{"id":1666,"date":"2025-01-23T11:44:16","date_gmt":"2025-01-23T09:44:16","guid":{"rendered":"https:\/\/linguistica.info\/b\/lei\/?page_id=1666"},"modified":"2025-06-29T14:33:25","modified_gmt":"2025-06-29T12:33:25","slug":"8-3-conjunctions","status":"publish","type":"page","link":"https:\/\/linguistica.info\/b\/leiwp\/toc\/8-sentence-meaning\/8-3-conjunctions\/","title":{"rendered":"8.3 Conjunctions"},"content":{"rendered":"

Truth tables are also useful in analyzing the meaning of conjunctions<\/strong> like and<\/em> and or<\/em>. Let us start with and<\/em><\/strong>, because it is fairly simple. How would you describe the meaning of and<\/em>? It is very difficult, most dictionaries do not even bother, giving definitions like \u2018used to indicate a connection between two things\u2019 or \u2018used to link two words, phrases or sentences\u2019. But using truth tables, it is very easy to show the semantic effect of joining two sentences with and<\/em>. Let p be example (1a), and q example (1b):<\/p>\n

\n
(1a)<\/div>\n
Zoe felled a tree.<\/em><\/div>\n<\/div>\n
\n
(1b)<\/div>\n
Aylin baked bagels.<\/em><\/div>\n<\/div>\n
\n
(1c)<\/div>\n
Zoe felled a tree and Aylin baked bagels.<\/em><\/div>\n<\/div>\n

We can then construct a truth table for these two sentences as well as the sentence in (1c), which connects (1a) and (1b) using and<\/em>. There are four logical possibilities: p and q could both be true, they could both be false, p could be true and q could be false or vice versa:<\/p>\n\n\n\n\n\n\n\n
\ud835\uddfd<\/th>\n\ud835\uddfe<\/th>\n\ud835\uddfd and<\/em> \ud835\uddfe<\/th>\n<\/tr>\n
T<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
F<\/td>\nT<\/td>\nF<\/td>\n<\/tr>\n
T<\/td>\nF<\/td>\nF<\/td>\n<\/tr>\n
F<\/td>\nF<\/td>\nF<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

As the third column shows, if we connect two statements using and<\/em>, then the combined statement is only true if both statements are true. If one or both of them are false, the combined statement is also false. This is the meaning of and<\/em> that is so difficult to describe using words!<\/p>\n

The case of or<\/em><\/strong> is more complicated. Look at the following sentence and the truth table:<\/p>\n

\n
(2)<\/div>\n
Zoe felled a tree or Aylin baked bagels.<\/em><\/div>\n<\/div>\n

 <\/p>\n\n\n\n\n\n\n\n
\ud835\uddfd<\/th>\n\ud835\uddfe<\/th>\n\ud835\uddfd OR<\/em> \ud835\uddfe<\/th>\n<\/tr>\n
T<\/td>\nT<\/td>\n?<\/td>\n<\/tr>\n
F<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
T<\/td>\nF<\/td>\nT<\/td>\n<\/tr>\n
F<\/td>\nF<\/td>\nF<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Starting from the bottom, obviously, if both p and q are false, then the combined sentence in (2) is also false. Also obviously, it is enough for one of the two statements to be true in order for the combined sentence to be true. But what if both are true? In logic, there are two types of or<\/em> \u2014 one, where the combined sentence in (2) is true if both p and q are true (with the symbol \u2228), and one, where (2) is false if both p and q are true (the so-called exclusive or<\/em><\/strong> with the symbol \u22bb).<\/p>\n

 <\/p>\n\n\n\n\n\n\n\n
\ud835\uddfd<\/th>\n\ud835\uddfe<\/th>\n\ud835\uddfd \u2228 \ud835\uddfe<\/th>\n\ud835\uddfd \u22bb \ud835\uddfe<\/th>\n<\/tr>\n
T<\/td>\nT<\/td>\nT<\/td>\nF<\/td>\n<\/tr>\n
F<\/td>\nT<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
T<\/td>\nF<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
F<\/td>\nF<\/td>\nF<\/td>\nF<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Which of these two kinds of \u2018or\u2019 is expressed by the English word or<\/em> depends very much on context. There are cases where two sentences contradict each other, so that only one of them can be true, as in (3a) \u2014 in this case, or<\/em> will obviously be interpreted as exclusive; there are cases where the hearer is unlikely to care about which of the two statements is true, as long as one of them is, as in (3b) \u2014 in this case, the hearer will not feel that they were lied to if both statements are true. And there are cases where it is important to the hearer that one, and only one of the statements is true (as in 3c) \u2014 in this case they are likely to interpret or<\/em> as exclusive and feel cheated if both turn out to be true:<\/p>\n

\n
(3a)<\/div>\n
Zoe wanted to know whether she passed the test or whether she failed the test.<\/em><\/div>\n<\/div>\n
\n
(3b)<\/div>\n
Zoe wanted bagels for dinner, so Aylin promised she would bake bagels or buy bagels.<\/em><\/div>\n<\/div>\n
\n
(3c)<\/div>\n
You will turn down the music or I will call the police.<\/em><\/div>\n<\/div>\n
\n

Draw truth tables for the following combined sentences:<\/p>\n

(i) if p then \u00acq: If you turn down the music, I will not call the police.<\/p>\n

(ii) p unless q: I will call the police unless you turn down the music.<\/p>\n

(iii) p because q: The neighbor called the police because the music was too loud<\/p>\n<\/div>\n

 <\/p>\n

\u2190<\/span> Previous section<\/a><\/span> Next section \u2192<\/span><\/a><\/span><\/p>\n

CC-BY-NC-SA 4.0, Written by Anatol Stefanowitsch<\/p>\n","protected":false},"excerpt":{"rendered":"

Truth tables are also useful in analyzing the meaning of conjunctions like and and or. Let us start with and, because it is fairly simple. How would you describe the meaning of and? It is very difficult, most dictionaries do not even bother, giving definitions like \u2018used to indicate a connection between two things\u2019 or […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1655,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1666","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/pages\/1666","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/comments?post=1666"}],"version-history":[{"count":13,"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/pages\/1666\/revisions"}],"predecessor-version":[{"id":2152,"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/pages\/1666\/revisions\/2152"}],"up":[{"embeddable":true,"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/pages\/1655"}],"wp:attachment":[{"href":"https:\/\/linguistica.info\/b\/leiwp\/wp-json\/wp\/v2\/media?parent=1666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}