On Wittgenstein's family resemblance and machine learning

Question

Wittgenstein proposed in his later philosophy the concept of family resemblance to describe groups which cannot be defined by a single (or simple set) of common features but instead display (from the SEP):

There is no reason to look, as we have done traditionally—and dogmatically—for one, essential core in which the meaning of a word is located and which is, therefore, common to all uses of that word. We should, instead, travel with the word’s uses through “a complicated network of similarities overlapping and criss-crossing” (PI 66). Family resemblance also serves to exhibit the lack of boundaries and the distance from exactness that characterize different uses of the same concept. Such boundaries and exactness are the definitive traits of form—be it Platonic form, Aristotelian form, or the general form of a proposition adumbrated in the Tractatus. It is from such forms that applications of concepts can be deduced, but this is precisely what Wittgenstein now eschews in favor of appeal to similarity of a kind with family resemblance.

Now consider a typical pattern recognition/machine learning problem: We have a set of photos some of which are of trees and some which are not. We want to classify them into two groups "photos of trees" and "photos of other things". No single criterion ("trunk/no trunk", "leaves/no leaves" , "green/not green") exists for deciding whether the photo is that of a tree or not, but a suitable pattern recognition algorithm such as a neural network or support vector machine will easily be able to separate the two classes of photos.

The thing about how such algorithms work: there is a sharp boundary between the two classes, it's just that it's too complicated to represent with a simple function or set of if-then rules. It can only be represented in a high dimension feature space which can't be visualized in 2D or 3D, but a sharp decision boundary still exists, otherwise the algorithms wouldn't work.

My questions:

• Based on this consideration, does Wittgenstein's family resemblance really boil down to a lack of sufficient knowledge?

• Is Wittgenstein wrong when he says that no boundaries or exact distances can be described for such notions? They can, they are just too complex to be described in a simple fashion?

• Or are there examples of family resemblance where no sharp boundary can be found no matter how complex the representation we use?

Answer 1

The answers to your questions are not going to be completely settled because they rely on specific theories of philosophy of language and language's relation to philosophy of mind. One very interesting thing to note before any explanations, however, is that Wittgenstein himself did not believe that machines could think. Additionally, he believes thinking "is centered around the human being; thus decidedly anthropocentric" as Obermeier points out. From Philosophical Investigations:

Aber eine Maschine kann doch nicht denken! - Ist das ein Erfahrungssatz? Nein. Wir sagen nur vom Mensch, und was ihm, ähnlich ist, es denke. (PI 360)

But surely a machine cannot think! - But is that an empirical statement? No. We say only of a human being and what is like one that it thinks. (PI 360)

He feels that we know a priori that machines cannot think because thinking is only something humans, or things like humans, do. He believes it would be a categorical mistake to think that machines can think. To that extent, it would most likely be the case that he would reject arguments for or against his theories of language and thought based off of artificial intelligence programs. However, one of the difficulties in his philosophy is that he was cryptic even to the people close to him and nobody knows for sure what he would or would not agree with. Maybe he would be so impressed with AI programs today that he would have a complete change of mind on his ideas, much the same way he changed his mind on the Tractatus; at this moment, we don't know what he would think and all we are left with is what he wrote.

Central to later Wittgenstein is his idea that meaning is use. The idea employed in family resemblance in relation to meaning being use is the idea that we cannot write down a perfect definition of game, however we can still know perfectly well when someone is referring to a game and when they are not. He argues that even though, to use his example, "game" can be used and understood in language, there is not one complete definition of the word.

Und so können wir durch die vielen, vielen anderen Gruppen von Spielen gehen. Ähnlichkeiten auftauchen und verschwinden sehen. Und das Ergebnis dieser Betrachtung lautet nun: Wir sehen ein kompliziertes Netz von Ähnlichkeiten, die einander übergreifen und kreuzen. Ähnlichkeiten im Großen und Kleinen. (PI 66)

And we can go through the many, many other groups of games in the same way, can see how similarities crop up and disappear. And the upshot of these considerations is: we see a complicated network of similarities overlapping and criss-crossing: similarities in the large and in the small. (PI 66)

To Wittgenstein, the problem does not boil down to epistemology. He believes that there absolutely does not exist a concrete definition; he does not believe that one exists but some people may just be ignorant to it. This view is based off of his theory that meaning is use. The word "game" derives its meaning from how people use it and people use it in such a way that it cannot be pinned down by one definition, instead its uses exhibit a family resemblance. From the SEP:

So different is this new perspective that Wittgenstein repeats: “Don’t think, but look!” (PI 66); and such looking is done vis a vis particular cases, not generalizations. In giving the meaning of a word, any explanatory generalization should be replaced by a description of use.

This view of language is in sharp contrast with theories such as the canonical Fregean/Russellian theory of meaning. Generally, Fregean/Russellian theories of meaning hold central the idea that propositions hold meaning and are somehow semantically related to the world. The idea that language, propositions, and definitions are well defined in central to this view. Even Wittgenstein shared this idea in his early days in the Tractatus:

2. What is the case—a fact—is the existence of states of affairs.
3. A logical picture of facts is a thought.
4. A thought is a proposition with a sense.

Ultimately, philosophers who subscribe to semantic theories of meaning would argue that Wittgenstein is wrong when he says that no boundaries can be formed. Inevitably they run into problems such as the Sorites paradox. These questions are still central questions in the philosophy of language and they do not yet have any answers with full consensus. What is clear, however, is that Wittgenstein believed that there are some words that cannot have a clear logical boundary condition (his example is "game") and philosophers on the other side of the theory of meaning, such as Davidson believe that we can.

The Sorites paradox poses one great example of words that seem to have no clear boundary condition and as such it is a central place where this discussion comes to light. From the SEP:

A challenge posed for the epistemic theorist's response is that on such a view the commonly supposed connection between meaning and use appears to be severed. While the margin-for-error principle discussed in Williamson (1994) might serve to explain how we could be ignorant of the postulated sharp boundaries were they to exist, it might be thought that since our use of vague terms does not draw sharp boundaries they could not possess them given the generally accepted connection between meaning and use.

As stated, he did not believe that machines could think. However if we extend his ideas to a philosopher who does believe that machines can think, she would argue that there exist some decision boundaries which a machine could never perfectly recognize, such as the decision boundary between games and non-games. Those philosophers who reject meaning as use would argue that a sufficiently strong AI program would always be able to find a decision boundary if the meaning of the criterion is well defined.

(The translation and source text I used for PI is Wiley-Blackwell 4th edition)

Answer 2

They can easily separate two types of photos because they employ approaches explicitly inspired by our brain function, in other words they repeat, in a simplified form, what we originally did in making such classifications. Does it mean that the pattern is "mind-independently" there? The answer depends on one's philosophical preferences, and there is a perennial debate about "invented" vs "discovered", nominalism vs realism, etc.

But I suspect that these algorithms will have trouble with pictures of certain shrubs and bushes, just like a human would. The official botanical definition, "a woody plant at least 5 metres high, with a main stem the lower part of which is usually unbranched", does not strike me as particularly sharp either. Sufficiently trained neuro-net will probably classify Pluto differently than Earth and Mars, but it is hard to see the distinction between planets and dwarf planets as sharp or written into the stars. To the extent that we can take it as evidence for philosophical positions the success of fuzzy methods in pattern recognition would rather indicate that Wittgenstein was right: our classifications rely on multiple resemblances and similarity measures, involve arbitrary choices and produce blurred results. "Sharp boundaries" are mostly degenerations or idealizations.

Wittgenstein himself in the Blue Book (1933-35) describes human learning process in terms reminiscent of training a neuro-net, before there was any hint of (artificial) neuro-nets:

"There is a tendency rooted in our usual forms of expression, to think that the man who has learnt to understand a general term, say, the term " leaf", has thereby come to possess a kind of general picture of a leaf, as opposed to pictures of particular leaves. He was shown different leaves when he learnt the meaning of the word "leaf "; and showing him the particular leaves was only a means to the end of producing "in him" an idea which we imagine to be some kind of general image." [quoted from Universals and Family Resemblances by Bambrough]

What is somewhat implicit in neuro-nets becomes explicit in clustering algorithms, also popular in pattern recognition. They are as if designed to Wittgenstein's family resemblance specifications:

"Clustering or cluster analysis involves assigning data points to clusters (also called buckets, bins, or classes), or homogeneous classes, such that items in the same class or cluster are as similar as possible, while items belonging to different classes are as dissimilar as possible. Clusters are identified via similarity measures. These similarity measures include distance, connectivity, and intensity."

One (which could be a neuro-net) selects "features", and groups objects based on the totality of their values, clustering then amounts to finding cluster centers, "paradigmatic representatives", around which other objects "cluster". Once those are found, whether in 3D or higher dimensional space, boundaries can be drawn between the clusters. This would work pretty much always, not just when we "see" a boundary, as with trees and non-trees. There are quality measures, of course, and they can be high or low. Shall we say that the boundary is "really" there whenever high quality clustering can be achieved? Or shall we say, a la Kant, that we (or the neuro-net) "put" it there by specifying the features and making other non-unique choices that such algorithms make? Even in visual 3D "sharp boundaries" are not as sharp as people feel:

"Edge detection is a critical part of many computer vision systems. Ideally, edges correspond to object boundaries, and therefore edge detection provides a means of segmenting the image into meaningful regions. However, the definition of what constitutes an edge is rather vague, heuristic, and even subjective." [from Fuzzy Models and Algorithms for Pattern Recognition and Image Processing]

Indeed, it is to account for this vagueness that "crisp" k-clustering algorithms were replaced with fuzzy c-clustering algorithms:

"The fuzzy clustering method assigns each training vector a set of membership values, one for each cluster, rather than assigning each training vector to one and only one cluster. Since it is more realistic, several research results have indicated that it is superior to the hard clustering algorithm." [from Image Segmentation by Hsieh et. al.]

Fuzzy "membership values" mean that each object is treated as belonging to every cluster, but to varying degrees. In the end the clustering can be hardened by assigning a cluster by maximum membership, and it turned out that retaining fuzziness in the process often leads to better sharp clusters.

Answer 3

I love the question and the answers by @Conifold and @Not_Here.

Suppose a machine learns to classify objects as either capable of thinking or not capable of thinking. Trained in the 80s and presented with the image of another computer it classifies it as not-capable of thinking. Trained again in the year 2100 and presented with the image of another computer it now classifies it as capable of thinking.

What has the machined learnt? a definition of what constitutes thinking or the legitimate use of the word "thinking" as it evolves in time?

Suppose a machine learns to classify images as representing trees or not-trees. It has learnt a function, say even a sharp boundary. But in what sense is that a definition of a thing?

Does it mean that it classifies images into trees or not-trees with 100% accuracy? What does it even mean for it to have 100% accuracy at such a task?

I think we can suppose a lower than 100% accuracy for non-trivial problem domains. Say it is 97% accurate, then what about the remaining 3%? it would appear that some members of the community of speakers disagree with the machine. will it learn from them or even teach them as it interacts with them? will said boundary change over time?

And what is that boundary anyway? suppose it is determined by some arbitrary threshold, say a score of 50%, and suppose the machine is presented with some input for which the computed score is 50%, and another input for which the score is 49.999%.

Suppose these inputs are pictures of school-buses. In what sense is it justified to determine that the first picture depicts a school-bus and the second does not?

What if the second picture is obtained from the first by slightly changing the value of a particular pixel in a way that most humans will not even perceive?

This example corresponds to an interesting phenomena called "adversarial" images that confuse neural networks but not humans:

Is the machine justified in using the boundary to declare a bus in the first case and not-a-bus in the second case?

Or would it be more justified in responding "I am not sure"?

If so, then in what sense is the sharpness of the boundary interesting or relevant?