who stress function and ignore biology are effectively creating a non-material Cartesian reality populated with functions or computations (rather than with Cartesian “ideas” or “thoughts”). Searle himself writes:

I believe we are now at a point where we can address this problem as a biological problem [of consciousness] like any other. For decades research has been impeded by two mistaken views: first, that consciousness is just a special sort of computer program, a special software in the hardware of the brain; and second that consciousness was just a matter of information processing. The right sort of information processing -- or on some views any sort of information processing --- would be sufficient to guarantee consciousness..... it is important to remind ourselves how profoundly anti-biological these views are. On these views brains do not really matter. We just happen to be implemented in brains, but any hardware that could carry the program or process the information would do just as well. I believe, on the contrary, that understanding the nature of consciousness crucially requires understanding how brain processes cause and realize consciousness.. ”

Searle continues:

Perhaps when we understand how brains do that, we can build conscious artifacts using some nonbiological materials that duplicate, and not merely simulate, the causal powers that brains have. But first we need to understand how brains do it.”

It can be said that there can be an artificial mind without having an artificial (human) brain. However, isn't that precisely the claim that's being disputed?

To John Searle, it's all about what he calls “causal powers".

This refers to the ostensible fact that a certain level of complexity is what's required to bring about those causal powers which are necessary for intentionality, mind and consciousness.

Despite that, Searle never never says (as far as I know) that biological brains are the only things capable - in principle - of bringing about consciousness and intentionality (therefore semantics, in Searle-speak). He only says that biological brains are the only things known which are complex enough to do so.

So it really is all about the biological and physical complexity of brains and therefore their causal powers.

His basic position (like Greenfield's) on this is that if computationalists or functionalists, for example, ignore the physical biology of brains and exclusively focus on syntax, computations or functions (the form/role rather than the physical embodiment), then that will surely lead to a kind of dualism. What he means by this is that there's a radical disjunction created between the actual physical reality of the brain and how these philosophers explain - or account for - intentionality, mind and consciousness.

Again, Searle doesn't believe that only brains can give rise to minds. Searle's position is that only brains do give rise to minds. He's emphasising an empirical fact; though he's not denying the logical and metaphysical possibility that other things can bring forth minds.

Gerald Edelman also holds the position that the mind

“can only be understood from a biological standpoint, not through physics or computer science or other approaches that ignore the structure of the brain”. 

Then Edelman - in order to demonstrate his point - puts the seemingly extreme position of “functionalists” (such as Marvin Minsky) who “say they can build an intelligent being without paying attention to anatomy”.

So if one says that biology matters, one's also saying that functions aren't everything (though not that functions are nothing).

Finally, according to Francis Crick, psychologists (as well as philosophers) 


“have treated the brain as a black box, which can be understood in terms merely of inputs and outputs rather than of internal mechanisms”.

Thus, to Greenfield, Searle, Edelman and Crick, consciousness really is all about biological brains.

References


Crick, Francis. (1996) quoted in The End of Science, by John Horgan
Edelman, Gerald. (1996) quoted in The End of Science, by John Horgan
Greenfield, Susan. (1999) quoted in Predictions: 30 Great Minds on the Future (edited by Sian Griffiths).
Searle, John. (1999) 'Consciousness'


Wednesday, 12 August 2015

Artificial Intelligence (AI): All About Algorithms?




...Thoughts-Computations-Rules-Algorithms...


Many "cognitivists" believe that the brain is a computer. (Sometimes they say “a kind of computer”.) Thus, as a result of this belief, they attempt to discover the computational processes which enable such things as perception and learning. However, expressed in that manner (as it often is), things are a little unclear.


Such cognitivists believe that the brain is also a machine – a computing machine.


Computationalists (computationalism is a branch of cognitivism) claim that all thought is computation. But what does that mean? Are the words 'thought' and 'computation' are virtual (or literal) synonyms?


This is more clearly the case because it seems that almost all conscious processes in the brain are deemed to be thoughts; and thus also deemed to be computations.


That not only includes the thought that 1 plus 1 equals 4 or that Snow is white; but also the rotation of a mental image in the mind, imagining the smell of a rose and so on. Then again, if rotating a mental image is classed as a thought, then why can't it also be classed as a computation? Especially since, in computationalism, they appear to by synonyms.


It all now depends on what we mean by the word 'computation'.


For a start, we can make the following claims:


i) All of a computer's processes are computations.


ii) Not all conscious human mental processes are computations.


Similarly, we can say:


iii) Many human mental processes are thoughts.


iv) No computer computations are thoughts (i.e. because thoughts have semantic content, intentionality, reference, etc.).


Rules Rule, Okay?


Is everything that happens consciously in the mind a computation? Or, perhaps more tellingly, is it all rule-governed? Jerry Fodor doesn't think so. He says that


some of the most striking things that people do – ‘creative’ things like writing poems, discovering laws, or, generally, having good ideas – don’t feel like species of rule-governed processes”.


The way Fodor puts his position doesn't really help matters Sure, such things may not “feel like species of rule-governed processes”. However, that doesn't mean that they aren't rule-governed processes. Far from it. This is the same phenomenological approach that's applied to free will. Here again most people “feel like” they have free will. Though, on close inspection, that claim (about what things feel like) amounts to almost nothing.


On Fodor's behalf it can now be asked what something's being rule-governed could possibly mean in the varied contexts of “writing poems, discovering laws, or, generally, having good ideas”. Are these disparate things really united by the following of rules (if at the non-conscious level)? Well that would depend on what's meant by the words “rules-governed”. 


We can take this somewhat further.


If writing poems, discovering laws and having good ideas are rule-governed, then these creative processes must be following some kinds of algorithm. And following on from that, they must be computable. What's more, this could mean that these processes are rote in some (or sometimes all) respects. Not in the sense of conscious acts of rote learning (or memory); but in the respect that the brain (or physiological system) has 'acquired' certain modules/faculties/etc. - or that such things are innate.


Haven't we simply moved from one technical term (i.e., 'rule-governed') to two more – 'algorithms' and 'computable'? After all, the words 'algorithms' and 'computations' can both be be cashed out in terms of following rules or being rule-governed.


So let's quote a definition of the word 'algorithm' as it's specifically used in reference to computers:


An algorithm is basically an instance of logic written in software by software developers to be effective for the intended 'target' computer(s) to produce output from given input (perhaps null).”


The mention of 'logic' (along with the very mechanical way of describing both what an algorithm does and how it comes to be) seems to make Fodor's earlier claim a little more convincing. Can we say that “an instance of logic” (or instances of logic) is required to “write poems, discover laws, or, generally, having good ideas”? Yes, we can! It's certainly the case that - in a limited sense - instances of logic/algorithms will be involved in these processes. The thing is, it surely can't be said that it's all about logic or algorithms. 

We can now say that logic or algorithms can be applied to some things (or to all things!) which aren't themselves logical or algorithmic.


Bad Computers


Kurt Gödel is often brought into the picture in order to show us what humans have and what computers (ostensibly) don't have.


For example, there's much talk about human brains having a "rule-free flexibility" and “unlimited mathematical abilities”. Thus there's also talk about “intuition” and “direct insight”. Of course these abilities can be seen to run free (conceptually speaking) of other things that computers don't have: such as qualia, emotions and suchlike. Then again, some would say that they all form a Gödelian package.


In concrete terms, there's the argument that humans can solve computational problems which computers can't solve. (Note that this hasn't got anything directly to do with computers not being able to write poems or have an orgasm.) This Gödelian claim that “no such limits apply to the human intellect” is, as Alan Turing argued in 1950, often “merely stated, without any sort of proof”.


In any case, various consequences are put forward as being a result of computers not having our (as it were) Gödel faculty. They include the fact that most computers crash for trivial reasons (e.g., because of faulty software or bad input). This is said to be due to the rule-fixated nature of computers; unlike human beings who have (as stated) a Gödel faculty.


All this is seen to be a direct result of computers needing a rule or algorithm for literally everything they do. More concretely, computers show no intuition or insight; and, in most cases, they don't learn from their mistakes or learn not to make mistakes. (Though this isn't true of all computers or even all aspects of each computer.)


Here again philosophers stress human uniqueness. Hubert Dreyfus, for example, argues that there are many examples of mental activity and behaviour that aren't a question of following rules. As Dreyfus himself puts it, computers lack the “immediate intuitive situational response that is characteristic of [human] expertise”. Consequently, persons 


“must depend almost entirely on intuition and hardly at all on analysis and comparison of alternatives”. 

Basically, some people argue that these Gödelian things can't be programmed into a computer.


The science writer John Horgan also tells us what computers are bad at. He writes:


“ Computers may excel at precisely defined tasks such as mathematics and chess.... but they still perform abysmally when confronted with the kind of problems – recognising a face or voice or walking down a crowded pavement – that human solve effortlessly.” (1996).


To state the obvious, the above are all programming problems. And they're programming problems because the number of variables the computer (as well as a person) needs to take into account when it comes to “recognising a face or voice or walking down a crowded pavement” are huge (or indefinite) in number. However, persons, it can be argued, don't (really?) need to be programmed in these cases: they react situationally. That is, persons can act upon - and react to - novel situations; even though (it can be said) these situations aren't entirely novel.


The philosopher George Rey also states the case that computers don't have a full logical package. He writes:


“Intelligence requires doing well under non-ideal conditions as well... But performing well under varied conditions is precisely what we know existing computers tend not to do. Decreasingly ideal cases require increasingly clever inferences to the best explanation in order for judgements to come out true; and characterising such inferences is one of the central problems confronting artificial intelligence...” (1986)


Here again we see that in all the cases in which a computer doesn't have a rule or algorithm to follow, then it doesn't know what to do. Of course you can create rules which tell a computer what to do when there are no existing rules; though that would depend on the nature of these meta-rules as well as upon the new conditions the computer is facing.


To sum up in the language of logic: computers aren't very good at “inferences to the best explanation” when they find themselves in “non-ideal conditions”.


Good Computers


Nonetheless, all sorts of new factors have been added to computers to simulate intuition or Gödelian intelligence. Such things as quantum computers based on “entangled qubits”, the introduction of random factors (e.g., annealing approaches) and hardware neural nets have been added into the computer-pot.


In any case, we already know about computer randomness. Even von Neumann machines can modify their own programmes (i.e., they can learn). That means that some of their responses (or output) are unpredictable. All this is achieved, in general, by equipping a computer with certain random elements which the computer can work on to produce outputs which are unexpected (i.e., which have moved beyond the programmed data). Indeed all this was theorised about by Turing as long ago as 1938.


Even with early Turing machines there was a requirement that such machines be able to follow their own rules or show what some people (at the time) called “initiative”. It was said that a programmer could engineer an element of randomness into the computer (or into the programme). That was what Alan Turing himself tried to do with his “Manchester computer” (1948-50). That meant that such randomness (as it were) would bring about “intuition” (or initiative) in the Turing machine – or even free will!


So when (not if):


i) A random element is introduced into a Turing machine (or a computer),


ii) and that computer manages to follow rules not laid down by the programmer,


iii) and as a result of that it solves its own problems,


iv) then that computer has learned something of its own accord or it even has “intuition”.


Thus there's no “appearance” about it! In this limited respect, the computer is free from its programmer. Or it has a “will” which is independent of its programmers. This isn't to say that it has either a mind or a (free) will in the human sense; though the independence (or freedom) is certainly real.


I think it would also be correct to say that a Turing machine “could have done something else” with the same input. That is, the same random change (mentioned by Turing) to the Turning machine can have different results in terms of what it produces. (E.g., a different calculation or even a different action – though a calculation is an action of sorts.)


More specifically in terms of today's computer programmes, there's what is called “machine learning” in which computer programmes have the ability to “self-modify”. These include programmes which themselves include ensemble learning, current-best-hypothesis learning, explanation-based learning, decision-tree learning, reinforcement learning, Bayesian statistical learning, instance-based learning and so on.


Despite all that, it's still said (by some) that none of these things (not even collectively) produce a Gödelian mind. That's because all these additions can still be reduced to Turing machines (along with their limitations). Sure, they make computers much better; though it's still said that they don't make them Gödelian.


References


Dreyfus, Herbert. (1992) What Computers Still Can't Do
Fodor, Jerry. (1975) The Language of Thought
Horgan, John. (1996) The End of Science
Rey, George. (1986) 'A Question about Consciousness'
Turing, Alan. (1939) 'Systems of logic defined by ordinals'
-- (1950) 'Computing Machinery and Intelligence', Mind LIX:433-460.


Monday, 10 August 2015

Advocates of Artificial Intelligence as Behaviourists


In extremely general terms, it can said that behaviourism was a response to the Cartesian (or, even more widely, Western) philosophical tradition in which behaviour, actions, and what is done by persons was seen as the outward expression of what goes on in the mind. Thus, in that sense, many of those who were initially involved in artificial intelligence (AI) were following in behaviourism's footsteps in that they believed that if a computer (or robot) behaved as if it had intelligence (or had a mind), then, almost by definition, it must actually be intelligent (or have a mind).



Many other currents in post-World War Two philosophy played-down the innards of the mind and, consequently, played-up behaviour. We had the work of the late Wittgenstein in which private mental states were seen as nothing more than "beetles in boxes". We also had Gilbert Ryle's The Concept of Mind and Quine saying that all there is to meaning is “overt behaviour”. And then functionalism (in the philosophy of mind) followed all that.


Specifically in terms of AI: it can fairly safely be said that many of the defenders of AI denied (or simply played-down) the distinction between actions (or behaviour) and what's supposed to be “behind” action (or behaviour). Thus if that "binary opposition" is rejected, then all we have to go on are the actions (or behaviour) of computers. And if computers pass the Turning test, then they're intelligent. Full stop. Indeed it's only a few behavioural steps forward from this to argue that computers actually have minds.


Of course if we follow this line to the letter, then it can be said that Zombies also have minds; as well as consciousness. And a thermostat has a little bit of a mind too.


If you think my last inclusion of a thermostat is ridiculous, then here's John Searle talking about the inventor of the term "artificial intelligence", John McCarthy. Searle writes:


“McCarthy says 'even a machine as simple as a thermostat can be said to have beliefs.' I admire McCarthy's courage. I once asked him 'What beliefs does your thermostat have?' And he said 'My thermostat has three beliefs – it believes it's too hot in here, it's too cold in here, and it's just right in here.'...” (1984)


Weak and Strong AI


This is where the distinction between strong and weak AI comes into play.


Weak AI proponents argue that it's unquestionably the case that some computers (or all computers?) act as if they're intelligent (or have minds). Though the operative words here are “as if”. Thus, they continue, it may take a little bit more time to develop computers which have "genuine intelligence" (whatever that is) or have minds. In other words, there has to be more than behaviour (or actions) to intelligence or mind.


Alan Turing himself put the weak AI position when he argued that it doesn't matter if a machine has a mind in the human sense: what matters is whether or not it can act in the way that human beings act – i.e. intelligently. (In those days that basically meant answering questions and solving mathematical problems.) In fact that was the crux of the Turing test which resulted in the Dartmouth proposal. Namely:


"Every aspect of learning or any other feature of intelligence can be so precisely described that a machine can be made to simulate it." (1955)


John Searle states the strong AI hypothesis (with all its behaviourist trappings) in the following way:


“The other minds reply (Yale). 'How do you know that other people understand Chinese or anything else? Only by their behaviour. Now the computer can pass the behavioural tests as well as they can (in principle), so if you are going to attribute cognition to other people you must in principle also attribute it to computers.'...” (1980)


Strong AI bites the bullet and denies the distinction between behaviour and mind/intelligence: 


If a computer acts (or behaves) as if it's intelligent (or has a mind), then it is intelligent (or has a mind). 

In other words, even though I've just written the words “as if”, there's no actual as if about it.


So why worry our pretty little heads about what must lie behind these expressions of mind or intelligence? In true behaviourist fashion, all we really need (or have!) is behaviour.


Sentience and Sapience


When it's said that there's no way that we can know (or tell) that a computer is sentient, it seems incredible. This is usually said about animals or even about other human beings. However, logically the same thing can indeed be said about computers; though, admittedly, not with the same force or implications.


Of course other human beings can tell us that they're sentient (even if they don't use the words “I'm sentient”). Animals, on the other hand, can hint (as it were) at their sentience. Then again, it's also possible that a future computer could do the same.


So let's get a little but more concrete about all this. 

I just mentioned that the display of intelligence (or mind) is deemed to be intelligence (or mind). And computers certainly display intelligence. For example, computers can solve problems, play games (e.g., chess), prove mathematical theorems, diagnose medical problems, use language and so on. What more do we want?


All these things are undoubtedly displays of intelligence; though are they also displays of mind? However, just as I mentioned the mind-behaviour binary opposition; so we have the intelligence-mind opposition too. That means we can construct an argument which takes us from behaviour to intelligence; and then from intelligence to mind. Thus:


         i) If a computer behaves intelligently,
        ii) then it is intelligent.
       iii) If computer is intelligent,
        v) then it must have a mind.


Prima facie, it does seem to be the case that when other people do intelligent things, then we (as good behaviourists) say that they're intelligent; whereas when the same actions are done by a computer it rarely evokes the same response (or, at the least, not exactly the same kind of response). After all, doesn't winning a game of chess match, etc. most people's criteria of a genuine display of intelligence?


References


Searle, John. (1984) Mind, Brains and Science. London: BBC Publications.
-- (1980) 'Minds, Brains, and Programs'. Behavioural and Brain Sciences 3.
J. McCarthy, M. L. Minsky, N. Rochester, C.E. Shannon. (1955) 'A Proposal for the Dartmouth Summer Research Project on Artificial Intelligence'

Holisms (2) – Donald Davidson


We have many versions of semantic holism in the philosophy of language and the philosophy of thought.

Take Donald Davidson.

Davidson believed that the

account of the truth-conditions for any one sentence is systematically related to the account of the truth-conditions for a whole range of other sentences”.

(We can now ask: How large must this range of other sentences be?)

We can clarify Davidson’s semantic holism in terms of the systematicity of a concept-expression and its possession. As Michael Luntley puts it:

The axiom governing any single concept expression does not itself specify the meaning of the expression; it does so only in the context of an overall theory that employs that axiom in a systematic manner to compute the meaning of whole sentences in which the concept expression figures.” (1999)

The starting point of Davidson’s theory is Frege’s Context Principle in which the meaning of an expression is determined by its context and place within a truth-valued sentence. Davidson extends Frege’s Context Principle to include other sentences in which the said expression occurs. It's from this group of sentences (large or small) that we can compute the expression’s meaning within the context of an overall theory.

We also have a well-known statement from Davidson on meaning-holism that's sometimes taken as a criticism of holism; though, at other times, simply taken as an explanation of the phenomenon.

In his paper, ‘Truth and Meaning’, Davidson writes:

If sentences depend for their meaning on their structure, and we understand the meaning of each item in the structure only as an abstraction from the totality of sentences in which it features, then we can give the meaning of any sentence (or word) only by giving the meaning of every sentence (and word) in the language.” (1967)

This may not mean that the individual speaker (or thinker) need understand (or know) every word and sentence in the language at the moment of his understanding: only that in effect the meaning of a word or sentence is ultimately determined by - and depends upon - the entire language (regardless of the complete understanding of the individual speaker or thinker).

For example, the possible moves in a game of chess are finite though very large. It needn't be the case that the individual chess-player understands (or knows) all the possible moves in the game of chess in order to make a single move (or understand the rules of chess generally).

The same with definitions.

There will come a time that the indefinite regress of definitions (or definitions of definitions) will come to end when the original definiendum comes back on the scene. However, it doesn't follow that the individual speaker (or thinker) need go through this indefinite regress in order to use (or understand) the word under definition - even if an indefinite regress is entailed by the original definition.

The individual speaker (or thinker) needs to begin somewhere; just as the epistemologist won't attempt to justify all his premises in an argument of justification. Even the semantic sceptic needs Wittgenstein’s ‘hinges’ to turn on in order to get his sceptical show on the road.

References

Davidson, Donald, 'Truth and Meaning' (1967)
Luntley, Michael, Contemporary Philosophy of Thought: Truth, World, Content (1999).