No, I’m not going to be able to get away with claiming that truth is beauty, and beauty, truth.
The first issue in understanding truth is recognizing that truth is a property of a proposition. (What’s a proposition? A proposition is a claim.) A proposition that is true has a certain kind of correspondence with the world about which it is making a claim. A proposition that is false does not have this correspondence.
At the most basic level, what we want from this correspondence seems pretty obvious: what the propositions says about the world matches up with how the world actually is.
So, if the world we’re talking about (which some philosophers or logicians will describe as our “universe of discourse”) contains three green spheres and a red tricycle and nothing else, then the claim:
There are three green spheres and one red tricycle.
will be true, as will the claim
There are more spheres than tricycles.
and the claim
There are fewer red things than green things.
as well as the claim
There are no cubes.
All of these propositions are accurate in their descriptions of our universe of discourse (a universe of discourse which admittedly doesn’t have much in it). The agreement between what the propositions are claiming and the world about which the propositions make their claims means that the claims are true.
On the other hand, for that same little world, the claims
There are three red spheres and one green tricycle.
There are only red things.
There are no green things.
There are more tambourines than spheres.
are all false. The descriptions these propositions offer of the universe of discourse do not correspond to how things really are in this universe.
When you have a complete inventory of the stuff in your world (and, if you like, of the things like spatial relations between objects, or parts-and-wholes relationships, and good stuff like that), it’s not too hard to evaluate whether a given proposition is true or false. But in a world like ours, where you’re not issued a full parts-list at the outset, telling whether a particular claim is true or false can get a lot harder.
There are some claims whose truth we can evaluate just on the basis of logical form (at least if we’re not working with a non-standard logic). For example,
There is an elephant in the room or there is not an elephant in the room.
is a true claim, something we can know without even checking the room for elephants. The form of this claim can be expressed in more general terms, if we let P stand in for the proposition “There is an elephant in the room,” as:
P or not-P
The underlying assumption is that propositions (like P) are either true or false (with no squishy in-between state of truthiness), which means either P is true, or it’s false — in which case not-P is true.
For similar reasons, we can judge a claim of the form
P and not-P
as false — since a proposition and its negation can’t both be true at the same time.
However, every now and then we have to face down a claim like
Schrödinger’s cat is dead or Schrödinger’s cat is not dead.
While the cat is in the box with the vial of cyanide rigged to open if the isotope decays — that is to say, before we’ve opened the box and made an observation of the cat’s state — the official stand on this claim from quantum mechanics is that the cat is neither alive nor dead, but rather in a superposition of the two states. Indeed, prior to the measurement, what the QM folks hold as true is
Schrödinger’s cat is dead and Schrödinger’s cat is not dead.
In other words, non-standard logics end up playing a role in some realms of human endeavor (like quantum mechanics) that are concerned with getting a handle on what we can say about the world that’s true. Quantum mechanics and other such fields of endeavor aside, though, standard logic usually gets the job done.
There are some other cases where we can assert that a claim is true (or false) on account of the definitions of the words in the claim. For example
All bachelors are unmarried.
is a true claim, at least in contexts where “bachelor” means “unmarried man”. Similarly, the claim
At 1 atm pressure, water freezes at 0 oC and boils at 100 oC.
is true because these properties of water were built in to the definition of the Celsius temperature scale. There are plenty of other claims, though, where we need more than definitions in order to establish whether the claims are true, for example:
There are 6 liters of water in this kettle.
A given sample of water contains twice as many atoms of hydrogen as atoms of oxygen.
A bucket of water was used to melt the Wicked Witch of the West.
I love the sprogs.
To assess the truth of any of these claims, we need to be able to get some accurate information about the state of things in the world — whether to measure the volume of water in the kettle (and to ensure that the liquid whose volume we’re measuring is in fact water), or to determine the ratio of hydrogen to oxygen atoms in a water sample (which might involve drawing inferences from the volumes of gases collected in the electrolysis of water). Assessing the truth of the claim about the Wicked Witch of the West may require that we struggle with philosophical issues about fictional universes.
That claim about my feelings for the sprogs is an interesting one from the point of view of determining its truth. Assuming we can pin down a reasonable standard version of love, I am the only one with any direct access to the “data” of my feelings for the sprogs. Others may be able to detect clues in my behavior that are usually concomitants of love … but that’s not the same thing as being able to direct the feeling itself. Still, I assure you, the claim is true.
Many of us will also be inclined to say that
Murder is wrong.
is a true claim. However, it’s harder to pin down precisely what kind of larger claim about the world this commitment of ours embodies. Is there a moral fact in the world about the wrongness of murder (and if so, can we expect the development at some future date of measuring devices that can detect moral facts like smoke-detectors detect smoke)? Are we making a claim about our emotional attitude toward murder (either individually or collectively)? Are we making a claim about the status of murder in our societal norms (which might be different from our emotional attitudes toward it)? Or about the advisability of murder given what we judge as our best interests?
Thinking hard about the metaphysical commitments that may be lurking beneath our moral assertions is the kind of thing that may send you back to thinking about something fluffier … like Schrödinger’s cat
An important point here is that we can draw a distinction between how things are and what we know (or could know) about how things are. If you take empirical evidence to be important in helping us come to knowledge about how things are, then you will have good reason to believe that there are some true claims about the world that we don’t have the data to recognize as true. Maybe someday we will get our hands on the evidence to establish some such claims as true. For other such claims, maybe the evidence will remain elusive.
There are at least a couple different ways people respond to the possibility that there may be quite a lot of truths out there that are hard for us to access. One response is to dispense with talk about truth or falsity in matters where there is not some reasonable way — at least in theory — to access the relevant facts about the world (or sensory data that would let us establish those facts). A different response is to entertain such talk while recognizing the possibility that we might never be in possession of data that would let us determine the truth values of some of our claims.
Some people are right at home dwelling in the possibilities. Other people will politely request that you give them just the established facts. A great deal may depend on whether we’re talking about what we can establish about how things are, or if instead we’re speculating about ways things could be.
This Basic Concepts post goes out, with my thanks, to Nick, who made a generous donation to my DonorsChoose challenge. The sprogs are still thinking about how to illustrate the concept of truth in a picture — if they figure it out, we’ll be getting you some artwork, too!