Lloyd Strickland is editor and translator of Leibniz’s Philosophical Papers (3 volumes, Oxford University Press, 2026). His current research has received project support from Emergent Ventures. In a 25+ year career, he has taught philosophy at Lancaster University, Manchester Metropolitan University (where he was Professor of Philosophy and Intellectual History), the University of Central Lancashire, and the University of Wales, Trinity Saint David. His research focuses on the history of western philosophy, especially the thought and reception of Gottfried Wilhelm Leibniz, on which he had published many journal articles and numerous books, including Leibniz on Binary: The Invention of Computer Arithmetic (MIT Press, 2022, with Harry Lewis), Leibniz's Key Philosophical Writings: A Guide (Oxford University Press, 2020, with Paul Lodge), Leibniz's Legacy and Impact (Routledge, 2019, with Julia Weckend), and Leibniz's Monadology (Edinburgh University Press, 2014).
A post by Lloyd Strickland
Philosophers have traditionally drawn a sharp boundary between the province of imagination and that of logic (see for example Malebranche 1997, 87-195; Spinoza 2002, 267-268). While logic is austere, rule-governed, and abstract, imagination is vivid, associative, and often unruly. If imagination has a place in philosophy at all, it is usually as a source of examples, heuristics, or perhaps error, not as something that could itself be subject to logic (but see Berto and Jago 2019, especially chapter 8; Canavotto, Berto, and Giordani 2020; Özgün and Schoonen 2022).
Gottfried Wilhelm Leibniz (1646—1716) disrupts this familiar contrast in a striking way. When outlining ‘universal mathesis’, a hypothetical higher order science of quantities and qualities, Leibniz describes it as ‘the science of imaginable things’ (2026b, 505) and goes so far as to call it ‘the logic of the imagination’ (2026b, 509). Leibniz is not saying here that imagination itself can be turned into a science, but rather is marking out a class of objects that fall under imagination—figures, magnitudes, forms, quantities, and their relations—yet can still be treated exactly. The ‘logic of the imagination’ is the logic proper to such objects.
To get a better idea of what he means, let’s start with Leibniz’s basic distinction between imagination and intellect. In common with other philosophers of his time, he takes imagination to be the faculty of producing and reproducing what has been perceived directly or indirectly, while intellect is concerned with demonstration, inference, and formal reasoning. Unlike the imagination, the intellect is capable of grasping purely intelligible and non-sensible things, such as those of metaphysics, moral philosophy, and theology. On this account, the imagination might seem to have little value to the philosopher.
Leibniz certainly cautions philosophers against over-reliance on the imagination. Many philosophical errors, he thinks, arise because people ‘are unable to go further than imagining things’ (Leibniz 2026a, 151). They mistake what can be pictured for what is possible, or what is vividly represented for what is true. Analogies may ‘affect the imagination’ without satisfying the mind (Leibniz 2026a, 389); ‘grand words and bold metaphors’ may produce ardour without understanding (Leibniz 2026a, 24). Left to itself, he says, imagination is not a reliable guide.
So how could there be a logic of what is imaginable? The answer lies in distinguishing imagination as a faculty from the objects that fall under it. Taken as a psychological power, imagination may be unreliable. But some objects of imagination have a determinate structure. Figures can be constructed, magnitudes compared, forms recognized, quantities measured. These are not merely private images passing through the mind but objects whose relations can be fixed and examined.
The ‘logic of the imagination’ is therefore not a logic of mental pictures as such, but a logic of sensible representations through which certain relations can be made available to thought. As Leibniz puts it, ‘Imagination generally revolves around two things, quality and quantity, that is, size and form, according to which things are said to be similar or dissimilar, equal or unequal’ (2026b, 509). Geometry provides the clearest illustration. When we reason about triangles, circles, or ratios, we often use diagrams. These diagrams fall under imagination: they can be seen, traced, and manipulated, although the reasoning is not reducible to what is seen. A proper demonstration, Leibniz insists, should not rely on the diagram alone. The diagram helps the imagination, but the proof must be framed so that its validity does not depend on the particular figure drawn.
Yet the diagram is not dispensable, as it plays a crucial role in guiding attention, organizing relations, and allowing us to survey a structure. In this sense, the figure belongs to a disciplined field of the imaginable: it is not a private mental picture, but an object whose relations can be constrained by construction and proof.
Leibniz also hopes to extend the lesson beyond geometry. Where objects cannot themselves be pictured (for example, being, cause, necessity, or justice), signs may still provide a sensible substitute for figures. This helps explain why Leibniz thinks many sciences should, as far as possible, make use of figures, formulas, or other well-designed signs: not because everything is literally spatial or visual, and not because metaphysical objects can become imaginable, but because reasoning often requires something that can be sensibly tracked. Images by themselves can mislead; signs and figures become useful when their relations are fixed by rules.
The phrase ‘logic of the imagination’ thus names a specific ideal: a system in which imaginable objects can be constructed, compared, combined, and transformed according to rules. In such a system, one could in principle reason ‘without any labour of the imagination or mental effort’, simply by manipulating characters according to a formal process (2026b, 356). But notice the paradox: even here, imagination is not entirely eliminated. It remains involved at a lower level, as the capacity to perceive and follow the manipulation of signs.
This helps explain why Leibniz places such importance on diagrams, tables, and structured representations even outside mathematics. In complex reasoning, the mind must navigate a labyrinth of considerations. Without guidance, it loses its way. What is needed, he says, is a ‘sensible thread’ that the imagination can follow. This thread may be a diagram, a sequence of symbols, or a classification scheme. It does not merely assist memory but structures inference, helping preserve order, completeness, and relations.
At this point, we can see more clearly why Leibniz contrasts imagination with distinct thought, and yet refuses to discard what falls under it. Thought, in its ideal form, is distinct, articulated, and independent of images. But human thought rarely achieves this directly. Instead, it often moves from confused perception through structured representations toward distinct understanding. Imaginable objects occupy a middle ground: they are more structured than raw sensation, but less transparent than pure intellect. This middle position is what makes them both dangerous and valuable: dangerous because what is vivid may be mistaken for what is clear, and valuable because, in the right cases, they can be constructed and ordered so as to support exact reasoning.
The notion of a ‘logic of the imagination’ is therefore best understood less as a rehabilitation of imagination in general than as a claim about a certain domain of objects. Some things that fall under imagination are not merely pictured; they can be constructed, compared, measured, and transformed according to rules. That is what makes them available for science. Signs then extend this availability: they allow us to preserve relations, order operations, and carry out reasoning that would otherwise exceed the mind’s unaided powers.
This idea has surprising contemporary resonance. In debates about mental models, diagrams, simulations, and visual reasoning, philosophers and cognitive scientists often ask whether such representations are genuinely cognitive or merely heuristic (see Johnson-Laird 1983; Pylyshyn 2003). Leibniz offers a third option: a diagram, model, or simulation is not reliable simply because it is vivid, but becomes reliable when there are rules for making it, reading it, and checking what follows from it (provided, Leibniz would add, that we do not mistake such representations for the ultimate structure of reality).
From this perspective, the opposition between imagination and logic begins to dissolve. There is no pure realm of logic untouched by representation, at least not for beings like us, and there is no reason to think that everything falling under imagination is inherently lawless. What matters is how representations are constructed, constrained, and integrated into reasoning.
Leibniz’s ‘logic of the imagination’ is thus neither a romantic elevation of images nor a reduction of thought to pictures. It is a programme for understanding how certain objects of imagination—figures, quantities, forms, and their relations—can become objects of exact reasoning. How far that programme can be extended is another question, and Leibniz himself recognized the difficulty. But the insight remains powerful: imagination is not philosophy’s junkyard, but instead is the domain of objects whose sensible form can be organized into structures that support thought. If that is right, then the most interesting question is no longer what imagination is, but what the objects of imagination can be made to show.
References
Berto, F. and Jago, M. 2019. Impossible Worlds. Oxford University Press.
Canavotto, I., Berto, F. and Giordani, A. 2020. "Voluntary Imagination: A Fine-Grained Analysis." Review of Symbolic Logic 15/2: 362-387.
Johnson-Laird, P. N. 1983. Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness. Harvard University Press.
Leibniz, G. W. 2026a. Philosophical Papers 1677—1686: Metaphysics, Natural Philosophy, Ethics, and Jurisprudence, L. Strickland (trans. and ed.). Oxford University Press.
Leibniz, G. W. 2026b. Philosophical Papers 1677—1686: Universal Language, Characteristic, Logic, Encyclopaedia, and General Science, L. Strickland (trans. and ed.). Oxford University Press.
Malebranche, N. 1997. The Search After Truth, T. M. Lennon and P. J. Olscamp (trans. and eds.). Cambridge University Press, 1997.
Özgün A. & Schoonen T. 2022. "The Logical Development of Pretense Imagination." Erkenntnis 89/6:1-27.
Pylyshyn, Z. W. 2003. Seeing and Visualizing: It's Not What You Think. MIT Press.
Spinoza, B. 2002. Complete Works. M. L. Morgan (ed), S. Shirley (trans.). Hackett.