If Philosophy

Some Types of Definitions

Oh, joy. Are we here to define ‘define’? That depends on what you mean… But no, not really. We’re here to look at some central types of definitions and see some ways in which they differ from each other. For every definition it is the case that they consist of a definiendum – that which is to be defined – and a definiens – that which is giving the meaning (or reference) of some expression or term. In this way, they are similar to explanations which also consist in analogous two parts. They come in different kinds, much like explanations, and we’ll now have a look at a few of them to have a more fine-grained understanding of their constituent parts.

Lexical definitions are definitions that, when accurate, reflect the common usage of a term or expression. That is to say, if we define ‘circle’ as something like ‘a two-dimensional figure with every point equidistant from an arbitrarily chosen and fixed center point’ we have provided a definition which can be either true or false. In this case it’s true. A lexical definition might, however, be false. This happens when a suggested definition does not reflect a term’s or expression’s common usage. Say, for instance, that we define ‘circle’ as ‘a two-dimensional figure which consists in three sides’. We’ve given the definiendum ‘circle’ the definiens of a triangle. This is plainly (or should that be ‘planely’?) false. Lexical definitions thus attempt to capture the common usage of a term, such as those collected in dictionaries and the like. They can, as such, be evaluated in terms of truth and falsehood.

Stipulative definitions, on the other hand, mainly prescribe a certain meaning onto a term or expression in a given context. They are not so much true or false as they are suitable or unsuitable. Say that someone wishes to define the term ‘large’ in the context of a specific natural museum’s mineral collection. This could mean samples having a volume of such-and-such a size, much larger than we would have as a standard for what constitutes a large sample in the department where they house replicas of different kinds of mice. A museum guide might then define ‘large’ as e.g. ‘a sample of a volume greater than one cubic meter’ and go on about describing the various minerals to the visitors. The suggested definition does not have to reflect common usage, but is rather a way of signaling how the term or expression is to be understood in the given context. They can be provided to alleviate issues of vagueness and ambiguities, but do not automatically do so. In this case, it might be a suitable definition. Using the supplied definiens in the context of the department where they house the replicas of different kinds of mice, however, might not be as suitable. Neither of the respective definitions in the given contexts is, however, true or false as such.

Ostensive definitions are definitions that are accomplished by pointing out some object or property and either give it a name, or use its already given name. Perhaps we could argue that the prototypes of the meter or kilogram were pointed to in this way at some point in the past, or at least that it is conceivable that we could say that a ‘meter’ is the length of this object to which I am now pointing. This is not an intensional definition that fixes a meaning of the definiendum, but an extensional one that makes use of the reference of some expression.

There are, of course, other kinds of definitions that could be listed here. Moreover, there are undoubtedly features of each that have not been captured in full. As such, this list could be viewed as incomprehensive. Hopefully, in the given context, this is an appropriate quality, however.


Definitions come in many different kinds. Some of them are lexical and so are intended to report common usage of terms and expressions. Stipulative definitions instead are intended to prescribe a usage of a term or expression in a given context. They are both intensional types of definition. That is to say, they provide a conceptual meaning in the definiens to the provided definiendum. Ostensive definitions are extensional and make use of the reference of an expression. They all function in various ways, but serve to elucidate the meanings of concepts and the things these concepts refer to.

Some Explanations

Sometimes we don’t understand something or other. Every now and then we ask someone to teach us how that something works. If we’re lucky they give us an explanation. Moreover, if we’re capable, we understand the story they tell us. Explanations facilitate understanding, in other words. Is that all there’s to it? At a surface level, it would seem so. Stories are made up of parts, though, and that goes for illuminating ones as well. Let’s have a look at a few of those parts.

When it comes to explanations, there are many kinds, and even more examples of these kinds, to consider. They all consist of at least two parts, however. The first of these we might call the explanandum. It’s a fancy term used to denote the things explained. The second of these can be called the explanans. This is a similarly fabulous little word that denotes the explaining bit in an explanation. Explanations thus consist in something that explains, and something that is being explained.

So, what kinds of explanations are there? Suffice it to say, there are plenty… Why? Maybe that’s because different tasks require different tools, regardless of whether those tasks are practical or intellectual. In either case, let’s begin by assuming that someone asks why the water in a particular canister is boiling. In order to explain this we might feel our understanding is best facilitated by the use of what can be called a causal explanation.

Causal Explanations

These involve laws and initial conditions. These parts might be exemplified like follows.

Law: Water boils when it is heated to 100 degrees Celsius subjected to 1 atmosphere of pressure.

Cause: A container of water is heated to 100 degrees Celsius.

Condition: The container is at sea level, subjected to 1 atmosphere of pressure.

This is what we could call the explanans. It gives a story of why we should expect that…

Explained Event: The water in the canister boils.

… the event that the water in the canister boils. That is, why our explanandum obtains. The law here denotes some generalization where one variable has a productive influence on some other variable. The cause is the instantiation of the first variable. The condition asserts the domain of application for the law; i.e. under which circumstances it holds true. Water boils at 100 degrees Celsius, but not everywhere. It depends on how much pressure it’s under, for instance. We arrive at the second variable (the effect) given this causal variable and condition. Causal explanations thus consist in stories that connect a cause to an effect through some law and set of initial conditions. If we’re lucky, we find the story illuminating enough that we can curiously move on to other questions, such as whether or not the law alluded to is true. That should settle this matter, probably…

Probabilistic Explanations

Let’s say we’re interested in something slightly different now that we have the structure at hand. Perhaps we’re wondering why so-and-so has fallen ill. One kind of explanation we could give is a causal explanation: “you see, all individuals who satisfy these descriptions end up ill, and ol’ Kim happens to have all the relevant traits”. However, we don’t always have such clear-cut universal laws. Sometimes we have to make do with probabilities. So, rather than arriving at our explanandum through deductive means, we use an inductive process. In short, we give a probabilistic explanation.

Probabilistic explanations roughly follow the same form as causal explanations do, but use probabilistic rather than deterministic laws. So, we might have a story like follows.

Probabilistic Law: Approximately 58 per cent of humans develop illness X by the age of 80, unless they have been vaccinated against it.

Cause: Kim is a person at the age of 80.

Condition: Kim has not been vaccinated against illness X.

The law in action here does not make it inevitable that Kim has the disease. It does, however, give us an account of why she has gotten this disease. It turns out (as per the argument) that she was more likely to get it than to not get it. (Tough break, Kim, we’re all rooting for you, I’m sure.) Like in the causal explanation, we have a similar structure. We have a law, cause and condition that constitute the explanans and an explained event constituting our explanandum. Now, I wonder if Kim asks herself what she did to deserve such an outcome. Maybe there isn’t such a thing, but if there is, we would like to know why she did it.

Intentional Explanations

Regardless of why Kim got this illness, she might recover. Illness X is a transitory thing, let’s say. Now Kim goes on to celebrate her newfound good level of health. Now we might ask why is she celebrating? Duh. She just got better, that’s just what you do. Sure, but let me put it this way. If she didn’t celebrate why would that be the case? Here, causal and probabilistic explanations don’t seem to do the trick, and neither does common sense as easily. When it comes to actions, we have a component of intentionality that isn’t so easily captured by these law-like generalisations or probabilistic accounts. Instead, what we’re after is an intentional explanation.

Again, the notions of explanandum and explanans come in handy. Here what we’re trying to explain is some action. So what’s doing the job of actually explaining such an action (i.e. the explanandum)? Well, we’re generally looking for a way of rationalising actions. We want them to make sense from the point of view of the agent (i.e. the person acting). If Kim doesn’t celebrate, this might be due to any number of reasons. But they all have something in common, namely that they would consist in a combination of a belief and a desire. Perhaps she believed that celebrating good health is a way to jinx herself, whereas not celebrating is the best way not to jinx herself. Let’s furthermore assume that she desires to remain in her newfound, and hopefully not transitory, good health. Therefore she refrains from celebrating. Not even with a little jig on the lonesome. Such belief-desire pairs make up the explanans of intentional explanations, and they make the actions “make sense” to us. Even if we are not so easily swayed by notions of being jinxed ourselves, we can understand that if someone does hold that belief, and has the desire not to jinx herself, she would refrain from acting in the way that would jinx her.

There are doubtless other stories to tell here, but these have been a few to get started with. While I might be dim, I hope the stories given here are less so.


Explanations are stories that facilitate understanding. Some are causal, some are probabilistic, and some are intentional. Causal explanations use causal laws, probabilistic explanations relates variables through probabilistic means, and intentional explanations consist in references to belief-desire pairs. Common for them all is that they consist of a thing being explained and a thing doing the explanation. We call these the explanandum and explanans, respectively.

The Hypothetico-Deductive Method

Some knowledge is what we might call “analytic”. Say that someone tells you that the definition of things being lime coloured is that they have a “greenish yellow tint” or something similar. From this you can deduce that all lime coloured things are greenish. Sweet! Other things are what we come to know through experience in more than just an enabling sense. (Not sweet… We have to get up from our armchairs and explore the world? Oh, well.) Consider the ever so famous statement that the evening star is identical to the morning star. There is nothing within the definitions of these concepts that allows us to assent to the proposition before us. Even so, it is true. But how can we come to know about such a thing? We might come to know it through careful observation using some sort of telescope, for example. Such an observation would provide us with the justification to assent to this proposition. It does so in a different but analogous way to how understanding the concept of “lime coloured” and “greenish yellow tint” justified our assenting to the proposition that all lime coloured things are greenish. Empirical and analytic justifications are different, but serve similar purposes.

The evening star and other faraway objects make up one example of things not yet seen, though there are many others as well. The same underlying method can be used to provide justification for claims about things not yet seen. Some things are, however, unobservable. For instance, some claims concern general statements. (That is, claims that all so-and-so are thus-and-so.) Let us suppose that someone claims that ingesting liquorice roots increases the longevity of all mammalian animals. How would we go about finding out whether that is the case or not? We have one particularly useful method to employ; the hypothetico-deductive one.

So, what is it, and why is it effective? It is a method that consists of about five steps and ends up at a positive or negative outcome that either speaks in favour of a claim, or against it; though it doesn’t verify or disprove it entirely. It’s a useful tool then to start to justify claims of as yet unobserved or general things. It is hypothetic because we suppose some state of affairs could be the case, and it is deductive because we logically draw out observable consequences of what follows from such a supposition. Let us see how it works in (theoretical) action.

Asking the Question

First off, you begin by asking a question. In our case it might be something like: “what is the relationship between liquorice roots and the longevity of mammalian animals?”.

Formulating a Hypothesis

Secondly, you provide a tentative answer to your question; what we call a “hypothesis”. Perhaps that: “ingesting at least 5 g of liquorice roots per day increases the longevity of mammalian animals”.

Deriving Observable Consequences

Thirdly, you wish to have the ability to test this possible answer, so you deduce observable consequences from it. To do so, you often have to make use of what is called “auxiliary hypotheses”. These are claims that connect the main hypothesis to the observable consequence. You could think of auxiliary hypotheses as construing a bridge spanning across a chasm and two mountaintops. The first mountaintop is the possible answer, i.e. our hypothesis; whereas the second is a possible observable state of affairs that would be the case if the hypothesis were true. There are many such mountaintops, but any combination of a hypothesis, auxiliary hypotheses, and observable consequences allows us to formulate a test implication. In our case, the observable consequence might be that serving at least 5 g of liquorice roots to one sample will yield a higher longevity as measured in days compared to a control group who did not receive such a snack. An auxiliary hypothesis helping us establish this claim is that longevity is about “life-span as measured in days” (for example).

The test implication always takes the same form. It states that if our hypothesis is true, and our auxiliary hypotheses are true, then we should be able to observe something in particular. In our case it has to do with observing an increased longevity in our test group. Alright, those are some preliminaries out of the way. Time to test!

Moving from Concepts to Testing

The fourth aspect is to put this test implication into action. Now that we have it clearly formulated, we are ready to go observe whether or not our observable consequence actually obtains in the world.

Results of the Test

If the observable consequence obtains, then we might say that the world is compatible with the hypothesis being true. We can’t say that the hypothesis has been shown to be true, only that it has not yet been ruled out as a possible state of affairs. If, however, the observable consequence does not obtain, we can infer that the combination of hypothesis and auxiliary hypotheses do not hold true. This simply means that not all of the claims are true. Perhaps the hypothesis is true, but the auxiliary hypotheses (again, think of these as the bridge between the hypothesis and observable consequence we failed to observe) are faulty. Perhaps the hypothesis is wrong, or perhaps both. All we can be certain of is that not all of them are true, if we cannot obtain our expected observable consequence.


Some knowledge is what we might call analytical. To know that bachelors are unmarried men we do not have to do more than grasp the concepts involved. Other kinds of knowledge depend on experience in some way for justification. Some knowledge is justified by use of the hypothetico-deductive method. It consists of five steps, namely (i) asking a question, (ii) formulating a hypothesis, (iii) deriving observable consequences, (iv) testing, and (v) receiving a result.

Normative Ethics: What Can We Do and What Should We Do?

Agents are individuals who can choose between courses of action. When she stands before such a choice, she might wonder what she is to do.

This question of course isn’t very specific. It might depend on what she’s setting out to do, right? I mean, if she wants to bake a cake then she might need to crack a few eggs. And if she wants to overthrow a despot, perhaps she might… need to crack a few eggs. But in the latter of these examples, there is a component that we probably find lacking in the first. We can call this the ethical component. It somehow seems to require us to ask yet another question of ourselves. I mean something like the following.

Okay, so this is the goal I have in mind, and I can accomplish it by doing this and that. That’s all good and well. But… Should I do this and that?

This question can be answered in a number of ways. The “should” part is usually tied to some kind of normative or ethical theory. There are many of these theories around but they can usually be grouped somewhat neatly into families of theory. Let’s turn to look at a few of them.


Consequentialism is the view that only the value of the consequences – or the effects – of an action matters when trying to determine if it is right or wrong morally. A famous version of consequentialism is that we should maximise the total amount of happiness in the world. This view is called act utilitarianism. Act utilitarianism claims that an action is right if and only if, and because, it maximises the total amount of well-being in the world. Any action that does not maximise the total amount of well-being is therefore wrong on this view.

Okay, so act utilitarianism puts a lot of emphasis on each individual action that is to be performed (or not to be performed). That might seem quite demanding. There is little room to treat those near and dear to us better than strangers we may or may not ever have met. Perhaps that’s not too bad though. Why shouldn’t we care about others equally? Happiness is happiness regardless of who experiences it, after all.[1] But then again, if a person’s organs could be harvested to save five other people, and if we presume their happiness over the course of their five lifetimes would be greater than could be achieved in the unwilling donor’s one lifetime… Why shouldn’t we do it? Perhaps because actions of this sort tend to undermine the trust between people.

Instead, we might focus on types of action. There’s another version of utilitarianism that, much like act utilitarianism, states that we ought to maximise well-being. This second version of utilitarianism puts an emphasis on rules, rather than individual actions directly, however. Instead of saying that an action is right if and only if, and because, it maximises well-being, it instead roughly says that an action is right if and only if, and because, it is prescribed by a rule that maximises well-being. Now our actions might seem more dependable and less prone to undermine the trust between people. However, act utilitarians might question this focus on rules. If more good can be promoted by breaking a rule, shouldn’t we? And like so the theorising continues.


Deontology is a view that, contrary to consequentialism, does not solely consider the effects or consequences of actions when determining what is right and wrong. Deontological theories often focus on what we have duties to do (or refrain from doing). So, say that harvesting the organs of some unwilling person maximises the amount of well-being in the world. Should we do it? A deontologist might answer no, since other things than the effects of doing so matters. The person whose organs are to be harvested might deserve to have her rights respected, or deserve to be treated as an end in herself. That last bit basically means that she is not only to be treated as an instrument for something else. Duties, on this view, put us and others under certain specific constraints that we ought to accept. Much in the way that if someone promises to do something, she is obligated to fulfil that promise. Some duties, according to deontologists, hold categorically, however. That is to say, the duties hold even if no one has expressed a desire or intent to act in accordance with them.

Depending on what duties are involved, and how they are ranked vis-à-vis each other, we may get more or less intuitive sets of duties that we ought to follow. If they conflict, however, it is not always easy to say what ought to be done. The classical example goes something like this. Imagine that we have a duty not to lie, but also a duty to be protective of others. Then some aggressive individual with the intent to murder a person comes up to us and asks us where this person is who just ran by us. What should we do? Lie? Protect the person? The weights or importance of the duties would have to tell us, but if they are on a par with each other the matter can’t easily be settled. This is therefore a challenge that the deontologist might have to face.

Another similar view is that we might focus on people’s rights. Rights typically come alongside duties. Say that a person who stands to have her organs harvested to save five others (rightfully) complains. What explains that her complaint is legitimate? That might be her right not to be harmed. The corollary duty, here, is that no one harms her. The nature of these rights, their force, whom they apply to are questions that deserve to be discussed. And people still do.

Virtue Ethics

Okay, so consequentialists focus on the effects of actions, and deontologists on what duties or rights there are. Virtue ethicists in their turn focus on the character traits of the one who stands to perform an action or to refrain from doing so. Rather than focusing on right-making principles for each and every instance of action, it looks to the character traits that are part of a good person throughout her whole life; or simply a good life. Is the action kind (assuming kindness is a virtue)? Is it brave (assuming braveness is a virtue)? There are a multitude of virtues a person might have, to varying extents. The focus for the virtue ethicists is basically the one obtained by going from the question “what is right?” to something like the question “what is a good life?” and here varying answers are possible to provide.

However, a person’s character traits are arguably not wholly within her control. Upbringing might have some part to play, or perhaps education, or perhaps we have varied predispositions toward acting in certain ways. So, it seems as though a person can be blamed for not being virtuous despite, perhaps, working equally as hard to be virtuous as someone who had a more fortunate history. Is this factor of luck to be removed or to be kept? Here the discussion between the different families of theory might well continue for some time.


Agents, as stipulated, are individuals who can realise some course of action or another. In some cases they might face the question not only of what they can do, but of what they should do. This question can take on a moral character. To answer whether she should or shouldn’t do whatever it is she is considering, we look to normative or ethical theories. I suggested that there are roughly three families of such theories. Consequentialists argue that actions are to be evaluated in terms of their effects. Deontologists, in turn, argue that actions are to be evaluated through the conformity to a set of duties or rights. Finally, virtue ethicists turn the question from “should I do this?” into “is this part of a good life?” and discussions keep going on both within each family of theory, as well as between them.

[1] Bentham allegedly once said that “every man is to count for one, nobody for more than one”.

Metaethics: What is Right, What is ‘Right’ and What is Right?

Metaethics is a field of study that deals with three types of question regarding morality. Namely, (i) ontological questions about whether there actually are such things as moral facts, (ii) questions concerning the semantics of moral judgements, and (iii) the epistemology of them; whether or not we can know what is right and how, if so. Let’s look at a few of these, and some of their potential answers.

The ontological question “are there moral facts?” may be answered either affirmatively, or negatively. We call these stances the realist and nihilist positions, respectively. The realist may then either be a naturalist or a non-naturalist. The naturalist argues that moral facts exist in the same way as natural facts do. There is nothing different in essence about moral facts in comparison to some natural fact, as for instance the length of a stick. The non-naturalist instead argues that there is something different about moral facts. Perhaps because they (supposedly) override desires that are incompatible with doing what is right, or perhaps they even motivate us to act in specific ways to some degree. The nihilist however, as already indicated, argues that moral facts don’t exist. According to them, the fabric of the world just doesn’t contain ethical value; we’re in a world without worth. I’m not entirely sure doom and gloom follows if this is so, though. Can you be broke if there’s no such thing as money? It’s not evident, but at least you probably won’t be in monetary debt. So there’s that.

The semantic type of questions deal with what terms such as ‘right’ and ‘wrong’ and ‘good’ and ‘bad’ mean or express. Descriptivists argue that moral concepts work as regular descriptive concepts. To say of an action that it is right or wrong is a lot like saying that an object is large or small. The expressivist, on the other hand, argues that moral concepts express our attitudes toward actions. According to the expressivist, to say that an action is right or wrong is roughly the same as going “yay for the action” or “boo for the action”. Neither of these statements can, strictly speaking, be true or false. The division between the descriptivist and expressivist lies exactly in this. Expressivists argue that the semantics of ethics is truth-evaluable. Expressivists argue the opposite.

Lastly, the epistemological question of whether we can know what is right or not may be answered, much like the first one, affirmatively or negatively. We may call the affirmative answer the cognitivist position, and the negative answer the sceptic position. There are some combinations of answers to these three types of questions that fit together more easily than others, but there are many different combinations. Assuming that knowledge is something like justified true belief, then we may only have knowledge of moral facts if descriptivism and realism are both true. How we may be justified in our beliefs about ethics, if at all, is of course a controversial topic. Do intuitions suffice? Whose, if so? How are conflicts to be resolved? These are among the first questions that pop up, but also among the most difficult questions to answer. I’ll leave these questions unresolved. Whatever answer is right, I’m probably going to be at least a little bit off the mark.


We have established that metaethics revolves around three types of question. These types are the ontological, semantic, and epistemological. The ontological question has two answers, the affirmative one being presented by the realist, the negative one by the nihilist. The semantic question about what ‘right’, ‘good’, ‘wrong, and ‘bad’ mean can be answered either as the descriptivist does; that they are predicates much like any other predicate, or as the expressivist does; that they are terms that express our positive or negative attitudes toward actions. Lastly, the epistemic question “can we have knowledge about moral facts?” may be answered positively, like the cognitivist does, or negatively, like the sceptic does. Many combinations exist. With a little luck, these labels may be of some help in thinking about these somewhat abstract matters. In that, I at least hope that I’m right.

Argumentation: Analysis and Evaluation

So far we’ve gathered that there are deductive and inductive arguments. They consist of premises and conclusions. So what? Well, analysing arguments in part involves deciding what form they have, and so if they are deductive or inductive. Once this is done, we can begin to evaluate them.

How do we evaluate them and so check their credibility, though? We don’t do it by simply looking at the conclusions and asking ourselves whether we’re inclined to agree with them or not. Instead we look to, and at, the premises. Why? Recall from Argumentation: From Premises to Conclusions that premises are propositions that are intended to justify conclusions. We’re therefore interested in whether they succeed or not. Even if the conclusion reached in some argument doesn’t sit well with us, the premises might provide ample reason for us to accept it. Insofar as we are rational that is, and being rational seems like the sort of thing we want to be.

Let’s look at an example argument to see what this entails. Consider the following:

P1) If Queen Elizabeth is in Buckingham Palace, then Queen Elizabeth is in London.

P2) Queen Elizabeth is in Buckingham Palace.


C) Queen Elizabeth is in London.

So, we’ve got an argument analysed into its component parts. Now we turn to evaluating it.

Evaluating Premises’ Tenability

At this point we have two tasks in front of us. We can (1) consider whether or not P1 and P2 are reasonable to believe, and we can (2) consider whether or not them being reasonable to believe provides us with good reason to accept the conclusion C; that Queen Elizabeth indeed is in London. Let’s begin with task number one. I may not know much about the British monarchy, but one thing I do know is that Buckingham Palace is situated in London. I once saw it on a trip by mistake. (Long story. Well, not really, it was a weekend trip.) Anyway, being in Buckingham Palace is sufficient for being in London, so P1 seems reasonable to accept. If someone is in that old building, then they’re in the capital city of England. Huzzah! Can we accept the argument now and move on? Not just yet.

What about the second premise (P2)? Now, it might seem reasonable to believe that Queen Elizabeth is in her palace, but just like Princess Peach in those old Super Mario games happened to be in another castle (time and time again…), so might the Queen of England be. In fact, she might be just about anywhere else. Right now I don’t find myself with very good reason to believe that she’s in Buckingham Palace. It’s approximately five p.m. as of writing this. Perhaps she’s gone to the pub two towns over for an after work get-together? Maybe not, but perhaps she’s off somewhere on official business. That seems like the sort of thing she would be up to. Therefore, I may not have sufficient reason to believe that she is in London. Note, however, that I didn’t start by assuming that she isn’t in London, but arrived there by way of evaluating the premises P1 and P2. So far so good. P1 and P2 have both been dealt with in terms of their tenability. Now we’re done, surely? Nope!

Evaluating Premises’ Relevance

Well, why aren’t we done? I’ve accepted P1 but rejected P2. That’s my purported reason for declining to accept the conclusion, C. If I had accepted both P1 and P2 then I would have been rationally forced to accept C. And as I said, rationality seems like the sort of thing we want to promote. If you don’t, I wish you luck dodging the barrage of ad hominems that you’ve probably got coming.

The point is this. Relevance is the degree to which a series of premises’ strengthen (or ‘support’) a conclusion under the assumption that the premises are true. The highest form of relevance is obtained by deductive arguments, since for these arguments, it is the case that if the premises are true then the conclusion must be true, too. The argument we’ve been discussing so far has been deductive, and I therefore deem the relevance to be as great as it can be.

This concept of relevance can, as might be expected, be applied to inductive arguments as well. Relevance is a matter of degree. Inductive arguments may well strengthen their conclusions by way of their premises, but since these can have false conclusions even when their premises are true, their premises’ relevance is never wholly complete. But in this instance, I do deem the premises to be oh-so relevant.

Sufficient and Necessary Conditions

Now, let’s get a little bit technical. I said that being in Buckingham Palace is sufficient for being in London. What’s that all about, anyway? Something, S, being a sufficient condition for E, is such that if S obtains, that is “enough” for E to also obtain. Whatever S and E may be short for, if S is sufficient for E, and S obtains, then we may be sure that E obtains as well. Okay, so what about E here? Do we have a fancy term for this term, too? Sure we do.

E is what we call a necessary condition for S. Why? Well, let’s think about this a little bit. We just said that if S obtains, then E obtains. But that means that we cannot have S be the case without E also being the case. That’s what it means for E to be a necessary condition of S. Think of it this way. If the Queen of England is in Buckingham Palace, then she must be in London. But that means that it’s necessary that she is in London if she is in Buckingham Palace. Of course, the Queen of England may be somewhere other than Buckingham Palace even though she is in London. Perhaps she’s visiting the parliament, or any number of other things that she could do in London. And that is precisely an example of the difference between sufficient and necessary conditions. Sufficient conditions bring about their correlate without fail, necessary conditions only allow for their sufficient correlates to obtain.

Okay, so much for that interlude. Let’s get back to whatever it was we were doing. Evaluating premises, was it? Sure. That. Take P1 for example:

P1) If Queen Elizabeth is in Buckingham Palace, then Queen Elizabeth is in London.

We might do well to evaluate this premise as true, given that being in Buckingham Palace is sufficient for being in London. Someone who did not know this, however, might respond that there’s no more reason to believe P1 than there is for her to believe that the number of grains of sand in the Sahara is even.

The proposition does not alter its truth-value regardless of this. The proposition is either true or false, but not both true and false at the same time. We therefore need to distinguish between taking something to be true (or false) and its being true (or false). When a deductive argument (those whose conclusions have to be true if their premises are true) has true premises, we call it sound.[1] Deductive, that is to say; valid, arguments can thus be either sound or unsound. A deductive argument is unsound if and only if at least one of its premises is false.

The same goes for considering premises to be false, and them actually being false. An argument may well be sound without my acknowledging that it is. Since omniscience isn’t one of the features us human beings come with, this gap is something we have to come to terms with. Whilst the gap cannot be removed entirely, we can do our best to make sure it is as small a gap as possible.


So, in the end, where are we at? We’ve said that once an argument is reconstructed, we can evaluate it. We do this by (1) looking to the credibility of the argument’s premises, and (2) checking their relevance for the proposed conclusion. In order to facilitate this work, an understanding of necessary and sufficient conditions helps. Necessary conditions of something must obtain if that something obtains. Sufficient conditions for something to obtain are such that if they obtain, that very something they were sufficient for obtains as well. We’ve also come to the conclusion that there’s a difference between taking something to be true (or false) and its being true (or false). We may not always evaluate arguments correctly, but we should probably do so fairly. The above might help in this endeavour. Or it might not. That’s for you to evaluate.

[1] This is not to be confused with that old question of whether a tree falling in the forest with no one around to here it makes a sound. We won’t be dealing with that question here and now.

Epistemic Coherentism and Foundationalism

Knowledge, as previously discussed, is analysed as justified true belief according to the classical definition. We established that truth is to be understood in an absolute – not relative – way and that belief is some form of intentional attitude of acceptance of some proposition. Justification, as noted, can be viewed in quite different ways. It can be said to be domain-specific and subject-relative. There are many other distinctions that can be made when it comes to epistemic justification.[1] Some like to talk about the distinction between a priori justification and a posteriori justification, whereas some like to go on about internalism and externalism. The first distinction deals with justification prior to, and after, experience. The second one has to do with whether justification requires that we grasp claims that support some belief, or whether it suffices that the justification is e.g. truth-conducive. These are all very interesting topics, but for now I suggest that we look to another very basic distinction, namely the one between coherentism and foundationalism.

Where do we start? Why not from the bottom and reach our way to the top – at least theoretically speaking. Foundationalism is a view about the structure of epistemic justification. On this view some “basic” beliefs are, in themselves, credible and can lend their support to other “non-basic” claims which aren’t credible or self-evident in the same way. Say that you have the law of identity, namely the claim that “x = x”; i.e. the claim that a thing is identical to itself. This law may then support claims about particular entities, say that “the writer of this text is the writer of this text” or “Dumbo is Dumbo”. Assuming we accept the law of identity as credible, we can use it to support the latter claims as well. Foundationalism about epistemic justification therefore takes certain things from granted, and from these construct (abstractly speaking) a foundation on which other layers of justified beliefs can stand. Once a non-basic belief is justified, it can then justify yet other layers of non-basic beliefs. The ultimate justification for these non-basic beliefs lies, however, in the basic beliefs.

Coherentism, in turn, shifts from a bottom-up structure of justification into something more akin to a network. On this view, beliefs are not justified by other already credible beliefs. Instead we have systems or “networks” (if you will) of beliefs that are justified (or not). Whereas in foundationalism basic beliefs justify other non-basic beliefs, coherentism does not view the connections between beliefs as justifying relations as such. Instead it is the coherence of the web of beliefs – how well they hang together as a whole – that captures the idea of justification. Say that someone, Smith, has the belief that the sun is a large object, and the belief that objects take up space, and the belief that on a scale from smallest to largest of everyday objects we have the sun somewhere around the top, …, and so on. How well these beliefs Smith has “fit” with each other, and how many the connections between the nodes in the network are, is what ultimately what justifies them as a whole. Of course, one can speak of how well justified singular beliefs are insofar as one bears in mind that it is the coherence of this belief with some assumed set (or “web”) of beliefs that is ultimately justified. The justification of a singular belief is therefore, in a sense, derivative from the justification of what we might call a person’s web of beliefs.


Foundationalism and coherentism are two radically different theories of epistemic justification. Foundationalism seeks to build our knowledge from credible or indubitable beliefs at the bottom, to other beliefs that may not be so indubitable. Coherentism turns this picture on its side and views justification as a feature of a system of beliefs. On the coherentist view, it is not the relations between particular nodes (beliefs) in the network of beliefs that serve the justifying role. Rather, it is the system of relations as a whole that makes up the person’s epistemic justification for her beliefs.

[1] The term ‘epistemic’ is used here because it has to do with ‘epistemology’ or “the study and theory of knowledge”.

Argumentation: From Premises to Conclusions

What is an argument? Oftentimes people speak of arguments as reasons to believe a particular statement. That usually works well, but we will try to be a bit more technical in our analysis. That way we can name different things differently, and hopefully speak of them a little more clearly.

Arguments, the way we are to understand them, are comprised of two types of entities, namely premises and conclusions. Premises are propositions that serve the role of trying to justify another proposition that, in the best of circumstances, follow logically from themselves. Themselves? The premises! In turn, we call the thing that premises are to justify for the conclusion. An example of an argument that consists of two premises and one conclusion follows.

P1) All cats are cute
P2) Felix is a cat


C) Felix is cute.

All three of these steps, as I just said, make up an example of an argument. P1 and P2 constitute the premises that serve to justify the conclusion, C, namely that Felix is cute. This argument is, moreover, what we classify as a deductively valid argument. Why? Well, briefly put, the argument is such that the conclusion must be true if (and I stress, if!) the premises are true in virtue of its form. An argument’s form, in brief, is given by the relations that hold between the premises and conclusions. If it is the case that all cats are cute and that the critter I’m pointing to right now, Felix, is a cat, then it would follow that Felix is cute. He’s a cat after all, and as P1 says, all cats are cute.

Now, even if it turned out that all cats weren’t cute, this argument is nevertheless deductively valid. Moreover, even if Felix isn’t a cat, the argument is still deductive. But why? “You just said that the premises are true in deductively valid arguments, didn’t you?” Well… Not quite.

The important thing to grasp here is the hypothetical nature of the definition. It states that if it happens to be the case that the premises are true then the world must be in such a way that the conclusion is true, too. When we are to determine whether an argument is deductive or not, it does not matter, strictly speaking, whether or not the premises in fact are true. We are only interested in what would have to be the case if they happen to be true. Try as hard as you can to imagine a world where it is the case that all cats are cute, where Felix happens to be a cat, yet Felix isn’t cute. You can’t.

Deductively valid arguments, to reiterate, are such that their conclusions must be true, if their premises are true. There are deductively valid arguments of many kinds, and some of them even have names. That one above about Felix is called a syllogism. Why? Aristotle said so, or something close to it at least. Other examples such as modus ponens and modus tollens exist. The names are not too important right now, but suffice it to say that while there are many deductively valid arguments that have been named, an infinite amount of others have not; despite all the time humans have spent studying the subject.

Phew! Surely, that’s got to be everything to it, right? Yeah, not quite. Again.

We now know roughly what a deductively valid argument is. But what’s the point of that? The point is that we can now distinguish these from another kind of argument. I’ll first give you the name of them, and hopefully explain what they are in short order. They’re called inductive arguments.

So, what are they? It might be easier to understand what they are by contrasting them with deductively valid arguments which we already have a grasp of. Whereas deductively valid arguments must have true conclusions when their premises are true, inductive arguments do not have to have true conclusions even if their premises are true. But why would we want to ever use such arguments? Surely we want our reasons for accepting a proposition to be conclusive! Yes, sure. Often that is the case. But sometimes we simply can’t reach such levels of confidence. I’ll illustrate why with an example of an inductive argument.

P1) Most people with English-speaking parents speak English fluently.
P2) Kim is a person with English-speaking parents.


C) Kim speaks English fluently.

Alright, so far so good. What’s different about this argument? Most importantly, for our current purposes, it’s the quantifier “most” having replaced the quantifier “all” from the first example argument. This allows room for Kim to be part of the group that speaks English fluently, but it also leaves some room for Kim to be part of the group that for whatever reason does not speak English fluently. How could this be so? One reason might be that Kim is only six months old. Expecting her to speak English fluently – or any language for that matter – is a bit much to ask at that age.

Inductive arguments, then, can have all of their premises being true, but still not have their conclusions’ truth guaranteed. It might well be the case that most people with English-speaking parents also speak English fluently. It might also well be the case that Kim is such a person. But, as we saw, that is not a guarantee of her aptitude in speaking English. If the undermining proposition that she is six months old is true, we might do best to treat the conclusion as false.

We use inductive arguments in areas of arguments where there are some uncertainties or probabilities less than 1 but greater than 0. That’s quite often. Not always, but often enough. They have their use, just like deductively valid arguments. Their areas of application differ, however, and it serves us well to be mindful about what kinds of arguments we supply for the conclusions we intend to reach. Moreover, it serves others well if we represent their points of view with as credible arguments as possible when we are to evaluate them. Sometimes that is by using deductive (or “valid”) arguments, at other times it is by categorising their points through inductive arguments.


We have reached the point where we can say that arguments consist of premises and conclusions. Premises are propositions that serve to justify some other statement. This other statement we call the conclusion. Deductively valid arguments are such that their conclusions must be true given that their premises are true. This is what we can call a ‘formal property’. The deductively valid arguments have true conclusions when their premises are true because of the way the premises and conclusions are related. Inductive arguments, by contrast, can have false conclusions even when their premises are all true. We can and may use both kinds of argument, but for somewhat different purposes. It’s therefore probably a good idea to be mindful of your own intentions, and those of others, when arguing.

The Classical Definition of Knowledge

What does it mean to say that you know something is the case? We might begin by answering this question through the classical definition of knowledge which stems from Plato. It states that a person, A,[1] knows that a proposition, P, holds if and only if the three following conditions are met:

(i) P is true,
(ii) A believes that P is the case, and
(iii) A is justified in believing that P is the case.

That P is true is to be understood in non-relative terms. That is to say, the concept of truth is treated as absolute. The proposition P is either true, or false, but not both at the same time.

The idea is that (i)-(iii) are individually necessary and jointly sufficient to have knowledge. The claim that they are jointly sufficient has been challenged, most famously by Edmund Gettier, but it nevertheless serves as a foundation for discussions about what constitutes knowledge. If something is not the case, then we cannot know that it is the case. If we do not believe something to be the case, then we do not know it, since knowing something (as per clause (ii)) entails that we believe it. Lastly, if we do not have good reasons for the belief that P is the case, then we do not know it either. We would scarcely like lady luck to decide for us whether we know something or not.

This classical definition deals with what can be called propositional knowledge. Propositional knowledge can roughly be likened to knowledge of facts. Propositional knowledge can in other words be distinguished from practical knowledge, for instance. I may know that the Earth is a spheroid in the first sense, whereas I may know how to ride a bike in the second sense. The distinction made in these two scenarios is precisely the one between propositional and non-propositional knowledge.

With these two types of knowledge in mind, we may return to the criteria (i)-(iii) listed above. That A believes that P means, simply put, that the person entertains a proposition and treats it as though it were the case. That the agent is justified in believing that P means that she has good epistemological reasons for entertaining it as though it were the case. Say that A believes the Earth to be spheroid on account of pictures being taken from satellites. This might constitute a good reason for believing this to be so. A picture taken of an equation such as “X + 1 = 3”, however, does not obviously constitute a good reason for believing that X is equal to 2. What would constitute good reason is some level of introspection grounded in some mathematical expertise.

Thus, we may speak of different forms of justification. We might make use of sense data and recordings of the causes of these in order to gain empirical knowledge. In another way, we might use our faculty of reason to justify beliefs about mathematics, language and logic, for example. The justificatory role is, we might say, domain-relative.

Aside from this, a person, A, who stands to review the photographs taken by satellites might be in a good position to believe that the Earth is spheroid. In other words, she is justified to believe this about the Earth’s shape. Imagine a scenario in the future when all technology and scientific knowledge has been wiped out from the face of the Earth. Say, because someone clumsily set off a number of nuclear devices. In this scenario, a person, B, might look as far as her eyes allow her to and still not have good reason to believe that the Earth is spheroid. This means that not only is justification domain-relative, it is also relative to individuals. The person A from our time has good reasons to believe something that the person B in the post-apocalyptic future does not.

What is more, assuming that A and B are similarly inclined to believe things on the basis of adequate evidence, we might find that A believes that the Earth is a spheroid, whereas B does not. This allows us to note that belief is relative to individuals as well. Indeed, I may believe many things you do not, and the reverse holds true as well. This is expected, but not self-evident until an analysis of the concept of belief has been supplied. Here, we may treat it as a subject-relative attitude of treating a possible state-of-affairs as an actual state-of-affairs.


To summarise, we have established that knowledge is (i) true, (ii) justified, (iii) belief. We have distinguished between propositional knowledge – knowledge of facts – and practical knowledge. We concluded that epistemic justification is domain-relative, and that justification is relative to individuals. Belief, as might be expected, is also relative to individuals. For instance, whereas I may believe that my fridge is empty, you might not believe that about my fridge, and vice versa.

[1] We’ll be making frequent use of variables throughout these sections. They will initially be introduced with some description, but these descriptions will not always accompany them afterwards. You can think of the letters as placeholders for other information. Sometimes (like here) they are shorthand for agents, sometimes for propositions. Sometimes for specific times, and other times they designate places. Variable symbols let us focus on the general form in our explications instead of being unnecessarily confused by the specific substantial things they refer to. They do so by clarifying what kinds of things we are interested in at different argument places without making use of particular instances of these kinds.