Two Logical Senses of ‘Argument’

Abstract

What is an argument? This foundational question in argumentation research cannot be answered univocally, because ‘argument’ is ambiguous. This paper has two goals. The first is to draw attention to a neglected distinction between two ordinary ‘logical’ senses of the term: an ‘objective’ and a ‘subjective’ one. The second is to define these senses. In the objective sense, an argument for (or against) a certain proposition is a reason for (or against) believing that proposition. In the subjective sense, it is a consideration intended to provide such a reason. After defining these two senses, the paper defends these definitions against several objections. In this connection, I argue, among other things, that conclusions are not internal parts of arguments; that premises and conclusions are not ‘speech acts’; that the subjective sense of ‘argument’ is robust against the charge of relativism; and that considerations can deserve the name ‘argument’ even if they do not provide actual support.

1 Introduction

People often have ‘arguments’ with each other. They also seek ‘arguments’ for or against specific considerations, claims, or views, and criticise other people’s ‘arguments’ while attempting to defend their own.

But, first and foremost, what is an argument? This question cannot be answered univocally, because ‘argument’ has different senses both in scientific research and in ordinary English. In my view, the first paragraph of this paper exemplifies, on its most natural reading, three different ordinary senses of ‘argument’: the ‘disagreement’ sense and two distinct ‘logical’ senses, which I call the ‘objective’ and the ‘subjective’. While the disagreement sense is well recognised, the existence of two distinct logical senses is not.

The paper has two main goals. The first is to distinguish between the subjective and objective senses of ‘argument’. This is important for the following reason. The subjective/objective ambiguity is subtle, and subtle ambiguities in key terms often go unnoticed. This can lead to confusion. For example, researchers might disagree on whether arguments have a certain property, without realising they are focusing on different senses of the term. In such cases, they are essentially talking past each other. In fact, a debate in argumentation theory may suffer from this very problem. It is about whether arguments involve intentional attitudes. Some say yes (e.g., Hitchcock 2007; Simard Smith and Moldovan 2011; Goodman 2018); others say no (e.g., Blair 2004; Goddu 2018). This paper suggests a possible resolution: both sides may be correct, in a sense. Those arguing for an intentional component may have the subjective sense of ‘argument’ in mind, while those arguing against it may have the objective sense.

The paper’s second goal is to provide an adequate definition of the term in each sense. The term ‘argument’ is as central to argumentation research as ‘knowledge’ is to epistemology or ‘existence’ is to ontology. Adequately defining the various senses of this term is of core theoretical interest (cf. Goodman 2018: 590).¹ Moreover, since the phenomena laypeople refer to when they use the term ‘argument’ are the subject of argumentation studies, such definitions provide more clarity about what exactly we are studying.

Before I start, I will clarify two points. First, some research tends to conflate terms such as ‘argument’, ‘making an argument’, and ‘argumentation’. My paper exclusively deals with the term ‘argument’. Second, when it comes to defining ‘argument’, some authors in the literature do not make it clear what kind of definition they aim to provide (cf. Blair 2001: 2–3).

When defining a term, we may intend to attach a (technical) sense or reference to an expression (‘stipulation’). Alternatively, we may intend to precisify an existing sense or reference of an expression (‘explication’, cf. Carnap 1947: 7–8; 1962: 3). Or we may intend to represent or clarify a sense or reference an expression already has (‘analytic’ or ‘lexical’ definition).

When researchers do not make it transparent what kind of definition they have in mind when defining ‘argument’, it is difficult to properly assess their definitions.² The definitions provided in this paper are meant to be analytic. They are intended to clarify ordinary senses of ‘argument’.³ Any other type of definition would fail to capture what people typically mean when they ask the initial question of this paper (‘What is an argument?’). As Simard Smith and Moldovan (2011: 12) emphasise,

the disagreement in the literature on argumentation is surely not about some stipulative definitions. It is the meaning of the natural language word ‘argument’ that definitions offered in the literature try to capture, and not the meaning of a term within some theory or another.

I shall proceed as follows. In Sect.  2, I briefly clarify the disagreement sense of ‘argument’. I then distinguish two ‘logical’ senses – a ‘subjective’ and an ‘objective’ one – and propose a definition of ‘argument’ in each of these senses. In Sect.  3, I relate my account to the relevant literature by addressing several possible objections to my definitions. In particular, I discuss the objection that conclusions are part of arguments (as in the standard definition); that premises or conclusions are not, or need not be, propositions (cf. Marraud 2018; Hitchcock 2021; Jacobs 2024); that my definition of ‘argument’ in the subjective sense faces a ‘relativity problem’ (cf. Goddu 2018; Goodman 2018); that this definition is too narrow (cf. Blair 2012; Pinto 2019; Svoboda 2020; Butterworth 2021); and finally that it is too broad (cf. Blair 2004; Davis 2011; McKeon 2024).

2 Two Logical Senses of ‘Argument’

Besides the logical senses of ‘argument’, there is another prominent and well-recognised ordinary sense of ‘argument’ which I call the ‘disagreement’ sense (cf., e.g., O’Keefe 1977; Blair 2001, 2021; Goodman 2018; Butterworth 2021; Hitchcock 2021). Let me call an argument in this sense a ‘D-argument’. (1) represents a case of a D-argument.

• (1) Pete had an argument with his girlfriend about whether God exists.

D-arguments are disagreements that can take different forms, such as that of a quarrel, a dispute, a debate, or a controversy (cf. Blair 2021: 87 − 9). The consistency of statements like (2) and (3) demonstrates that D-arguments are events and as such have a temporal location.

• (2) Their argument lasted two hours.

• (3) The argument took place a week ago.

D-arguments are things you have with someone about or over something, things you can be engaged in, and things you can win or lose (cf. O’Keefe 1977: 121).

As is well-known, the disagreement sense of ‘argument’ is not the only one. However, what other senses the term has is up for debate.⁴ Goodman (2018) contrasts the disagreement sense of ‘argument’ with what he calls the ‘logical’ or ‘argument-as-object’ sense. What Goodman and other researchers might have missed is that there are two logical senses of ‘argument’.⁵ In the following, I will use constructed examples to clarify these two senses. Constructed examples are often neater and more compact than real-life ones. If the hypothesised senses really exist, well-constructed examples should be able to trigger them in the minds of competent speakers of English just as effectively as real-life instances. For readers who disagree with this methodological choice, the appendix to this paper provides several real-life examples for both senses of ‘argument’.

Let us start by considering (4).

• (4) A healthy vegan diet is not feasible for everyone. But that is not an argument that no one should adopt a vegan diet.

The sense of ‘argument’ instantiated in (4) is intuitively captured by reference to the notion of ‘support’, which is employed by many standard textbook definitions of ‘argument’ (see, e.g., Govier 2013: 20; Hughes et al. 2015: 4; Vaughn 2018: 10; Morrow and Weston 2019; xix; Dowden 2020: 25).

On a natural interpretation, (4) may be understood as implying that the fact that a healthy vegan diet is not feasible for everyone does not support (or not compellingly support) the proposition that no one should adopt a vegan diet. That the notion of ‘support’ is appropriate for capturing this sense of ‘argument’ is confirmed by further examples:

• (5) After a few hours of deliberation, I came up with many arguments for the existence of God.

• (6) Some people tried to argue that nothing is real. But really, there are no arguments for such an absurd view.

• (7) Evil is not always viewed as an argument for atheism, but rather as an argument for unconventional forms of theism.

It is natural to understand these examples as follows: (5) implies that the speaker came up with many reasons supporting the proposition that God exists; (6) implies that nothing (compellingly) supports the view that nothing is real; and (7) implies that the existence of evil is sometimes viewed as supporting unconventional forms of theism.

An obvious question is what ‘support’ is supposed to mean in this context. While it is obvious what it means for pillars to support a pedestal, it seems less obvious what it should mean for something to ‘support’ a proposition. I suggest that ‘support’ in this context can be analysed in terms of ‘reason for belief’ (see Davis 2011: 6; Wright 2012: 44; Wilson 2020: 6; see also Feldman 2013: 22 and 36; Morrow and Weston 2019: 5; Bowell et al. 2020: 70; Dowden 2020: 59, 281, and 313). Consider the following reformulations of (4), (5), (6), and (7):

• (4R)  A healthy vegan diet is not feasible for everyone. But that is not a (compelling) reason for believing that no one should adopt a vegan diet. 

• (5R) After a few hours of deliberation, I came up with many reasons for believing in the existence of God.

• (6R) Some people tried to argue that nothing is real. But really, there are no (compelling) reasons for believing such an absurd view.

• (7R) Evil is not always viewed as a reason for believing in atheism, but rather as a reason for believing in unconventional forms of theism.

There is a difference in style between the original statements and the reformulations. However, the reformulations all seem to have a reading in which they convey the same content. This intuition is supported by the fact that both (8) and (9) are blatantly inconsistent (‘#’).

• (8) # The existence of evil is an argument for atheism, but not a reason for believing in atheism.

• (9) # The existence of evil is a reason for believing in atheism, but not an argument for it.

Up to this point, I have only considered cases of ‘positive’ arguments: arguments for a particular proposition. However, there are also ‘negative’ arguments: arguments against a particular proposition.

• (10) Is the potential of drugs to be addictive an argument against their use?

On my proposal, negative arguments are captured by the corresponding notion of ‘reason against belief’.

• (10R) Is the potential of drugs to be addictive a reason against believing that they should be used?

I call the sense of ‘argument’ instantiated by (4)-(10) the ‘objective’ logical sense of ‘argument’, and arguments referred to by this sense ‘objective L-arguments’.

Before proposing a definition, it is important to clarify my goal. My goal in this paper is to provide definitions that are at least extensionally adequate. At the same time, I hope that they come as close as possible to intensional adequacy. For a definition to be ‘extensionally’ adequate, it must capture the reference of the term defined in the sense under consideration. For it to be ‘intensionally’ adequate, it must capture what competent speakers have in mind when they correctly use the term in that sense.

I propose to define ‘argument’ in the objective logical sense as follows:

Definition

‘Objective L-Argument’

That something is an ‘objective L-argument’ for (or against) proposition p means that it is a reason for (or against) believing p⁶

It is worth noting that the term ‘reason’ here refers specifically to justificatory reasons – reasons-for-or-against-belief – not to other kinds of reasons, such as causal or explanatory ones.⁷ Furthermore, the definition remains neutral on the precise nature of justificatory reasons. For example, it leaves open whether they are facts and whether they are context-sensitive. Addressing such metaphysical questions is beyond the scope of this paper.

Objective L-arguments sharply contrast with D-arguments. They are not things you ‘have with someone’, or things that you can be ‘engaged in’, or things you can ‘win’ or ‘lose’. Moreover, they are not temporally located the way D-arguments are. Thus, (11) and (12) are inconsistent.

• (11) # The argument that farm animals are capable of suffering lasted two hours.

• (12) # The argument that farm animals are capable of suffering took place in 1975.

One peculiarity of objective L-arguments is that they cannot be illogical, or non-starters. Suppose we are looking for arguments for the view that every human being is inherently evil. Thus, (13) and (14) would not represent cases of objective L-arguments for this view.

• (13) A few human beings are evil.

• (14) Scientists have proved that there is an evil gene in human beings.

If (13) and (14) represented objective L-arguments for the view that every human being is inherently evil, they would have to represent actual reasons for believing that every human being is inherently evil. However, they do not. (13) is plausibly true, but the (putative) fact that a few human beings are evil is no reason for believing that every human being is inherently evil. (14) cannot represent a reason for believing this view either, because it is demonstrably false.

But certainly – some may insist – there is a sense of ‘argument’ in which arguments can be illogical or non-starters. Butterworth (2021: 343), for instance, finds the idea that ‘there are no bad or invalid arguments’ to be ‘plainly counter-intuitive’, and Goodman (2018: 594) criticises definitions that entail ‘there are no terrible arguments’. I agree. Here, the ‘subjective’ sense of ‘argument’ comes into play. Let me call the entities referred to by this sense ‘subjective’ L-arguments. The difference between objective and subjective L-arguments is indicated by Blair (2004: 143) in the following passage:

It is important to distinguish between an argument and some person’s (or persons’) argument. Someone’s argument consists of a proposition and the consideration which that person takes to support it or offers as support for […]. A person’s argument can contain premises that are irrelevant as support for their conclusion. Indeed, all the “reasons” a person takes or offers as support for a proposition can be completely irrelevant to it. We still correctly speak of that person’s “argument.”

What Blair calls ‘someone’s argument’ is what I am aiming at with the term ‘subjective L-argument’. As Blair indicates, a subjective L-argument, unlike an objective one, can fail to support its target proposition – the ‘conclusion’. The following example serves to illustrate this point.

• (15) Pete: The use of animals for our purposes is completely justified, for the Bible says that humans have dominion over animals.

Mary: Come on, that’s not an argument.

Pete offers an argument for his view. Mary’s response – ‘that’s not an argument’ – seems incorrect, because Pete clearly is offering one. The apparent contradiction is resolved by applying the distinction between objective and subjective L-arguments. Mary is correct if she means Pete has not offered an objective L-argument. The fact that the Bible mentions dominion over animals is (arguably) not an actual reason to believe that using animals for human purposes is completely justified. However, Pete has offered a subjective L-argument. He has presented a consideration that is intended by him to provide a (sufficient) reason for believing his view. Other references to subjective L-arguments are represented by (16)-(18).

• (16) One argument Pete makes against festivals is the huge amount of trash they create.

• (17) The church’s arguments against legalising euthanasia are poor.

• (18) In the following, I summarise the most important arguments in the literature.

In each case, there is a reference to one or more arguments-of-someone. (18) illustrates that a statement including the term ‘argument’ can suggest a subjective interpretation even if the respective subjects are not explicitly named.

Objective L-arguments and subjective L-arguments share certain properties. For example, both can be weak or strong,⁸conclusive or inconclusive. However, subjective L-arguments can possess properties that objective L-arguments cannot, such as being fallacious, viciously circular, or a non-starter. Another difference is that while subjective L-arguments presuppose the existence of subjects with a certain mental attitude, objective L-arguments do not. As Hitchcock puts it, ‘it seems consistent with our ordinary use of the term “argument” in its reason-giving sense to say that there are arguments that nobody has ever thought of and nobody ever will’ (2021: 102). One connection between subjective and objective L-arguments is expressed by the following conditional: If a subjective L-argument is weak, strong, conclusive, or inconclusive, it is because it coincides with a weak, strong, conclusive, or inconclusive objective L-argument. Suppose that Pete’s argument for the existence of his own hands is that he can see, move, and feel them. This is a strong subjective L-argument exactly because it coincides with a strong objective L-argument: as a matter of fact, the ability to see, move, and feel one’s hands is a strong (actual) reason for believing that one’s hands exist.

An anonymous referee critically inquired whether my distinction between objective and subjective L-arguments is merely a distinction between argument and inference, argument and reasoning, or argument and perceived argument.

‘Inference’ is ambiguous. In one sense, it refers to the process of inferring. In another sense, it refers to propositions inferred. That subjective L-arguments are not inferences in the latter sense is obvious. However, they are not inferences in the former sense either, because they are not processes at all. They are objects. Referring to Pete’s argument against festivals means referring to an object of an intentional attitude, not to cognitive processes of Pete.

‘Reasoning’ is ambiguous as well. But there is no sense in which the nature of reasoning is qualitatively identical with the nature of subjective L-arguments. Admittedly, in some cases, ‘reasoning’ and ‘subjective L-argument’ might be taken to refer to the same entity. If Pete offers only a single argument for the existence of God, both ‘Pete’s argument for the existence of God’ and ‘Pete’s reasoning for the existence of God’ can naturally be interpreted as referring to the same thing. However, this does not mean there is no qualitative difference between the nature of reasoning and the nature of subjective L-arguments. This becomes clear when we look at how the words behave grammatically. ‘Argument’ acts as a count noun, while ‘reasoning’ acts as a mass noun. Suppose Pete has three distinct considerations to support the existence of God. It is perfectly natural to say, ‘Pete has three arguments for the existence of God’. But it is ungrammatical to say, ‘Pete has three reasonings for the existence of God’.

Finally, while your ‘perceiving’ something to be an objective L-argument might be your reason for offering a subjective L-argument, subjective L-arguments cannot be equated with ‘perceived’ arguments. If you say ‘Dawkins’ arguments against religion are weak’, you are not referring to considerations that are merely perceived by Dawkins to provide reasons against religion; you are referring to considerations that are intended by him to provide such reasons.⁹

Having clarified the difference between subjective and objective L-arguments, I now propose a definition of ‘argument’ in the ‘subjective’ logical sense.

Definition

‘Subjective L-Argument’

That something is a ‘subjective L-argument’ for (or against) proposition p means that it is a consideration intended by someone to provide a reason for (or against) believing p.¹⁰

(17) implies that the church has arguments against legalising euthanasia, and states that they are poor. Applying the proposed definition, referring to these arguments means referring to considerations intended by the church to provide reasons against believing that euthanasia should be legalised.

I discuss details of this definition in the next section. One point, however, deserves brief attention here. Standard definitions of ‘argument’ treat arguments as sets of propositions; the present definition treats them as considerations. While I believe that employing the notion of ‘set of propositions’ yields an extensionally adequate definition, it seems to me that using the notion of ‘consideration’ makes the definition intensionally more adequate. Since the concept of a set is rather sophisticated, competent speakers of English likely do not have it in mind when they use the term ‘argument’ in the subjective sense. As I conceive of this notion, ‘consideration’ refers (in one of its senses) to the content of a specific type of thinking process, which may include one or more propositions.

To summarise, I have argued in this section that, besides the disagreement sense of ‘argument’, there are two logical senses: an objective and a subjective one. In the objective sense, an argument is a reason for or against belief; in the subjective sense, it is a consideration intended by someone to provide a reason for (or against) belief.

3 Possible Objections

In the following, I discuss in detail possible objections to my definitions of the logical senses of ‘argument’. The objections draw on several ideas from the relevant literature.

3.1 Conclusions as Part of Arguments

While differing in detail, most definitions of ‘argument’ in logic and critical thinking textbooks have one thing in common: they define ‘argument’ as a set of statements or propositions. In this set, one statement or proposition – the ‘conclusion’ – is (taken, intended, or claimed to be) supported by the others – the ‘premises’ (cf., e.g., Johnson and Blair 1994: 10; Davis 2011: 6; Wright 2012: 405; Feldman 2013: 16; Govier 2013: 1; Copi et al. 2014: 6; Kelley 2014: 69; Hughes et al. 2015: 4; Vaughn 2018: 16; Bowell et al. 2020: 11; Dowden 2020: 25; Wilson 2020: 6; cf. also Blair 2001: 3–6; Goddu 2018; Blair 2021: 91 − 2 for examples of such definitions). My focus here is on the fact that according to these definitions, the ‘conclusion’ is part of the argument itself.¹¹

According to my definitions, neither objective nor subjective L-arguments are such that the conclusion is part of them. Authors who intend their definitions as analyses of ‘argument’ might criticise my definitions for this fact. I argue that conclusions are not part of arguments in either sense.¹² Consider (19).

• (19) The fact that factory farming causes animals great suffering is a strong argument against allowing it.

(19) has a reading in which it refers to an objective L-argument for the idea that factory farming should not be allowed. The argument is represented by the that-clause and reads: factory farming causes animals great suffering. Thus, according to my reading, the conclusion – factory farming should not be allowed – is not part of the argument. Consider another example (adapted from Cottrell 2023: 36).

• (20) Mary: Longer prison sentences should be introduced. First, heavy punishments deter criminals. Second, current penalties for crime are too lenient and don’t deter criminals. Third, since prison sentences were reduced, crime has increased. Finally, victims need to see that perpetrators of crimes are punished.

On my interpretation, (20) represents four separate subjective L-arguments in support of the view that longer prison sentences should be introduced. Standard textbook definitions would imply that (20) contains four separate (non-numerically identical) conclusions. But the natural and, in my view, correct reading is that it represents (numerically) one conclusion and four arguments in support of it. For example, the first argument is that heavy punishments deter criminals. And here again, the that-clause seems to fully represent the argument. It would be unnatural to say: ‘Wait, this is only part of Mary’s first argument. You forgot the conclusion.’

Although conclusions are not part of arguments – neither of objective nor subjective L-arguments – I believe that the idea of an argument in each of these logical senses involves the idea of a conclusion. To clarify this point, let me offer an analogy. The idea of a mother involves the idea of a child. You cannot entertain the idea of a mother without the idea of a child occurring to you. Correspondingly, you cannot say without self-contradiction that someone is a mother but has no child and has never had one. Nevertheless, a child is not part of a mother but an entity distinct from the mother. In the same way, the idea of an argument involves the idea of a conclusion. An argument is necessarily an argument for or against something, that is, it is necessarily targeted at a conclusion. Correspondingly, you cannot say without self-contradiction that something is an argument, but it is not an argument for or against anything. In short, ‘mother’ and ‘argument’ are ‘relational nouns’, nouns with a relational sense. My definitions of ‘argument’ are consistent with this observation.

3.2 Non-Propositionality Objection

According to my definitions, a ‘subjective L-argument’ is a consideration consisting of one or more propositions directed at another proposition; and an ‘objective L-argument’ is a reason for or against believing a proposition. I use the term ‘proposition’ in the traditional sense, which is described by Davis (2021) as follows:

The term proposition is traditionally used for the entities that are: (i) the primary bearers of truth and falsity; (ii) the entities expressed by declarative sentences; and (iii) the objects of belief, assertion, and other speech acts and propositional attitudes.

Some authors suggest that premises or conclusions of arguments are not, or need not be, propositions. One suggestion is that they are sets of sentence types or tokens. In my view, Goodman (2018) has successfully rejected this suggestion in the following passage.

I can surely consider Anselm’s Ontological Argument. When I do so, however, I am not considering any set or collection of sentence tokens uttered or inscribed by Anselm – I am not in contact with them. Nor am I considering any set or collection of sentence types that those tokens were instances of – I am ignorant of Latin. (591)

Another suggestion, made by Hitchcock (2021), is that arguments are sets of ‘illocutionary act’ types (cf. ibid.: 105).¹³ I begin with Hitchcock’s view that premises in an argument are types of illocutionary acts. Consider (21) and (22).

• (21) Suppose that there is life on other planets in the universe. Then it makes sense to look for it.

• (22) There is life on other planets in the universe. So it makes sense to look for it.

Hitchcock presupposes that both (21) and (22) represent arguments. These (alleged) arguments, he suggests, have the same conclusion, but the premises are different, even though they express the same proposition: the proposition that there is life on other planets in the universe. ‘The difference’, Hitchcock claims, ‘is in the illocutionary act performed by someone who utters the premiss in standard contexts. In uttering argument [(21)], the author hypothesises the propositional content of the premiss. In uttering argument [(22)], […] the author asserts the proposition’ (ibid.: 102-3).

The main problem I see with Hitchcock’s idea is its assumption that (21) represents an argument. It does not. If (21) were used by someone – say, Mary – to express an argument, we should be able to fill the blank in the following statement in an adequate way:

Mary argues for the view that it makes sense to look for life on other planets (= conclusion). Her argument is ___.

But how should we fill this blank? We cannot say, ‘Her argument is that there is life on other planets in the universe’, since that corresponds to what is expressed by (22). Nor can we say, ‘Her argument is that we (should) suppose that there is life on other planets in the universe’, as this would be inadequate. As others have noted, constructions of the form ‘Suppose X. Then Y.’ are not conventionally used to express arguments, but rather to express conditionals indirectly (cf. Govier 2013: 10; Davis 2011: 13). Thus, (21) indirectly expresses what is directly expressed by (23).

• (23) If there is life on other planets in the universe, then it makes sense to look for it.

Given Hitchcock’s reading, (23) would have to be directed at the conclusion that it makes sense to look for it. But it is not. ‘It makes sense to look for it’ is simply part of the conditional statement, not a separate proposition to which the conditional is directed.

Further evidence that (21) does not represent an argument can be drawn from the following consideration. If (21) represented an argument, its conclusion being that it makes sense to look for life on other planets, then we would expect that we could insert typical conclusion indicators without any significant change of meaning. But we cannot. For example, replacing ‘then’ with ‘therefore’, ‘consequently’, or ‘this suggests that’ would significantly change the meaning.

Finally, if (21) represented an argument, it should be possible to use (21) to give a reason for believing the respective conclusion. After all, it is the ‘reason-giving’ sense of ‘argument’ Hitchcock has in mind here (cf. ibid.: 101). However, (21), taken in itself, cannot be used to give a reason for believing the conclusion. These observations lead me to conclude that (21) does not represent an argument, and that Hitchcock’s suggestion is therefore untenable.

Before proceeding, I should clarify that my view does not deny the possibility of ‘hypothetical’ arguments. I merely maintain that (21) does not represent one. The following text sequence illustrates a possible hypothetical argument: ‘Suppose that moral facts did not exist. Then it would not be a fact that Hitler’s persecution of the Jews was wrong. This is absurd. Therefore, moral facts exist.’

Let us now turn to Hitchcock’s view that conclusions are types of illocutionary acts. His argument is based on the following examples:

• (24) There is a forecast of thundershowers, so let’s cancel the picnic.

• (25) I know how difficult it will be for you to get the milk, so I promise you that I will pick it up on the way home.

• (26) My conduct was inexcusable, so I apologise most sincerely.

• (27) The evidence establishes beyond a reasonable doubt that you committed the crime of which you are accused, so I thereby find you guilty as charged.

Hitchcock argues that ‘[w]hen these arguments are expressed in standard contexts, their conclusions are respectively [24] a directive, [25] a commissive, [26] an expressive, and [27] a declarative’ (ibid.: 104). From this he concludes that ‘the conclusion of an argument can be an illocutionary act type of any kind’ (ibid.).

This line of reasoning has a similar problem. It presupposes that (24)-(27) represent arguments. Why should we think so? What is striking about Hitchcock’s examples is that in each case the second sentence is introduced with ‘so’. ‘So’ is used to indicate conclusions. This might be a major reason why Hitchcock believes that the examples represent arguments. The problem is that while ‘so’ is in fact used to indicate conclusions, this is not the only use (cf. Govier 2013: 15; Lack and Rousseau 2016: 56 − 7; Wilson 2020: 39). For example, it is also used to indicate explanations, as (28) shows.

• (28) I was tired, so I went to bed.

Thus, the mere presence of ‘so’ in a passage does not entail the presence of a conclusion. Now, one could still argue that the examples (24)-(27) each have a reading in which ‘so’ functions as a conclusion indicator. But if that were the case, it should be possible to replace ‘so’ with another, reliable conclusion indicator without significant change of meaning. Fairly reliable conclusion indicators are expressions such as ‘it follows’, ‘this shows’, ‘from this we can conclude’, or ‘this proves’. If we replace ‘so’ with any of these indicators, the result is either a grammatically unacceptable (‘*’) text sequence or a text sequence with a meaning which is significantly different (‘↮’). Consider (29)-(32).

• (29) * There is a forecast of thundershowers, it follows (that) let’s cancel the picnic.

• (30) ↮ I know how difficult it will be for you to get the milk, this shows that I promise you that I will pick it up on the way home.

• (31) ↮ My conduct was inexcusable; from this we can conclude that I apologise most sincerely.

• (32) ↮ The evidence establishes beyond a reasonable doubt that you committed the crime of which you are accused, this proves that I thereby find you guilty as charged.

This observation strongly suggests that (24)-(27) do not represent arguments. Hence, this suggestion too is unpromising.

A similar suggestion comes from Marraud (2018). Marraud argues for the possibility of arguments that are ‘characterized by the fact that one of [their] premises is a directive – i.e., what is expressed by a directive sentence: a general instruction how to proceed or act’ (ibid.: 310). An example of a directive is: Look at the tablecloths (cf. ibid.: 311). Since directives are non-propositional, Marraud’s claim would falsify my account of subjective L-arguments – provided that he targets the same ordinary sense of ‘argument’ that I address.

Consider Marraud’s paradigmatic example for such an argument. Marraud imagines a case in which two people, Nicholas and Martin, ‘are arguing about whether The Gargantua is a fine restaurant or just a casual eatery’ (ibid.). Nicholas, seeing that the tablecloths are white linen, says: ‘Look at the tablecloths: this is a classy restaurant’ (ibid.).

In this example, it is natural to interpret Nicholas as arguing that The Gargantua is a fine restaurant. But in my view, the natural interpretation is that Nicholas’ utterance is elliptical. With the utterance quoted, he implicitly says that the tablecloths in The Gargantua are white linen. And he intends what he implicitly says to provide a (sufficient) reason for believing that The Gargantua is a classy restaurant.

Marraud seems to reject a reading along these lines. Instead, he suggests that it is more plausible to represent Nicholas’ argument as follows: ‘Look at the tablecloths in The Gargantua. So, The Gargantua is a classy restaurant’ (cf. ibid.: 315). Marraud’s suggestion is that the (main) premise of Nicholas’ argument really is a directive. I reject this suggestion. If it were correct, the proposed representation should be linguistically acceptable. It is not. If its unacceptability is not immediately apparent, consider the following alternative representations, where ‘so’ is replaced by ‘therefore’ and ‘it follows’, respectively.

• (33) * Look at the tablecloths. Therefore, The Gargantua is a classy restaurant.

• (34) * Look at the tablecloths. It follows that The Gargantua is a classy restaurant.

If Marraud’s suggestion were correct, these representations should be acceptable, but they are not. Therefore, Marraud’s suggestion is implausible as it stands, construed as a suggestion regarding the subjective sense of ‘argument’ with which I am concerned.

Finally, consider a suggestion by Jacobs (2024). He maintains that ‘[a]ny act can be justified or criticised, supported, undercut, or otherwise disputed by arguments’ (1273). He proposes that even cheers (‘Hooray!’) and curses (‘Damn!’) are possible targets of arguments (cf. ibid.: fn. 9). If Jacobs’ suggestion is that acts can be conclusions of arguments, then I do not find it convincing.

The impression that acts can be conclusions probably arises from certain linguistically unproblematic ways of speaking, such as the following: ‘Pete justified his act of cursing with a convincing argument.’ ‘Mary’s presence is a strong argument for going to the party!’ In both cases, one might get the impression that the conclusions of the arguments mentioned are acts (the act of cursing, the act of going to the party). The impression is deceptive. When we say ‘Pete justified his act of cursing with a convincing argument’ we mean that Pete offered a convincing argument for believing that his act was justified; and when we say ‘Mary’s presence is a strong argument for going to the party’ we mean that Mary’s presence is a strong argument for believing that I (or we) should go to the party (or that going to the party is a good idea). Upon closer examination, the actual conclusion in both cases is a proposition.

By analogy, consider someone saying, ‘I believe in God.’ This phrasing suggests that the content of their belief is a non-propositional entity, namely the idea of God. However, we know that saying ‘I believe in God’ simply means ‘I believe that God exists’, showing that the content of belief is a proposition.

These considerations can be generalised. Whenever we claim to offer arguments for or against acts, it is not the acts themselves that are the conclusions, but propositions evaluating them. For instance, when I say, ‘There’s a compelling argument for starting the project early’, it should be understood as saying, ‘There’s a compelling argument for believing that starting the project early is good (or that we should start the project early)’.

I will conclude this section by addressing a concern from an anonymous referee. The concern is that rejecting the view that acts are conclusions would imply rejecting the possibility of ‘practical’ arguments. Since practical arguments are common and widely recognised as genuine arguments, one might think that my conception of arguments – whether objective or subjective L-arguments – is inadequate.

In my view, the conclusions of practical arguments are not acts. Instead, they target specific evaluative or normative conclusions. An argument for ‘going to the party’ is an argument for believing that going to the party is good (or that we should go to the party). An argument against ‘torturing babies’ is an argument against believing that torturing babies is acceptable (or right).

Of course, a critic might concede that evaluative or normative conclusions are not acts but still suggest that they are not propositions. The problem is that this suggestion is far from evident. Indeed, it is highly contested. Thus, among the 227 metaethics experts who participated in the PhilPapers 2020 survey, over 75% accept or lean towards ‘cognitivism’ (cf. Bourget and Chalmers 2023), a view implying that conclusions involving evaluative or normative (ethical) concepts can be propositions. This evidence does not eliminate the possibility that such conclusions are non-propositional. However, it shows that accusing my account of precluding practical arguments carries a considerable burden of proof.

3.3 The Relativity Objection

I now turn to Goddu’s (2018) attack on what he calls ‘intentional definitions of argument’. According to such definitions, ‘we need more than just sentences or statements or propositions [to have an argument], but also the intention, sometimes expressed in terms of claiming, affirming, or supposing that the statements are related in the correct way’ (ibid.: 340). This description suggests that my definition of ‘subjective L-argument’ is an intentional definition. According to my definition, something is not a subjective L-argument unless it is intended by someone to be a reason for (or against) believing a certain proposition.

I will focus on the objection that applies most directly to my account. I call it the ‘Relativity Objection’.¹⁴ To start with, Goddu points to the putative problem of conflicting intentions:

I intend or claim statement X follows from others, but you do not – do we have an argument or not? If we do, then why does the intention that X follows trump either the failure to intend X follows or the active intention that X does not follow? If not, then why does the failure to intend or the active intention that X does not follow trump the intention that X follows[?] (Ibid.: 342).

Applied to my account, the objection might be construed as follows: Suppose that Pete intends a certain consideration to provide a reason for believing p. Mary, however, does not intend this consideration to provide a reason for believing p (= scenario I), or even intends it to provide a reason against believing p (= scenario II). It is unclear whether a corresponding argument exists in such cases. Goddu might suggest this unclarity reveals a defect in my ‘intentional’ definition.

This objection fails when applied to my account. On my account, the assessment of these two scenarios is clear. In scenario I, there is one argument. It is an argument of Pete’s, but not an argument of Mary’s. In scenario II, there are two arguments: an argument of Pete’s and an argument of Mary’s – which is incompatible with Pete’s argument. Goddu seems to anticipate such an assessment:

One could avoid this problem by relativizing arguments to agents. Since I intend X follows, the group of statements is an argument for me, but since you do not so intend, either by failing to intend or by actively intending X not follow, the group of statements is not an argument for you. But such a solution makes substantive debate about whether someone is giving an argument or not impossible and yet argumentation theorists argue and debate about whether a particular passage of text is or is not an argument all the time. (Ibid.)

Goddu suggests that advocates of intentional definitions might adopt a ‘relativistic’ interpretation. Such an interpretation entails that arguments have only a relative existence, not an absolute one. An argument exists only for S, where S is the subject with the relevant intentional attitude.

The first thing to note is that ‘A is an argument for S’ has two readings: an ordinary, non-relativistic reading and a relativistic reading. On its ordinary reading, ‘A is an argument for S’ means more or less the same as A is believed by S to be an argument. This does not seem to be the reading Goddu is aiming at. It seems that Goddu is aiming at the relativistic reading, according to which ‘A is an argument for S’ means something like A exists relative to S.

I agree with Goddu that applying a ‘relativistic’ interpretation is a problematic strategy, although for a different reason. I take the view that there is no such thing as ‘relative’ existence. If something exists, then it exists ‘absolutely’ (cf. Gibson 1998: 6–7; Dörge and Holweger 2021: 4963). A relativistic interpretation therefore entails the non-existence of subjective L-arguments. The main question is whether my evaluation of the aforementioned scenarios commits me to such an interpretation. I argue that it does not.

I claimed that in scenario I, there is one argument. It is an argument of Pete’s, not an argument of Mary’s. Note the subtle but crucial difference between ‘an argument for Pete’ and ‘an argument of Pete’s’. The former allows a relativistic interpretation. The latter does not. Just as there is no interpretation under which ‘This is a book of Pete’s’ implies the book exists only relative to Pete, there is no interpretation under which ‘A is an argument of Pete’s’ implies that A exists only relative to Pete.

So, my assessment of scenario I is not committed to a relativistic interpretation. The same reasoning applies to my assessment of scenario II. I claimed that there are two arguments in this scenario: an argument of Pete’s and an argument of Mary’s. This does not entail that there is an argument existing only relative to Pete and another one existing only relative to Mary.

3.4 Narrowness Objection: The ‘Intention’-Condition

According to my definition, a consideration is not an ‘argument’ in the subjective sense unless it is intended to provide a reason for (or against) believing another proposition. Many others, too, define ‘argument’ with reference to the notion of ‘intending’ or notions that are (nearly) synonymous. Examples are provided by Blair (2001: 5–6; 2021: 91 − 2) and Goddu (2018: 339 − 40). It may be objected that the notion of ‘intending’ makes the definition too narrow. Thus, Svoboda (2020) suggests that ‘presenting’ a consideration ‘as an argument’ is sufficient for granting that consideration ‘the status of an argument even if nobody […] actually believed (and has believed) that the conclusion is supported by the premises’ (541).¹⁵ Svoboda asks us to imagine that a philosopher writes a logic textbook for his students in which he includes fabricated ‘sample arguments’ for testing purposes. Svoboda suggests that such ‘sample arguments’ are genuine arguments even if neither the author nor anyone else believes (and has ever believed) that the premises of these ‘arguments’ support the conclusion. Imagine that the book contains the following exercise:

• (35) Check whether the following argument is valid: Some cats report that Father Christmas is a cat. Therefore, Father Christmas is a cat.

Plausibly, no one has ever believed the proposition that some cats report that Father Christmas is a cat to support the proposition that Father Christmas is a cat. Yet, as Svoboda would suggest, it seems perfectly natural for the philosopher to call this set of propositions an ‘argument’.

I see two problems with Svoboda’s objection. To start with, presenting a consideration as an argument is claimed by Svoboda to be sufficient for the existence of an argument. While plausible in some cases, this suggestion seems implausible in others. Suppose that someone presents the propositions expressed by the statements in (36) as an argument, without intending for any of these propositions to support another (or believing that there is any relation of support among them).

• (36) Roses are red. Violets are blue. Sugar is sweet. And so are you.

It seems implausible to claim that the propositions expressed by the statements in (36) represent an ‘argument’ in any ordinary sense of the term. It may be objected that this example is unrealistic, since hardly anyone would ever present such a sequence of propositions as an argument. Such an objection misses the point. In semantic issues, examples do not have to be realistic; they only have to be logically consistent.

The second problem with Svoboda’s objection is that there is a plausible non-semantic explanation for why it feels natural to call a collection of propositions like that in (35) an ‘argument’. When asked to assess whether the ‘argument’ expressed in a text sequence is valid, a student must inevitably interpret that sequence. Interpreting a text sequence in this context involves trying to figure out what someone producing this text sequence would most likely intend to convey by it. Thus, a text sequence such as that in (35) is read as if there were someone who intended it to express an argument. With this in mind, it seems only natural to speak of an ‘argument’ in such a case, even if, literally speaking, there is no argument there. If the author of this exercise wished to be overly precise, he might write: ‘Imagine that someone expressed an argument in the following text sequence. Check whether this (hypothetical) argument is valid’.

This might also explain why it is natural to speak of an ‘argument’ in the case of (35), but not in the case of (36). In (35), the two statements are connected by a conclusion indicator (‘therefore’), and the propositions expressed by those statements have at least some (albeit very weak) logical connection. This makes it easy to imagine that this sequence of statements is used by someone to express an argument. In the case of (36), the statements are not accompanied by any argumentation indicator, and the propositions expressed by them do not have any apparent logical connection. Thus, it is extremely hard to imagine that someone would use this sequence of statements to express an argument.

To conclude, we have reason to doubt Svoboda’s objection. Despite this result, one could of course still object that the ‘intending’ condition in my definition of ‘subjective L-argument’ makes the definition too narrow. One loose suggestion that can be derived from the literature is that the term ‘argument’ in its subjective logical sense already applies when a consideration is merely believed, rather than intended, to provide a reason for believing a given proposition. Thus, Blair (2012: 198) and Butterworth (2021: 338), for instance, rightly suggest that such definitional differences should be discussed.

Imagine Mary thinking about what reasons there might be for the introduction of longer prison sentences. She is thinking to herself: ‘The deterrence of criminals is certainly one reason in favour of it’. Is Mary’s mere belief that the deterrence of criminals provides a reason for believing that longer prison sentences should be introduced sufficient for the existence of a subjective L-argument? Is this condition sufficient to correctly say that the proposition that heavy punishments deter criminals is ‘one of Mary’s arguments’? My intuition says ‘no’. Certainly, Mary believes this to be an objective L-argument, and she now ‘has an argument’ – in the sense that she is now mentally aware of an objective L-argument. But it does not seem right to say an argument of Mary’s came into existence. Thus, I do not find it inconsistent to say: ‘True, Mary thought that the deterrence of criminals speaks in favour of longer prison sentences, yet she never used this as an argument’.

Another indication that mere belief might be too weak for the existence of subjective L-arguments is provided by the following example: Imagine that Mary is involved in a debate on the said question. However, in the debate she argues against the introduction of longer prison sentences. During the debate, Pete, one of her opponents, makes the argument that heavy punishments deter criminals. Suppose she finds the argument convincing. That is, she comes to believe that the deterrence of criminals provides a reason for introducing longer prison sentences. Would it be correct to say that this constitutes a subjective L-argument, i.e., that Mary’s mere belief makes it one of her arguments? I do not think so.

I acknowledge that the evidence provided here is not conclusive and that intuitions regarding my examples may diverge. I think that a final resolution of this problem requires further investigation. For now, we can reasonably conclude that arguments in the subjective sense likely require intending, rather than mere belief.

3.5 Narrowness Objection: Cognitive Attitudes Other Than Belief

It may be argued that my definitions of ‘argument’ are too narrow because they are restricted to ‘reasons for or against believing a proposition’.¹⁶ This definition, the objection suggests, excludes reasons for adopting other cognitive attitudes. As Pinto (2019: 252) rightly points out, arguing often involves exchanging reasons for adopting various cognitive attitudes, such as ‘reasons for doubting, reasons for presuming, and so on’. Limiting the definition to reasons for believing seems to leave out all these other reasons.

While I agree with Pinto that we frequently offer reasons for doubting or presuming, I do not believe this requires broadening the definition of an objective L-argument. As discussed in Sect.  3.2, ordinary language often uses deceptive shorthand. Just as offering an argument ‘for going to the party’ is elliptical for offering an argument ‘for believing that we should go to the party’, the same logic seems to apply to cognitive attitudes. Thus, providing a ‘reason for doubting p’ can be analysed as providing a ‘reason for believing that p is doubtful’ (or ‘believing that one should doubt p’). Similarly, it seems that a ‘reason for presuming p’ translates to a ‘reason for believing that p is plausible’. If these considerations are correct, my definitions are not too narrow in this respect.

3.6 Broadness Objection: Non-Support Cases

It may be objected that some entities that are, according to my definition, subjective L-arguments, are not properly called ‘arguments’ in any ordinary sense of the term. Building on Blair (2004: 143-4), McKeon (2024) defends a ‘normative’ concept of argument:

An argument […] is a collection of propositions all but one of which are taken or have been taken to be reasons for the remaining one, and in addition the former constitute a reason for the remaining one. (Ibid.: 256; emphasis added)

According to my definition, it is sufficient for the existence of a subjective L-argument that a consideration is intended by someone to provide a reason for believing a proposition, regardless of whether it actually does. By contrast, McKeon suggests that a consideration is an argument only if it provides an actual reason. For McKeon, a consideration that offers no actual support is not a ‘bad argument’. It is a ‘pseudo-argument’ or a ‘non-argument’ (cf. ibid.: 260).

McKeon acknowledges that this view seems to conflict with ordinary language. Consider (37)-(42).

• (37) Many theistic arguments fail to support the existence of God.

• (38) She presented two arguments. Her first was weak, but her second was completely disconnected from her claim.

• (39) His argument begs the question.

• (40) That politician’s argument was an attack on his opponent’s character. It didn’t provide a reason to support his own policy.

• (41) The conspiracy theory is built on one central argument that has no connection to the known facts.

• (42) Her last argument was pure nonsense.

Statements like these are extremely common, and they do not seem to be inconsistent even though they suggest the existence of arguments that do not provide any reason for belief.

McKeon suggests that such statements should be understood as exemplifying merely a manner of speaking, a useful ‘façon de parler’ (cf. ibid.: 259).

Yet it is unclear whether McKeon’s characterisation is meant to suggest that these statements do not reflect an ordinary sense of ‘argument’.¹⁷ If it is not, then McKeon does not necessarily reject my analysis of the subjective sense of ‘argument’.

However, if it is, then he would have to elaborate on what he actually means by a ‘mere manner of speaking’ and provide the evidence necessary to establish that statements like (37)-(42) fit the description. As far as I can see, neither is found in McKeon’s article. This might be further evidence that McKeon’s ‘normative concept’ of ‘argument’ is not intended to reflect an ordinary sense of the term.

3.7 Broadness Objection: The ‘Provide-a-Reason’-Condition

According to my definition of ‘subjective L-argument’, a consideration must be intended to provide a reason for or against believing p. One might object that this provide-a-reason condition is too weak. Davis (2011: 2), for example, suggests that ‘[a]n argument is a sequence of statements, some of which are offered as providing a sufficient reason to believe the others’ (emphasis added). Intending to provide a sufficient reason is stronger than merely intending to provide a reason. However, does the subjective sense of ‘argument’ require this stronger condition? I believe it does not.

Consider a city council member, Mrs Fox, advocating funding a new public park. She offers three considerations in support of this idea: ‘First, it will increase property values. Second, it provides a safe space for children. Third, green spaces improve residents’ mental health’. Suppose an attendee, Jane, goes home later. Her husband asks what Mrs Fox’s arguments for the park were. Jane replies: ‘She had three main arguments. One was about property values, another was about safety for kids, and the third was about mental health’. In her reply, she refers to each of Mrs Fox’s considerations in support of funding the park as an ‘argument’. This seems natural even though Mrs Fox clearly did not intend any of these considerations to provide a sufficient reason to fund the park.

One could object that Jane’s report was inaccurate; strictly speaking, Mrs Fox was not offering three separate arguments. Instead, she was offering a single argument with three premises which, together, were meant to provide a sufficient reason. Thus, only the overall consideration deserves the name of ‘argument’, while the three considerations of Mrs Fox are merely premises of that argument.¹⁸

I am not convinced by this objection. Mrs Fox herself could have introduced her considerations by saying, ‘My first argument is …’ and so on. This would not have given the impression that she aimed to provide three sufficient considerations, or that she expressed herself misleadingly.

Of course, we could analyse Mrs Fox’s case as involving an argument composed of three considerations which, together, were meant to provide a sufficient reason. However, this is compatible with regarding each of these three considerations as an ‘argument’ in its own right. In my view, the term ‘argument’ can apply to both ‘complex’ arguments and ‘simple’ arguments that compose them.

Let me finally clarify that while I doubt that the sufficiency condition is adequate when defining ‘argument’ in its subjective sense, I suspect that it is adequate when defining the notion of someone’s ‘overall argumentation’.

As I conceive of this notion, an overall argumentation with regard to some proposition p is the product of arguing that p is (not) the case; and ‘arguing that p is (not) the case’ seems to entail intending a set of propositions to provide a sufficient reason for believing that p is (not) the case.¹⁹ Thus, (43) and (44) seem to be inconsistent, when taken literally.

• (43) In the following, I argue that she will win the election, but I think that my argumentation will not provide a sufficient reason for believing that.

• (44) I argue that she will win the election. But in fact, I think it is more likely that she will lose.

4 Conclusion

This paper has argued for a little-recognised distinction between two ‘logical’ senses of ‘argument’: an objective and a subjective sense. I have proposed a definition for each. In the objective sense, an argument is a reason for (or against) believing a proposition. In the subjective sense, it is a consideration intended to provide such a reason.

I have also defended these definitions against several objections. I argued that conclusions are not part of arguments and that argument components and the target propositions of arguments are not ‘speech acts’. I also suggested that my definition of ‘subjective L-argument’ is immune to Goddu’s Relativity Objection and that it is neither too broad nor too narrow in key respects.

While other objections may exist, this paper hopefully provides strong reasons to believe (I) that these two logical senses are part of ordinary English and (II) that my definitions are extensionally adequate and at least close to being intensionally adequate.

If correct, these results raise several questions for future research. Do these two senses help resolve the debate over whether arguments are ‘intentional’? Should argumentation theory adopt these ordinary senses, or should it retain standard technical definitions? Are these senses better suited for analysing real-world discourse? Finally, are there other important logical senses of ‘argument’ in ordinary English?²⁰