Anyone who believes that Sinner's forehand is better than Laver's is Foolish.

Hyperintensionality¹ in Tennis and Other Domains 

Tennis appears simple: two players, a net, a ball, and a racket. Yet, behind its apparent linearity lie technical, historical, and even philosophical complexities. A revealing example is the discussion about “Rod Laver’s forehand” (a 1960s icon) versus “Jannik Sinner’s forehand” (a rising star in the 2020s).

At a glance, we might say they both play “the same stroke“—the forehand. However, at a more subtle level, this comparison raises a series of questions about the nature of the technical gesture’s identity, the role of historical and technological contexts, and even philosophical categories (such as intensionality and hyperintensionality).
In everyday language, when a commentator or a fan compares “Laver’s forehand” to “Sinner’s forehand,” they do so without much complication. The implicit assumption is that both are performing “the same stroke,” that is, a tennis gesture where the ball is hit from the body’s dominant side.
But as soon as we ask in what sense they are the same stroke, and we try to define all the parameters precisely, the possibility arises that, at a strictly conceptual level, “Laver’s forehand” and “Sinner’s forehand” are so different as to be almost incommensurable. In this article, we will explore how the philosophy of language and metaphysics can shed light on this apparent tension: on one hand, a single stroke (“the tennis forehand”), and on the other, numerous historical and individual variants that, when analyzed in detail, turn out to be radically different.
We will focus on the distinction between intensionality, extensionality, and hyperintensionality to understand why a concept might appear to be “the same” yet reveal essential differences upon closer analysis.

The ‘Forehand’: Between Poor and Rich Definitions

The Poor (Intensional) Definition  If we stop at a very generic definition, we might say: “The forehand is a tennis stroke executed by hitting the ball from the dominant side of the body.” This level of description is extremely broad: it makes no mention of grip, arm angle, stance, footwork, racket material, type of ball, playing surface, or the player’s biomechanics. All that matters is that the ball is hit from the dominant side.
Advantage: This definition is valid in any tennis context. If someone hits the ball from the dominant side, we can say they “played a forehand.”
Disadvantage: It flattens historical and technical differences. It does not capture the substantial evolution of the forehand between the 1960s and today, nor the peculiarities of each individual player.
The Rich (Intensional) Definition  At the opposite pole, imagine we compile a nearly exhaustive definition of “Laver’s forehand,” including:
Type of racket (wood, with certain natural strings, with specific weights and balances typical of the 1960s), predominant playing surface (grass and concrete of the time, with different speeds and bounces from today),
Laver’s biomechanics (height, physique, preparation style, arm speed, swing width, follow-through), training methods of the time, and so forth…

If we did the same for Sinner, we would obtain a list of highly specific parameters, with graphite rackets and modern materials, new generation balls, slower surfaces (in today’s circuit), grip, higher execution speed, and a technical-didactical baggage matured over decades of tennis evolution. At this point, the “exhaustive” definition of Laver’s forehand and that of Sinner could never coincide. They would be two properties too different to be identified in a single notion of “forehand” valid in all possible worlds: just change one single detail (materials, physicality, era) and we find ourselves in completely different situations.

Extension, Intension, and Hyperintension

The Extension 
The extension of a term is the set of objects to which that term applies. For example, the extension of “cat” in a given world is the set of all cats that exist in that world. In the sports context, we might say that the extension of “forehand” (in a general sense) is the set of all tennis strokes executed from the dominant side of the body, including those of Laver, those of Sinner, and every other tennis player. If we limit ourselves to the extensional level, there is no problem in saying that Laver’s forehand and Sinner’s forehand both fall into the same category, that is, into the same set of strokes: “the forehands.”
The Intension
Informally, the intension of a term is its “meaning” or the “conceptual content” that makes us identify certain objects as “cats” or certain strokes as “forehands.” When we say “forehand,” we refer, intensionally, to a tennis stroke that has certain fundamental characteristics (the body position, the racket from the dominant side, etc.). There are various degrees of richness in intension. A “poor” intension is enough to say: in every possible world, if I see a tennis player hitting the ball from the dominant side, it’s a forehand. But it specifies nothing about the material of the racket, the style, the amplitude of the movement, etc. Thus, a forehand from the 1960s and a forehand from 2025 remain “the same type of stroke” according to the generic intension.
The Hyperintension
We speak of hyperintensionality when two expressions, although necessarily equivalent (or, for predicates, necessarily coextensive) (i.e., valid for the same objects or true in the same way, in all possible worlds), are nevertheless not substitutable without altering the meaning or the way of presenting the object. A famous example: “2+2” and “2+2” and “log₂(16)” both have a value of 4 and, in every possible world, are 4. Yet, in a more refined context, we might want to distinguish those two statements because they convey different modes of presentation. Applied to tennis, “Laver’s forehand” and “Sinner’s forehand” might, at a certain level of abstraction, be considered the same property (stroke from the dominant side), and thus coincide under the general (thin) definition of “forehand.” However, we invoke hyperintensionality when we want to say that, even though they coincide in satisfying the general definition of “forehand,” they remain irreducibly different: that is, we cannot exchange “Laver’s forehand” with “Sinner’s forehand” as if they were identical.

To summarize, in logic and philosophy, we distinguish between intension and extension. While two expressions can share the same extension, and can even be necessarily equivalent, substitutability salva veritate fails ( i.e. You can’t say, preserving truth, ‘Clark Kent is flying’ when talking about Superman if you don’t know it or if it isn’t true.) in hyperintensional contexts. (Strictly speaking, the “Clark Kent/Superman” case is the standard illustration of intensional opacity in belief or knowledge reports; I use it here to flag how substitution can fail, and then the discussion moves to the stronger hyperintensional point.) In these contexts, the “way in which” content is presented, with all its nuances, connotations, and cognitive modes, becomes crucial. Below, we examine three examples unrelated to tennis, then apply what we’ve learned to the comparison between Sinner’s forehand and Laver’s.

Musical Example: Beethoven’s Ninth Symphony, Rock vs. Symphonic Versions 

Imagine two performances of Beethoven’s Ninth Symphony. 

Extensional: Both recordings refer to the same work, Beethoven’s Ninth, and satisfy the same intensional definition (a composition by Beethoven, with the same score, characterized by the famous “Ode to Joy” in the finale). 

Hyperintensional:  In the symphonic version, the performance strictly follows classical orchestral conventions, highlighting the original structure and traditional pathos of the work. In the rock version, the arrangement transforms the piece with electric instruments and modern rhythms, creating a mode of presentation that alters its aesthetic experience and cultural connotations. In a context where the “way in which” the work is performed is crucial—such as in musical criticism that considers originality, innovation, and historical fidelity,—the substitutability between the two versions fails, despite both designating the same work.

Artistic Example: A Cubist Work by Picasso vs. a Cubist Work by Braque 

Consider the concept of a “cubist work,” intensionally defined as: “An image created through the decomposition and recomposition of forms, where the representation of reality is fragmented and reorganized according to geometric principles.” 

Extensional: A painting by Pablo Picasso and one by Georges Braque both fall into this category: both are cubist works that, intensionally defined, display similar elements and serve the function of representing a fragmented reality. 

Hyperintensional:  Picasso’s approach has often been interpreted as radical and innovative, characterized by a certain revolutionary “aura” and color choices that defined an era. Braque’s work, while formally similar, carries a different sensitivity and expressive history, highlighted by his choice of stroke, materials, and conception of pictorial space. In the critical context where the “way in which” the work communicates and fits into its time is crucial, the substitutability between the two works—despite sharing the same basic definition—is problematic.

Mathematical Example: “2+2=4” vs. “√16=4” In mathematics, consider two expressions: 

Expression A: “2+2=4”

 Expression B: “The square root of 16 is 4” 

Extensional: Both expressions designate the number 4, and in a purely numerical context, one might consider them interchangeable. 

Hyperintensional:  The expression “2+2=4” is a necessary truth of elementary mathematics, derived from fundamental arithmetic rules. The expression “√16=4” refers to the definition of the principal root of a positive number, which, while conventionally 4, hides the peculiarity that, in other contexts (such as quadratic equations), the number −4 plays a similar role. In certain epistemic or educational contexts, the “way in which” the number 4 is presented—whether as the sum of 2 and 2 or as the square root of 16—can influence the understanding or perception of mathematical truth. Thus, substitutability salva veritate (“preserving truth”) is not entirely neutral when considering the cognitive and educational modes with which these concepts are learned and conveyed. For instance, one might know precisely that 4 equals 2+2 but be unaware that it equals √16.

Application to Tennis: Sinner’s Forehand vs. Laver’s

 In tennis, the intensional definition of the “forehand” might be formulated as follows:  “The stroke executed with the dominant hand, through a fluid movement of the racket, aimed at directing the ball into the opponent’s court.” 

Extensional: Both the forehand executed by Jannik Sinner and that by Rod Laver meet this definition and, observed as facts, perform the same function in a match. So both are forehand 

Hyperintensional: 
Laver’s forehand is expressed in a different historical and technological context: wooden rackets, traditional training methodologies, and an aesthetic sensibility typical of his time. 
Sinner’s forehand arises in an era of technological innovations, with advanced materials, video analysis, and modern athletic preparations that influence its technique and effectiveness.  Although both are extensionally “forehands,” the modes of execution, cultural context, and technologies used confer on each a different “way of presenting” themselves.
Consequently, in a hyperintensional critical evaluation, neutral substitutability—the idea that they can be judged identically—fails. (This is exactly why “better” is not settled by thin sameness: it forces a choice of metric and background assumptions.)

The Other Side of the Swing: Those who dismiss these as mere philosophical nuances or needless subtleties are MISTAKEN

Many rightly argue that a stroke from the 1960s, with wooden rackets, different balls, and fast and various surfaces, has a biomechanics more distant from a modern backhand than a contemporary two-handed backhand is from a baseball “swing.” Why? Because while modern baseball has vast differences (bat, rules, game objectives), by observing only the segment of the gesture (the torso rotation, the way of transferring weight, the tool’s position), we might discover biomechanical analogies closer to a contemporary two-handed backhand than to a one-handed backhand of the 60s.

This paradox highlights that: remaining on a generic description (“stroke from the non-dominant side“) does not allow us to grasp all the differences that matter to the contemporary tennis player. Over-enriching the definition reveals that we are talking about “two very different strokes,” rather than a historical variant of the same stroke. The philosophy of language intervenes precisely to tell us that a term like “backhand” can work well in a practical context (defining an action by Laver and Sinner), but, at a conceptual level, if we claim to be talking about the same stroke and it can be measured in all details, we risk falling into contradictions or excessive simplifications.

FAILURE OF REDUCTIONISM

Someone, thinking like Timothy Williamson, might say: “No problem, just analyze with infinite precision the physical components of the two strokes and we could give an absolute value to Sinner’s forehand and Laver’s, beyond the differences” (super-rich intension). 

Not really. Indeed, it is highly unlikely that Sinner, with his type of talent, would have excelled in the 1960s, and vice versa: surely both would have had excellent eye-hand coordination in different historical periods, i.e. they would have been great players, but probably would not have excelled with their characteristics if they had exchanged eras.

One might even go further and consider that the physical aspect, the phenotype, would have varied: perhaps Sinner in the sixties would have struggled to sustain his physicality (1.93m), while Laver, if born at the beginning of the 2000s, would have become taller and more powerful. Thus, the issue is probably radical: Sinner in the ’60s would not have existed, as we know him, and so would Laver in the 2000s: physically. Like it or not, the Timothy Williamsons of today’s sports debate (if only we had more of them!)

Take Home
 The examples of Beethoven’s Ninth (rock vs. symphonic versions), the cubist works of Picasso and Braque, and the expressions “2+2=4” vs. “√16=4” illustrate how mere extensional identity and a superficial intensional definition are not sufficient in hyperintensional contexts. In such contexts, the “way in which” meaning is presented and contextualized plays a crucial role in determining the interpretive value of a proposition. Similarly, in tennis, while recognizing that Sinner’s forehand and Laver’s satisfy the same basic definition, the hyperintensional differences—technical, historical, and cultural—prevent a direct and neutral comparison. 
Therefore, uncritically asserting the superiority of one forehand over the other, without considering these nuances, amounts to neglecting the complexities of meaning and experience. 

Anyone who believes Sinner’s forehand is better than Laver’s is foolish because they ignore the rich ways in which the gesture is imbued with different meanings in their respective contexts.

An example, widely accepted among experts without debate, from outside of dance: Pavlova's grand jeté vs. Copeland's.

The Intensional Definition Intensionally, the grand jeté can be defined as:
"A choreographic jump in which the dancer, pushing forcefully from the ground, extends their legs in the air in a wide and continuous movement, symbolizing lightness and elegance."

This abstract definition captures the essential properties of the movement: the push, the extension of the legs, and the aesthetic aspect that transpires.

The Extension Extensionally, every execution of the grand jeté—regardless of the era or the performer—falls into the category of the grand jeté. Thus, the jump performed by the famous Anna Pavlova and that performed today by Misty Copeland (or another modern prima donna) both satisfy the same functional description.

The Hyperintensional Difference Despite the identical intension and, in some respects, extensional equivalence (both jumps “are grand jetés”), Pavlova's execution and that of a modern dancer like Copeland are not interchangeable in a hyperintensional critical context. Here’s why:

Technical and Material Context: The training techniques, body knowledge, and even the clothing and surfaces on which dancing occurs are radically different. Pavlova, representing an era where technique was shaped by classical aesthetic models, performed the grand jeté under conditions and with methodologies that today would seem almost artisanal. Copeland, on the other hand, performs in a context of technical and scientific innovations, where biomechanics and support technology have revolutionized movement.

Cultural and Historical Context: Pavlova's interpretation of the grand jeté carries with it a historical and emotional aura, an "aura" that stems from being emblematic of an era and an aesthetic now irrevocably tied to the tradition of classical ballet. The modern performance, while respecting the same definition, is contextualized in a global landscape where cultural influences, artistic innovation, and contemporary techniques play a central role.

Modes of Perception and Evaluation: If in a purely intensional context we substituted Pavlova's “grand jeté” with that of Copeland, the truth value would not change: both performances are grand jetés. However, in a hyperintensional context—for example, in specialized criticism or in the formation of an aesthetic taste—the manner in which the movement is realized, the “how” it is perceived and evaluated, varies substantially. The historicity, technique, and personal interpretation are elements that are not exhausted in the simple abstract definition. i.e., in Pavlova's time Copeland's Jeté would have been considered incorrect, simply.

Conclusions The example of the grand jeté in dance highlights how, even if two executions can be intensionally and extensionally identical, hyperintensional differences prevent a neutral and salva veritate substitution. Just like in tennis, where Rod Laver's forehand and Jannik Sinner's respond to the same definition but cannot be judged interchangeably due to historical and technical contexts, in dance one cannot absolutely state that Pavlova's classical execution is "superior" or "inferior" to the modern one by Copeland without taking into account the rich hyperintensional nuances.

Therefore, those who insist on uncritically proclaiming the superiority—in an absolute sense—of the grand jeté performed according to classical tradition, ignoring the complexity of execution and perception contexts, demonstrate a reductive and philosophically unfounded view. In hyperintensional terms, anyone who believes Pavlova's grand jeté is better than Copeland's is a fool.

By Andrea Scaglione

📖 Further Reading: Impossible Worlds by Francesco Berto & Mark Jago

Tennis, like philosophy, is often a game of perspectives—what seems simple on the surface can reveal hidden complexities upon deeper examination. The debate surrounding Sinner’s forehand and Laver’s, much like discussions on hyperintensionality, is not just about comparing strokes but about understanding the contextual frameworks in which they exist.

In Impossible Worlds, Berto and Jago explore how different interpretations of reality can coexist, challenging the notion that we can objectively compare entities across radically different contexts. Just as Sinner and Laver’s forehands belong to distinct technological, cultural, and biomechanical realities, Berto and Jago argue that our understanding of “possible worlds” must account for the nuances that separate them.

📚 For those interested in how philosophy can deepen our perception of tennis, sport, and beyond, Impossible Worlds offers a compelling parallel to the way we think about greatness in different eras.

🔗 Impossible Worlds on Goodreads