Truth and meaning

One traditional approach to meaning “truth-conditional semantics”. Put simply, this approach is based on three assumptions:

1. Sentences (or at least declarative sentences) have truth conditions – a set of things that must be true about the real world in order for the content of the sentence (also called the proposition) to be true.
2. The meaning of a (declarative) sentence can be captured entirely in terms of its truth conditions (if we can describe the truth conditions of a sentence, we have described its meaning).
3. Any part of the communicative function of a sentence that cannot be captured in terms of truth conditions is not part of its meaning in the strict sense, sometimes called “sentence meaning” (it may be part of what is sometimes called “speaker meaning”), something we will come back to in a few weeks.

Let us look at the following example:

(1) Donald Trump incited a violent mob to storm the US Capitol.

The following is an attempt to list the things that must be true about the world in order for this sentence to be true:

a. There is a person named Donald Trump (DT)
b. There is a group of people (G)
c. There is a place named the US capitol (C)
d. G is willing to use violence
e. G should not be in C
f. DT did (said) something to G
g. Because of (f), G entered C by force
h. DT knew (d)
i. DT wanted (g) to happen

The idea is that the conditions in (a-i) describe the meaning of (1). Note that is a completely different question from the question whether (1) is, in fact, true.

Now consider the sentence in (2):

(2) A violent mob was incited by Donald Trump to storm the US Capitol.

Note that it has the same truth conditions as (1) – whenever (1) is true (2) is true, and whenever (1) is false, (2) is false. In other words: (1) and (2) have the same meaning! This does not mean that they are completely identical in terms of their communicative function. For example, (1) puts the focus on the person referred to as Donald Trump, while (2) puts the focus on the group described as violent mob. But this is part of speaker meaning (putting the focus on one or the other does not change the meaning of the sentences themselves).

Uses of truth-conditional semantics

Most modern semantic theories do not assume this is a good way of describing the meaning of sentences, but truth-conditions are nevertheless an extremely useful tool for understanding relationships between propositions. Let us look at some of these relations.

Paraphrase

Grammatical paraphrase

We already saw that truth conditions can be used to show that two different grammatical structures have the same meaning: (1) and (2) differ only in that one is an active sentence and the other a passive sentence – since they have the same meaning, we can conclude that active and passive sentences are always paraphrases of each other – that these two grammatical structures have the same meaning.

This can be more formally expressed by using a so-called “truth table”. We call the proposition of the first sentence “p” and that of the second sentence “q”, and then we determine how the truth (or falsity) of paffects the truth of qand vice versa.

p: Donald Trump incited a violent mob to storm the US Capitol.
q: A violent mob was incited by Donald Trump to storm the US Capitol.

Truth tables:

p	q
T	T
F	F

q	p
T	T
F	F

(These tables are read as follows: “If [proposition in first column] is [true/false], then [proposition in second column] is [true/false]”; for example, the first row of the first table means “If p is true, q is true”).

Paraphrase (lexical)

We would get the same truth tables for the propositions of the following pair of sentences:

p: Donald Trump incited a violent mob to storm the US Capitol.
q: Donald Trump egged on a violent mob to storm the US Capitol.

These are also paraphrases of each other, in this case, because incite and egg on mean the same thing (except that one is formal an one is colloquial, but that is a difference in speaker meaning).

Paraphrase (referential)

And we would get the same truth tables for the propositions of the following pair of sentences:

p: Donald Trump incited a violent mob to storm the US Capitol.
q: The president of the USA incited a violent mob to storm the US Capitol.

In this case, the reason is not that Donald Trump and The president of the USA mean the same thing (names don’t have meaning at all), but that (at the time of writing) they refer to the same person.

Contradiction (Negation)

The opposite of paraphrase is contradiction – this is a situation where if p is true, qmust be false and vice versa –(only one of p or q can be true). The clearest case of contradiction is provided by pairs of sentences that are identical except for the fact that one of them is negated:

p: Donald Trump incited a violent mob to storm the US Capitol.
q: Donald Trump did not incite a violent mob to storm the US Capitol.

Truth tables:

p	q
T	F
F	T

q	p
T	F
F	T

Entailment

A very interesting relationship between two propositions is that of entailment – a situation where one proposition logically follows from another. Consider the following examples:

p: Donald Trump persuaded a violent mob to storm the US Capitol.
q: A violent mob planned to storm the US Capitol.

Here, if pis true, then qmust be true – to persuade someone to do something means that they plan to do it (and will do it unless someone stops them or they change their mind later). However, the two sentences are not paraphrases, because if q is true, p could be true or false – if it is true that a violent mob planned to storm the US Capitol, the reason could be that Donald Trump persuaded them, but it does not have to be. In other words, the relationship only goes on one direction (q follows from p, not the other way around).

Truth tables:

p	q
T	T
F	T/F

q	p
T	T/F
F	F

This is interesting, because the entailment is triggered by the meaning of the verb persuade – if we choose a verb like urge, which at first looks similar and might be given as a synonym in a thesaurus, the entailment disappears. Consinder:

p: Donald Trump urged a violent mob to storm the US Capitol.
q: A violent mob planned to storm the US Capitol.

Truth tables:

p	q
T	T/F
F	T/F

q	p
T	T/F
F	T/F

Negative entailment

Another relation between propositions is that of negative entailment: here, if p is true, q must be false but if p is false, q can be true or false. Consider:

p: Donald Trump persuaded a violent mob to storm the US Capitol.
q: The mob planned to stay away from the US Capitol.

If Donald Trump persuaded the violent mob to storm the Capitol, it cannot be true that the mob planned to stay away from the Capitol (this would mean that they were not persuaded). However, if Donald Trump did not persuade them, they could either plan to stay away, or they could plan to storm it for some other reason.

Truth tables:

p	q
T	F
F	T/F

q	p
T	T/F
F	F

Presupposition

Finally, the most interesting relationship between two propositions is that of presupposition. Here, qmust be true regardless of whether p is true or not. Consider:

p: The president of the USA incited a violent mob to storm the US Capitol.
q: There is a president of the USA

If the president of the USA incited a violent mob to storm the US Capitol, then there must be a president of the USA – otherwise he could not have done what is claimed. However, if the president of the USA did not incite a violent mob to storm the US Capitol, then there must also be a president of the USA – otherwise it does not make sense to talk about things he did not do. In other words: q must be true before it makes any sense to think about the truth or falsity of p; if q is false, p is meaningless.

Truth tables:

p	q
T	T
F	T

q	p
T	T/F
F	F

Frequent sources of presupposition

Presuppositions are triggered by all kinds of linguistic structures. Some of the most frequent ones are the following:

1. Definite descriptions

p: The president of the USA incited a violent mob to storm the US Capitol.
q: There is a president of the USA.

2. Factive verbs

p: Donald Trump regrets inciting a violent mob to storm the US Capitol.
q: Donald Trump incited a violent mob to storm the US Capitol.

3. Implicative verbs

p: Donald Trump managed to incite a violent mob to storm the US Capitol.
q: Donald Trump tried to incite a violent mob to storm the US Capitol.

4. Verbs of change and continuation

p: Donald Trump ceased/continued to incite a violent mob to storm the US Capitol.
q: Donald Trump had been inciting a violent mob to storm the US Capitol.

5. Iterative expressions

p: Donald Trump again incited a violent mob to storm the US Capitol
q: Donald Trump had incited a violent mob to storm the US Capitol at least once before.

6. Temporal clauses

p: While inciting a violent mob to storm the US Capitol, Donald Trump was hoping he could remain president of the USA
q: Donald Trump was inciting a violent mob to storm the US Capitol.

In addition to the main take-away points from the previous post, there was a short discussion of the relation between meaning, sounds and writing.

1. Please get used to thinking about sounds and letters as completely separate elements of linguistic structure. Especially in English, it does not make sense to say that “a letter is pronounced in a particular way” or “a sound is written in a particular way”. Linguistic are units that link sound and meaning, writing is irrelevant to this link.

2. However, of course most speech communities use some form of writing, so it is an interesting question how written forms are related to sound an meaning. Remember the different types of writing systems we talked about in Week 1. How might they fit into a model of linguistic signs? For logographic writing systems, this is relatively easy to answer: the written form must be linked directly to the meaning side of a linguistic sign. It is related to the sound only because the sound is also related to this meaning (see Slide 8, example from Chinese). For phonographic writing systems we could imagine a separate level of “signs” where the form is a particular character and the “meaning” is a particular sound, as in the Japanese example on Slide 8 (the word [inu] is written by using the characters corresponding to the syllables [i] and [nu]).

We could imagine the same for English, but this would fail because d does not always stand for [d] (it stands for [t] in walked, for example), o does not always stand for [ɔ] (it stands for [u] in boot and [oʊ] in home, for example), and g does not always stand for [ɡ] (it stands for [f] in enough). So while in “shallow” orthographies like Spanish, we may think of letters as having sounds as their “meaning”, in deep orthographies like English, the written form must be attached directly to the meaning, as in Chinese.

These are the major take-aways from today’s lecture.

1. In spoken languages, signs are combinations of a meaning concept (a mental knowledge structure of some sort, simply referred to as concept) and a sound concept (a mental representation of a particular sequence of phonemes, referred to as an acoustic image in early structuralist linguistics, more likely referred to as a phonemic representation nowadays).

2. The link between sound and meaning is arbitrary for almost all linguistic signs, i.e., there is no reason why this particular sound should be linked to this particular meaning. Take the word fire – it refers to “combustion or burning, in which substances combine chemically with oxygen from the air and typically give out bright light, heat, and smoke” (Oxford New American Dictionary), but nothing about the sound sequence /ˈfaɪɚ/ (AmE) or  /ˈfaɪə/ (BrE) has a logical connection to this meaning – speakers simply have to learn the association.

3. Such arbitrary signs are called symbols. There are two other types of sign: iconic signs, where the form resembles the meaning, and indexical signs, where the form correlates with the meaning in our experience.

4. There are a few apparent exceptions to arbitrariness in language: some words, like cuckoo, resemble (some aspect) of their meaning (in this case, the noise that the bird makes) – they are partially iconic. However, the iconicity is limited: first, we still have to learn that a cuckoo is called cuckoo, but a rooster is not called cockadoodledoo; second, the similarity is very marginal, concerning not the meaning (here: the bird) itself, but only a peripheral aspect (the noise the bird makes). Some people also argue that there are indexical signs, like the word ouch that might be an intuitive reflex of pain. Again, the indexicality is limited: first, we don’t have to say ouch when we feel pain, but there has to be smoke if there is fire; second, there is a lot of variation in different languages concerning the noise associated with pain, showing that these expressions, too, are largely arbitrary.

5. In other words: arbitrariness is a very basic and general principle of human language.

6. Signs may be simple, like fire, which does not consist of smaller signs, or complex, like fire fighter, which consists of smaller signs, fire, fight, and -er. Signs that cannot be split up into smaller signs are called morphemes.

7. Morphemes can combine into larger words and words can combine into phrases and sentences. This allows us to express an infinite number of thoughts with a limited inventory of morphemes. Interestingly, the morphemes themselves are complex on the level of sounds: they consist of one or more phonemes (typically more than one) that do not have meaning themselves. This property of language is called duality of patterning (or double articulation): on the first level, (meaningful) morphemes are combined into larger meaningful structures, on the second level, meaningless phonemes are combined into  larger meaningless structures (syllables). This allows us to use a limited set of phonemes (English has between 30 and 40, depending on which variety we are talking about) to create a limitless number of morphemes (nobody knows how many morphemes English has, but several tens of thousands is a good guess).

The first point of this week’s lecture was to impress on you the fact that writing systems are not an inherent “part” of language, as

1. languages can have more than one writing system (e.g. Serbian, whose speakers use both the Latin and the Cyrillic alphabets);
2. a speech community can shift from one writing system to another very suddenly (e.g. Turkish, which shifted from Arabic to Latin in 1928);
3. changes within a writing system can be decreed by law (as in the case of the German spelling reform),

None of these things are possible with the sound system of a language or with other aspects of linguistic structure.

The second point was to provide an overview of writing systems, as shown in the following slide:

The third point was to point out that English has a segmental writing system, but not a very transparent one – as opposed, for example, to Spanish:

The reasons for the intransparent orthography of English are largely historical. There are four main reasons:

1. For many words, the spelling became fixed early, so when the sound system of English changed, the spelling no longer corresponded to the pronunciation – for example dream was pronounced [drɛam] in Old English, which is fairly transparent, and while the pronunciation changed to [driːm] (due to general sound changes in English), the spelling did not change with it, thus becoming intransparent.
2. For other words, the spelling was adjusted at some point in an attempt to capture the new pronunciation – depending on when this happened, different ways of representing a sound were used, leading to inconsistencies.
3. For yet other words, the spelling was adjusted to match what people thought was the original pronunciation (etymologizing spellings). For example, the word salmon was always pronounced without an [l] – Middle English [saːˈmuːn], Modern English [ˈsæmən], as it was borrowed from Norman French samoun. However, because the ultimate Latin root salmō contains an <l>, this was added to the English spelling in an attempt at etymological authenticity.
4. Loan words typically retain their spelling wholly or partially when borrowed into English.

The final point of the lecture was to draw awareness to the fact that it may be useful to have an orthography that does not correspond to the pronunciation very closely, as it means that homophones (words that sound the same but mean different things) can be disambiguated in writing (for example, by, bye and buy. In this sense, English spelling has some properties of logographic writing systems.

Course description

The module consists of two parts – the lecture “Survey of Language and Linguistics”, which is mostly taught in the form of a live lecture in a video conference format and which all students attend together, and the seminars “Introduction to Linguistics”, for which students are split up into groups and which are taught as a mixture of recorded presentations and live video sessions.

In the lecture, I will introduce each week’s topic in broad terms and provide a general space for discussion, as well as trying to provide a general linguistic education. In the seminars, your instructors will then get into the details of linguistic terminology and analysis.

The lecture takes place in my “Webex” video conference room, which you can access under http://fu-berlin.webex.com/meet/anatol.stefanowitsch can sign in with your ZEDAT email address and password. It is possible to use this video conferencing system in your web browser, but I recommend that you install the Webex Meetings app on your preferred device, as the quality is much better!

Course schedule

02.11.2020 | Introduction
09.11.2020 | Speech and writing
16.11.2020 | Phonetics
23.11.2020 | Phonology
30.11.2020 | From Phonology to Morphology
07.12.2020 | Morphology
14.12.2020 | Syntax I: Words and phrases
04.01.2021 | Syntax II: Grammatical relations
11.01.2021 | Semantics I: Sentences
18.01.2021 | Semantics II: Lexical semantics
25.01.2021 | Pragmatics
01.02.2021 | Text linguistics
08.02.2021 | Linguistic research at the Freie Universität Berlin
15.02.2021 | Outlook: Empirical methods
22.02.2021 | Exam