The blog of Dr Glenn Andrew Peoples on Theology, Philosophy, and Social Issues

Nuts and Bolts 003: Analytic and Synthetic Truth


When he was presented with the accused man Jesus of Nazareth, the governer Pontius Pilate asked a question laden with philosophical importance: “What is truth?” It’s a question that I think was adequately answered centuries earlier by Plato: “The essence of truth is to say of what is that it is, and to say of what is not that it is not.” In normal english, the essence of truth-telling is to tell it like it really is.

In this edition of the nuts and bolts ( a series in which I cover the fundamentals of philosophy and later, theology), I won’t be wading through theories of truth. What I am going to do, prompted by a recent conversation, is to discuss the distinction between two different kinds of truths: analytic and synthetic. It might sound a bit artificial at first to talk about distinguishing between different sorts of truth. Some statements are true, and some are not. Right? Bear with me.

Here’s a list of statements that is true: 1) Write now Glenn is typing up a blog post about truth, 2) I just had a mochaccino, 3) Everything is the same as itself, 4) our van is blue, 5) a square has four sides, 6) 4 + 4 = 8. To say that the statements are true is to say that they correspond to the facts. However, this list consists of two different sorts of claims, and each type is true for different reasons.

Look at statements 1, 2 and 4. They are true because of how the facts just happened to be. Things could have been different. Things could have turned out so that I typed this blog post tomorrow, or an hour earlier than right now. I might not have had a mochaccino – I could have had a hot chocolate, or just a glass of water, but I happened to have a  mochaccino. Our car could easily have been painted a different colour. The facts just played out in such a way that these claims are true, but things could easily have been different. These claims are called “synthetic” claims, because they bring things together in a kind of synthesis. Take statement four. It brings together the idea of our van and also the idea of blueness. These two things don’t necessarily belong together, but just because of the facts as they are, these things have come together in the fact that our van is blue, and so the ideas are brought together in this statement. All synthetic truths are like this. For example the statement “rape is wrong” brings together the idea of rape and the idea of wrongness. “Microsoft Windows sucks” brings together an operating system and the quality of being suckful. Or think of more philosophical contexts. Imagine that someone has just presented an argument that you think is  fallacious. Saying “that argument is fallacious” or “that conclusion does not follow” (which is the same as saying “your argument is invalid”) would also be a synthetic statement, bringing together her argument or premise, and the concept of being fallacious or invalid.

Now look at statements 3, 5 and 6. They’re also true, but not for the same reason. True, they also line up with the facts, but they don’t just happen to line up with the facts. In fact the facts could not possibly have been any other way in these cases. Look at statement 5. Yes a square does, in fact, have four sides, but that’s because in order for something to be a square it must have four sides. Having four sides is part of the very definition of being square. Stated differently, there is no possible world in which statement 5 is false. The same is true of statements 3 and 6. Everything is the same as itself, because if at any given point in time, something is different from object x, then that thing is not object x but a different object. Likewise, there will never be a time when things change so that 4 plus 4 equals something other than 8. Statements like these are not synthetic, they are “analytic.” This is because they don’t bring two different ideas together. Look again at the statement about squares having four sides. Just by analysing the meaning of the terms, we see that the statement is true. We don’t need to do any evidence gathering to realise that 4 + 4 = 8. Analytic statements are true by definition.

Be wary of people presenting arguments or claims and giving them a bit of extra rhetorical “ompf” by throwing in the phrase “by definition.” For example over at Scott Klarr’s blog you’ll read: “If a god is not composed of matter or energy, then that god, by definition, does not exist.” This is not true at all. Sure, someone might wish to argue that in fact nothing but physical matter and energy exists, and because of this fact, a God who is not physical does not exist. But none of this is a question of definition, it’s a question of fact – facts that people clearly do not agree on.

As a second example, take the comments of an anonymous author here: “If, in order for a belief to be rational, I must have reasons for the belief, then faith is, by definition, not rational.” Again, this just misuses the phrase “by definition.” The author misleadingly suggests that s/he is talking about an analytic truth. The author might think that things held as articles of religious faith are in fact not supported by reasons, but this is a matter of contestable opinion, and certainly not merely a matter of definition. Even if it’s true, it would only be true because we checked the reasons that all religious people held their beliefs, and we discovered that they have no reasons for their beliefs.

So there you go: Analytic vs Synthetic truth.

Glenn Peoples


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  1. Kenny

    Hey Glenn,

    Do you think that something’s being a necessary truth is sufficient for its being an analytic truth?

  2. Hi Kenny. That might be true, but I’m not dogmatic about it. Obviously all analytic truths are necessary truths (true in all possible worlds), but I’m not certain that it works the other way around. It might.

  3. Kenny

    Okay. For what it’s worth, it seems to me that not all necessary truths are analytic. Most substantive philosophical theses are necessarily true if true, but it seems that few substantive philosophical theses are analytic. I think it is a necessary truth that God exists, but it doesn’t seem like an analytic truth that God exists. And so on.

  4. I would be interested on where you would place self evident truths. I have been reviewing this categorisation from Adler. It would seem to me that definitional and and calculational truths are analytical (eg. mathematics and logic).

    But what of the axioms one starts with that are not defined (or calculated)? The law of non contradiction is a self evident truth, not calculated, nor defined; so does it fit into synthetic? But it does not seem falsifiable.

  5. bethyada, self evident truths are truths that enjoy a certain degree of obviousness. This will in some cases be because they are analytically true, but certinly not always.

    The law of non-contradiction is basically a mathematical/logical fact. But other things, like “I am aware of something right now” are self-evident, but certainly neither necessarily nor analytically true.

  6. Thanks Glenn. I am just trying to clarify things in my own mind.

    I tend to see analytical as synonymous to calculational, though it is important to recognise how terms are used. Essentially I see analytical truth (as per your post) as truth that is not (potentially) falsifiable.

    “3 + 2 = 5” is not falsifiable. “My car is red” is falsifiable.

    Using your examples we have (as I see it) analytical truth comprising of
    1. definitional truth (accepted nomenclature);
    2. calculational truth (truths derived by reason based on definitions); and
    3. self-evident axioms (non-subjective truths that are obvious but not provable).

    1. is trivially true. 2 is dependant on 1 and 3. 3 is foundationally true.

  7. bethyada, I wouldn’t include point 3. Self evident truths are only sometimes analytic truths. For example, I gave the example “I am aware of something.” That’s self evidently true, but it could have been false. I might never have been born, for example. So it’s not an analytic truth.

  8. Yeah, I got your point Glenn. But some are, as you suggest; thus I have used the term “axiom” to differentiate from synthetic self-evident truths. Else where would law of non contradiction fit. It is analytic but I don’t see that it can fit into 1 or 2. That, or we have another category of truths.

    I am familiar with the concept of different types of science, and the nature of maths and logic. I am just trying to understand an exhaustive categorisation of reality or truth (as per my earlier link).

    I don’t have any issue with your post in general, just thinking thoughts out loud 🙂

  9. Oh yeah, I realise we’re not disagreeing or anything….

    I’d put the law of noncontradiction in mathematical facts actually, as it’s algebra (which is not really different from symbolic logic).

  10. What is truth?

    Truth is truth; truth is itself, it cannot be reduced to something else.

    Pilot’s question was foolish, or, at best, silly: the question itself presupposes that truth is truth and that one may both know truth and know that one knows truth.

  11. Nobody denies that truth is truth. But then, asdfg is asdfg too. Unfortunately, statements of that nature tend not to inform, since while they are analytically true, they don’t convey any descriptive facts.

  12. Richard R

    ‘1) Write now Glenn is typing up a blog post about truth’

    Spelling mistake!!!!!

  13. Jared

    Glen, thanks very much for the posts in this series! I’m learning a lot.

    I’d like to engage with one point you made, though. You said that “Rape is wrong” is a synthetic truth because it brings together two concepts: rape and wrongness. However, I’d like to take a stab at making a case that this statement is analytic.

    If you think about the meaning of the term “Evil,” it could be defined as something like “whatever is unpleasant, undesirable or destructive to or for a person.” This would include pain, suffering, cancer, tsunami’s, holocausts, etc. at one end of the spectrum as well as hangnails and other minor annoyances at the other. One could include in this list the experience of having an undesired sexual act forced upon one’s self. This is an evil in my very specific definition of the term. Not because it has been arbitrarily placed in an “Evil” category, but because it IS undesired and unpleasant to the victim. To say that rape is an evil, is simply to apply the law of identity: rape is but one variety of evil–evil being defined as above as “unpleasant and/or destructive things that can happen to someone.” Another way of phrasing the concept of “perpetrating an evil on someone else” in English is to say that you “wrong” them. To “wrong” someone is to do something that is “wrong.” So to say that rape is “wrong,” is to place it in an equation with “wrong” or “perpetrate evil” on one side and “rape” on the other side of the equation. It is not as if rape is a neutral thing that can take on the property of being wrong/evil or not: its definition (forcing something unwanted on someone else) entails wrongess. If it were not undesired, it would not be rape. “Undesired” is an essential property of rape; without it you don’t have rape. And “Undesired” is equivalent to “evil.” And “wrong” is simply a synonym for “to perpetrate evil.”

    Does this make sense? I’m not sure if I’ve done my best at laying it out.

  14. Jared, if we define wrong in terms of unpleasantness and/or destructiveness, we run into a few problems. Punishing people is unpleasant, and fighting in war can be destructive even where the cause is just.

    What’s more, if we put too much content of the sort you indicate into the very meaning of “evil,” we put an end to certain genuine disputes in an artificual way. We can’t ask, for example, if torture is always wrong, because it reduces down to “is torture torture?” The trouble is, questions like “is rape wrong” or “is torture wrong” just sound to most people like real questions. They sound like questions that are substantial, and not centred on tautologies.

    So in the sense of moral evil, I don’t think we can define it in terms of certain classes of act (e.g. any act that harms, any act that is unpleasant etc).

    I’m inclined to agree that most acts that are harmful or unpleasant to another are wrong, but not by definition. It is wrong to do them, but there are other things we could do to people that are also wrong (e.g. lust after them). While it’s true, for instance, that “undesired” is an essential aspect of rape, in order to be capable of asking the question “is it always wrong to inflict undesired acts upon people,” the word “wrong” must be completely free of any meaning contained in the meaning of “inflicting undesired action.” Otherwise, we’re asking: “is it always wrong to do wrong?” Sure, there’s an easy answer, but not a very helpful one.

    I think you’d be much better off getting rid of the semantic connection between evil and harm, and instead talk in terms of harm/unpleasantness being an evil-making-property, where those features cause acts to be wrong. That way we can still ask normal english questions like “is rape wrong” even where we think the answer is obvious. Yes rape is wrong because it is a kind of harm, and acts should be deemed evil if they harm, for harm makes things wrong.

    Of course, this claim, that harm makes an act wrong, is debateable, but at least it allows us to ask meaningful questions about which acts are wrong and which are not.

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