Truthmaker theory

Last updated

Truthmaker theory is "the branch of metaphysics that explores the relationships between what is true and what exists". [1] The basic intuition behind truthmaker theory is that truth depends on being. For example, a perceptual experience of a green tree may be said to be true because there actually is a green tree. But if there was no tree there, it would be false. So the experience by itself does not ensure its truth or falsehood, it depends on something else. Expressed more generally, truthmaker theory is the thesis that "the truth of truthbearers depends on the existence of truthmakers". A perceptual experience is the truthbearer in the example above. Various representational entities, like beliefs, thoughts or assertions can act as truthbearers. Truthmaker theorists are divided about what type of entity plays the role of truthmaker; popular candidates include states of affairs and tropes.


Truthmaker maximalism is the thesis that every truth has a truthmaker. An alternative view is truthmaker atomism, the thesis that only atomic sentences have truthmakers. Truthmaker atomism remains true to the basic intuition that truth depends on being by holding that the truth of molecular sentences depends on the truth of atomic sentences, whose truth in turn depends on being. All non-maximalist positions accept that there are truthmaker gaps: truths without truthmakers. Opponents have tried to disprove truthmaker theory by showing that there are so-called deep truthmaker gaps: truthbearers that not only lack a truthmaker but whose truths do not even depend on being. Various principles governing the truthmaking relation have been proposed in order to make the intuitions about the role and nature of truthmaking explicit. Truthmaker theory is closely related to the correspondence theory of truth, but not identical to it. Truthmaker theory has been applied to various fields in metaphysics, often with the goal of exposing ontological cheaters: theorists who are committed to certain beliefs but do not or cannot account for the existence of a truthmaker for these beliefs.


In Truth-Makers (1984), Kevin Mulligan, Peter Simons and Barry Smith introduced the truth-maker idea as a contribution to the correspondence theory of truth. [2] Logically atomic empirical sentences such as "John kissed Mary" have truthmakers, typically events or tropes corresponding to the main verbs of the sentences in question. Mulligan et al. explore extensions of this idea to sentences of other sorts, but they do not embrace any position of truthmaker maximalism, according to which every truthbearer has a truthmaker.

This maximalist position leads to philosophical difficulties, such as the question of what the truthmaker for an ethical, modal or mathematical truthbearer could be. Someone who is deeply enough committed to truthmakers and who simultaneously doubts that a truthmaker could be found for a certain kind of truthbearer will simply deny that that truthbearer could be true. Those who find the Parmenidean insight sufficiently compelling often take it to be a particularly enlightening metaphysical pursuit to search for truthmakers of these kinds of propositions.

Another difficulty for the claim that every truthbearer has a truthmaker is with negations of existential propositions (or, equivalently, universal propositions). In the example of asking if unicorns exist, proposals include the totality of all things, [3] or some worldly state of affairs such as x1's not being a unicorn, x2's not being a unicorn, ..., and everything's being x1, or x2, or ... (the latter suggestion is due to Richard M. Gale).

David Lewis has proposed a more moderate version of the truthmaker theory on which truthmakers are only required for positive propositions (e.g., there must be a truthmaker for the proposition that there are horses, but not for the equally true proposition that there are no unicorns). What makes a negative proposition p true is the lack of a falsemaker for it, i.e., the lack of a truthmaker for the negation of p. Thus what makes it true that there are no unicorns is the lack of a truthmaker for the proposition that there are unicorns, i.e., the lack of unicorns. [4]

Truthmaker theorists differ as to what entities are the truthmakers of various truthbearers. Some say that the truthmaker of the proposition that Socrates is sitting (assuming he is) is "Socrates' being seated" (whatever exactly that might turn out to be on the correct ontology) and in general the truthmaker of the truthbearer expressed by a sentence s can be denoted by the participial nominalization of s. Others will say that the truthmaker of the proposition that Socrates is sitting is just "Socrates" himself. In any case, the truthmaker is supposed to be something concrete, and on the first view is that whose existence is reported by the truthbearer and on the second view is that which the truthbearer is about.

While the existence of truthmakers may seem an abstruse question, concrete instances are at the heart of a number of philosophical issues. Thus, J. L. Mackie has argued that the truthmakers of moral claims would be "queer entities", too strange to exist, and hence all moral claims are false. [5] Alternatively, a divine command metaethicist may insist that the only possible candidate for a truthmaker of a moral claim is a command from a perfect God, and hence if moral claims are true and a truthmaker theory holds, then God exists. Thus the disagreement between various metaethical schools is in part a disagreement over what kinds of truthmakers moral claims would have if these claims were true and over whether such truthmakers exist.

Truthmaker gaps

A truthmaker gap is a truth that lacks a truthmaker. Truthmaker maximalists hold that there are no truthmaker gaps: every truth has a truthmaker. [6] Truthmaker non-maximalists, on the hand, allow that some truths lack a truthmaker. Truthmaker non-maximalists still count as truthmaker theorists in the sense that they hold onto the core intuition of truthmaker theory that truth depends on being. [1]

Atomic truthmaker theories, which have their root in logical atomism, are examples of such a position. According to them, only atomic sentences have truthmakers. [7] A sentence is atomic or simple if it does not have other sentences as proper parts. [8] For example, "The sun is shining" is an atomic sentence while "The sun is shining and the wind is blowing" is a non-atomic or molecular sentence since it is made up of two sentences linked by the conjunction "and". In propositional calculus molecular sentences are composed through truth-functional logical connectives. [9] Molecular sentences lack truthmakers according to atomic truthmaker theories and therefore constitute truthmaker gaps. But the fact that the truth values of molecular sentences depends on the truth values of its constituents (if only truth-functional connectives are allowed) ensures that truth still depends on being. [7]

This type of truthmaker gap has been called a "shallow" truthmaker gap. Shallow truthmaker gaps are contrasted with "deep" truthmaker gaps. Deep truthmaker gaps are truths that do not depend on being. [1] They therefore pose a challenge to any type of truthmaker theory. In terms of possible worlds, a deep truthmaker gap is a proposition that is true in one possible world and false in another where there is no difference between these two worlds beside the truth value of this proposition. Critics of truthmaker theory have tried to find deep truthmaker gaps in order to refute truthmaker theory in general. [10] [11]

Truthmaking principles

Various principles governing the truthmaking relation have been proposed. [1] [6] They aim to make our intuitions about the role and nature of truthmaking explicit.

The entailment principle states that if entity e is a truthmaker for proposition p and p entails proposition q then e is also a truthmaker for q.

The conjunction principle states that if entity e is a truthmaker for the conjunction of proposition p and proposition q then e is also a truthmaker for p.

The disjunction principle states that if entity e is a truthmaker for the disjunction of proposition p and proposition q then e is either a truthmaker of p or a truthmaker of q.

These principles seem intuitively to be true but it has been shown that they lead to implausible conclusions when combined with other plausible principles. [12] [13]

Relation to the correspondence theory of truth

The correspondence theory of truth states that truth consists in correspondence with reality. [7] Or in the words of Thomas Aquinas: "A judgment is said to be true when it conforms to the external reality". [14] Truthmaker theory is closely related to correspondence theory; some authors see it as a modern version of correspondence theory. [15] The similarity between the two can be seen in the following example definitions:

But despite the obvious similarities there are a few important differences between truthmaker theory and correspondence theory. For one, correspondence theory aims to give a substantive account or a definition of what truth is. Truthmaker theory, on the other hand, has the goal of determining how truth depends on being. [16] So it presupposes the notion of truth instead of defining it. While it seems natural to combine truthmaker theory with a correspondence-conception of truth, this is not necessary. [1] Another difference between the two theories is that correspondence is a symmetric relation while the truthmaking relation is asymmetric. [17]


Arguments based on truthmaker theory have been used in various fields to criticize so-called "ontological cheaters". [17] [7] An ontological cheater is someone who is committed to a certain belief but does not or cannot account for the existence of a truthmaker for this belief. If such a belief was true then its truth would be brute or free-floating: it would be disconnected from any underlying reality. This is opposed to the basic intuition behind truthmaker theory that truth depends on being. [18]

Defense strategies open to theorists accused of ontological cheating include denying that the proposition in question is true, denying the legitimacy of truthmaker theory as a whole or finding a so-called "proxy" or "trace" within their preferred ontology. [19] A proxy or trace, in this context, is an entity that can act as a truthmaker for the proposition in question even though it is not obvious that this proposition is about this entity. An example of such a strategy in actualism is to use actual but abstract objects as proxies for propositions about possible objects, whose existence is denied by actualism. [20]


One such criticism has been leveled against presentism. Presentism is the view that only the present exists, i.e. that past entities or events lack existence. [21] Eternalism is the opposite of presentism. It holds that past, present and future existents are equally real. Beliefs about the past and the future are very common, for example the belief that dinosaurs existed. Providing a truthmaker for this belief is quite straightforward for eternalists: they may claim that the dinosaurs themselves or facts about dinosaurs act as truthmakers. This is unproblematic since, for eternalists, past entities have regular existence. This strategy is not available to the presentists since they deny that past entities have existence. [1] But there seem to be no obvious truthmaker candidates for this belief among the present entities. The presentist would have to be labeled an ontological cheater unless he can find a truthmaker within his ontology. [18]


Phenomenalism has been subjected to a similar criticism. [22] Phenomenalism is the view that only phenomena exist. It is opposed to the common sense intuition that the material objects we perceive exist independently of our perceptual experiences of them and that they even exist when not perceived. [23] This includes for example the belief that valuables locked inside a safe do not cease to exist despite the fact that no one observes them in there, which would, of course, defeat the purpose of locking them inside in the first place. The phenomenalist faces the problem of how to account for the truth of this belief. [1] A well-known solution to this problem comes from John Stuart Mill. He claimed that we can account for unperceived objects in terms of counterfactual conditionals: It is true that the valuables are in the safe because if someone looked inside then this person would have a corresponding sensory impression. But this solution does not satisfy the truthmaker theorist since it still leaves open what the truthmaker for this counterfactual conditional is. It is not clear how such a truthmaker could be found within the phenomenalist ontology. [1] [24]


Actualism is the view that everything there is actual, i.e. that only actual things have existence. [20] Actualism contrasts with possibilism, the view that there are some entities that are merely possible. Actualists face the problem of how to account for the truthmakers of modal truths, like "it was possible for the Cuban Missile Crisis to escalate into a full-scale nuclear war", "there could have been purple cows" or "it is necessary that all cows are animals". Actualists have proposed various solutions, but there is no consensus as to which one is the best solution. [25] [26]

A well-known account relies on the notion of possible worlds, conceived as actual abstract objects, for example as maximal consistent sets of propositions or of states of affairs. [27] A set of propositions is maximal if, for any statement p, either p or not-p is a member. [28] Possible worlds act as truthmakers for modal truths. For example, there is a possible world which is inhabited by purple cows. This world is a truthmaker for "there could have been purple cows". Cows are animals in all possible worlds that are inhabited by cows. So all worlds are the truthmaker of "it is necessary that all cows are animals". This account relies heavily on a logical notion of modality, since possibility and necessity are defined in terms of consistency. This dependency has prompted some philosophers to assert that no truthmakers at all are needed for modal truths, that modal truths are true "by default". [25] [29] This position involves abandoning truthmaker maximalism.

An alternative solution to the problem of truthmakers for modal truths is based on the notion of "essence". [26] [30] Objects have their properties either essentially or accidentally. The essence of an object involves all the properties it has essentially. The essence of a thing defines its nature: what it fundamentally is. On this type of account, the truthmaker for "it is necessary that all cows are animals" is that it belongs to the essence of cows to be animals. The truthmaker for "there could have been purple cows" is that color is not essential to cows. Some essentialist theories focus on object essences, i.e. that certain properties are essential to a specific object. Other essentialist theories focus on kind essences, i.e. that certain properties are essential to the kind or species of the object in question. [26]

See also

Related Research Articles

Ontology Branch of philosophy that studies concepts such as existence, being, becoming, and reality

Ontology is the branch of philosophy that studies concepts such as existence, being, becoming, and reality. It includes the questions of how entities are grouped into basic categories and which of these entities exist on the most fundamental level. Ontology is sometimes referred to as the science of being and belongs to the major branch of philosophy known as metaphysics.

Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only imaginary. The term is also used to refer to the ontological status of things, indicating their existence. In physical terms, reality is the totality of a system, known and unknown. Philosophical questions about the nature of reality or existence or being are considered under the rubric of ontology, which is a major branch of metaphysics in the Western philosophical tradition. Ontological questions also feature in diverse branches of philosophy, including the philosophy of science, philosophy of religion, philosophy of mathematics, and philosophical logic. These include questions about whether only physical objects are real, whether reality is fundamentally immaterial, whether hypothetical unobservable entities posited by scientific theories exist, whether God exists, whether numbers and other abstract objects exist, and whether possible worlds exist.

Understood in a narrow sense, philosophical logic is the area of philosophy that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic.

Phenomenalism is the view that physical objects cannot justifiably be said to exist in themselves, but only as perceptual phenomena or sensory stimuli situated in time and in space. In particular, some forms of phenomenalism reduce all talk about physical objects in the external world to talk about bundles of sense data.

Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators and , representing possibility and necessity respectively. For instance the modal formula can be read as "possibly " while can be read as "necessarily ". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When is used to represent epistemic necessity, states that is epistemically necessary, or in other words that it is known. When is used to represent deontic necessity, states that is a moral or legal obligation.

In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes that world.

In philosophy, metaphysical necessity, sometimes called broad logical necessity, is one of many different kinds of necessity, which sits between logical necessity and nomological necessity, in the sense that logical necessity entails metaphysical necessity, but not vice versa, and metaphysical necessity entails physical necessity, but not vice versa. A proposition is said to be necessary if it could not have failed to be the case. Nomological necessity is necessity according to the laws of physics and logical necessity is necessity according to the laws of logic, while metaphysical necessities are necessary in the sense that the world could not possibly have been otherwise. What facts are metaphysically necessary, and on what basis we might view certain facts as metaphysically but not logically necessary are subjects of substantial discussion in contemporary philosophy.

A possible world is a complete and consistent way the world is or could have been. They are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their metaphysical status has been a subject of controversy in philosophy, with modal realists such as David Lewis arguing that they are literally existing alternate realities, and others such as Robert Stalnaker arguing that they are not.

In analytic philosophy, actualism is the view that everything there is is actual. Another phrasing of the thesis is that the domain of unrestricted quantification ranges over all and only actual existents.

Philosophical realism is usually not treated as a position of its own but as a stance towards other subject matters. Realism about a certain kind of thing is the thesis that this kind of thing has mind-independent existence, i.e. that it is not just a mere appearance in the eye of the beholder. This includes a number of positions within epistemology and metaphysics which express that a given thing instead exists independently of knowledge, thought, or understanding. This can apply to items such as the physical world, the past and future, other minds, and the self, though may also apply less directly to things such as universals, mathematical truths, moral truths, and thought itself. However, realism may also include various positions which instead reject metaphysical treatments of reality entirely.

Modal realism is the view propounded by David Kellogg Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours." It is based on the following tenets: possible worlds exist; possible worlds are not different in kind from the actual world; possible worlds are irreducible entities; the term actual in actual world is indexical, i.e. any subject can declare their world to be the actual one, much as they label the place they are "here" and the time they are "now".

Philosophical presentism is the view that neither the future nor the past exists. In some versions of presentism, the view is extended to timeless objects or ideas. According to presentism, events and entities that are wholly past or wholly future do not exist at all. Presentism contrasts with eternalism and the growing block theory of time, which hold that past events, like the Battle of Manzikert, and past entities, like Alexander the Great's warhorse Bucephalus, really exist although not in the present. Eternalism extends to future events as well.

An infinite regress is an infinite series of entities governed by a recursive principle that determines how each entity in the series depends on or is produced by its predecessor. In the epistemic regress, for example, a belief is justified because it is based on another belief that is justified. But this other belief is itself in need of one more justified belief for itself to be justified and so on. An infinite regress argument is an argument against a theory based on the fact that this theory leads to an infinite regress. For such an argument to be successful, it has to demonstrate not just that the theory in question entails an infinite regress but also that this regress is vicious. There are different ways in which a regress can be vicious. The most serious form of viciousness involves a contradiction in the form of metaphysical impossibility. Other forms occur when the infinite regress is responsible for the theory in question being implausible or for its failure to solve the problem it was formulated to solve. Traditionally, it was often assumed without much argument that each infinite regress is vicious but this assumption has been put into question in contemporary philosophy. While some philosophers have explicitly defended theories with infinite regresses, the more common strategy has been to reformulate the theory in question in a way that avoids the regress. One such strategy is foundationalism, which posits that there is a first element in the series from which all the other elements arise but which is not itself explained this way. Another way is coherentism, which is based on a holistic explanation that usually sees the entities in question not as a linear series but as an interconnected network. Infinite regress arguments have been made in various areas of philosophy. Famous examples include the cosmological argument, Bradley's regress and regress arguments in epistemology.

In philosophical logic, the concept of an impossible world is used to model certain phenomena that cannot be adequately handled using ordinary possible worlds. An impossible world, w, is the same sort of thing as a possible world , except that it is in some sense "impossible." Depending on the context, this may mean that some contradictions are true at w, that the normal laws of logic or of metaphysics fail to hold at w, or both.

Meta-ontology is the study of the field of inquiry known as Ontology. The goal of meta-ontology is to clarify what ontology is about and how to interpret the meaning of ontological claims. Different meta-ontological theories disagree on what the goal of ontology is and whether a given issue or theory lies within the scope of ontology. There is no universal agreement whether meta-ontology is a separate field of inquiry besides ontology or whether it is just one branch of ontology.

Meinong's jungle is the name given by Richard Routley (1980) to the repository of non-existent objects in the ontology of Alexius Meinong.

Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems relate to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterization, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consistency and completeness.

Logic Study of correct reasoning

Logic is the study of correct reasoning or good arguments. It is often defined in a more narrow sense as the science of deductively valid inferences or of logical truths. In this sense, it is equivalent to formal logic and constitutes a formal science investigating how conclusions follow from premises in a topic-neutral way or which propositions are true only in virtue of the logical vocabulary they contain. When used as a countable noun, the term "a logic" refers to a logical formal system. Formal logic contrasts with informal logic, which is also part of logic when understood in the widest sense. There is no general agreement on how the two are to be distinguished. One prominent approach associates their difference with the study of arguments expressed in formal or informal languages. Another characterizes informal logic as the study of ampliative inferences, in contrast to the deductive inferences studied by formal logic. But it is also common to link their difference to the distinction between formal and informal fallacies.

Grounding is a topic in metaphysics. Consider an ordinary physical object, such as a table, and the atoms it is made of. Without the atoms, the table would not exist. The table's existence depends on the existence of the atoms. This kind of dependence is called "grounding" to distinguish it from other kinds of dependence, such as the dependence of an effect on its cause. It is sometimes called metaphysical or ontological dependence.

Modal realism is the view that the actual and the non-actual are equally real. It contrasts with actualism, the view that fundamental reality is restricted to actuality. Extended modal realism, as developed by Takashi Yagisawa, differs from other versions of modal realism, such as David Lewis' views, in several important aspects. Possible worlds are conceived as points or indices of the modal dimension rather than as isolated space-time structures. Regular objects are extended not only in the spatial and the temporal dimensions but also in the modal dimension: some of their parts belong to non-actual worlds. Among these non-actual worlds within the modal dimension are not just possible worlds but also impossible worlds. There is only one universe encompassing everything that is real in the widest sense: the actual, the possible and the impossible.


  1. 1 2 3 4 5 6 7 8 Asay, Jamin. "Truthmaker Theory". Internet Encyclopedia of Philosophy.
  2. Mulligan, Kevin; Simons, Peter; Smith, Barry (1984). "Truth-Makers". Philosophy and Phenomenological Research. 44 (3): 287–321. doi:10.2307/2107686. JSTOR   2107686.
  3. Armstrong, D. M. (2010). "10. Limits". Sketch for a Systematic Metaphysics. Oxford, UK: Oxford University Press UK.
  4. Rosen, Gideon; Lewis, David. "Postscript to 'Things qua truthmakers': negative existentials". Real Metaphysics: Essays in Honour of D.H. Mellor. Routledge. ISBN   978-0-415-24981-2.
  5. Mackie, John Leslie (1977). Ethics: Inventing Right and Wrong. Penguin Books.
  6. 1 2 Armstrong, D. M. "2. The general theory of truthmaking". Truth and Truthmakers. Cambridge University Press.
  7. 1 2 3 4 Koons, Robert C.; Pickavance, Timothy. "2 Truthmakers". The Atlas of Reality: A Comprehensive Guide to Metaphysics. John Wiley & Sons. ISBN   978-1-119-11611-0.
  8. Bergmann, Gustav (1960). "Ineffability, Ontology, and Method". Philosophical Review. 69 (1): 18–40. doi:10.2307/2182265. JSTOR   2182265.
  9. Magnus, P. D.; Button, Tim; Thomas-Bolduc, Aaron; Zach, Richard; Trueman, Robert. "II Truth-functional logic". Forall X: Calgary. An Introduction to Formal Logic.
  10. Milne, Peter (2005). "Not Every Truth has a Truthmaker". Analysis. 65 (3): 221–224. doi:10.1111/j.1467-8284.2005.00553.x.
  11. Barrio, Eduardo; Rodriguez-Pereyra, Gonzalo (2015). "Truthmaker Maximalism Defended Again". Analysis. 75 (1): 3–8. doi:10.1093/analys/anu121.
  12. Read, Stephen (2000). "Truthmakers and the Disjunction Thesis". Mind. 109 (433): 67–79. doi:10.1093/mind/109.433.67. ISSN   0026-4423. JSTOR   2659994.
  13. Tałasiewicz, Mieszko; Odrowąż-Sypniewska, Joanna; Wciórka, Wojciech; Wilkin, Piotr (1 September 2013). "Do we need a new theory of truthmaking? Some comments on Disjunction Thesis, Conjunction Thesis, Entailment Principle and explanation". Philosophical Studies. 165 (2): 591–604. doi: 10.1007/s11098-012-9964-x . ISSN   1573-0883. S2CID   170114895.
  14. "Correspondence Theory of Truth", in Stanford Encyclopedia of Philosophy (citing De Veritate Q.1, A.1–3 and Summa Theologiae , I. Q.16).
  15. Armstrong, D. M. (1997). A World of States of Affairs. Cambridge University Press. p. 128.
  16. Beebee, Helen; Dodd, Julian. Truthmakers: The Contemporary Debate. Clarendon Press. pp. 13–14.
  17. 1 2 MacBride, Fraser (2020). "Truthmakers". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.
  18. 1 2 Sider, Theodore (2001). "2. Against Presentism". Four Dimensionalism: An Ontology of Persistence and Time. Oxford University Press.
  19. Emery, Nina (2020). "Actualism, Presentism and the Grounding Objection". Erkenntnis. 85 (1): 23–43. doi:10.1007/s10670-018-0016-6.
  20. 1 2 Menzel, Christopher (2018). "Actualism". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.
  21. Ingram, David; Tallant, Jonathan (2018). "Presentism". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.
  22. Armstrong, D. M. "1. An introduction to truthmakers". Truth and Truthmakers. Cambridge University Press.
  23. The Editors of Encyclopaedia Britannica. "Phenomenalism". Encyclopedia Britannica. Encyclopædia Britannica.
  24. Armstrong, David Malet. "C. B. Martin, counterfactuals, causality and conditionals". Cause, Mind, and Reality: Essays Honoring C. B. Martin. Norwell: Kluwer.
  25. 1 2 Cameron, Ross Paul (2008). "Truthmakers and Modality". Synthese. 164 (2): 261–280. doi:10.1007/s11229-007-9225-2.
  26. 1 2 3 Vetter, Barbara (2011). "Recent Work: Modality Without Possible Worlds". Analysis. 71 (4): 742–754. doi:10.1093/analys/anr077.
  27. Plantinga, Alvin (1976). "Actualism and Possible Worlds". Theoria. 42 (1–3): 139–160. doi:10.1111/j.1755-2567.1976.tb00681.x.
  28. Parent, Ted. "Modal Metaphysics". Internet Encyclopedia of Philosophy.
  29. Mellor, D. H. "Real Metaphysics: Replies". Real Metaphysics: Essays in honour of D. H. Mellor. Routledge.
  30. Fine, Kit (1994). "Essence and Modality". Philosophical Perspectives. 8: 1–16. doi:10.2307/2214160.

Further reading