1. Natural language processing Logic of attitudes
Lesson 8: Notional attitudes of seeking and finding

2. Logic of attitudes propositional attitudes notional attitudes
Tom Att1 (believes, knows, thinks), that P
Att1/(): relation of an individual to a proposition
Att1*/(n): relation of an individual to a hyperproposition
notional attitudes
Tom Att2 (is seeking, finding, solving, contemplating, designing, wishing, …) P
Att2/(): relation of an individual to an intension
Att2*/(n): relation of an individual to a hyperintension
Both come in two variants: de dicto and de re

3. Seeking and finding Seek/() or Seek*/(n)
Sentences about seeking are not used to describe an activity to obtain something that we know what it is or where it is. When seeking we want to find out something that we don’t know.
A detective can seek the murderer it the detective doesn’t know who is the murderer. And if he knows this then he can try to find out where the murderer is.
Hence the seeker is related to a condition and wants to find out what meets this condition, if anything; seeking can fail.
We can seek a unicorn or Pegasus though these are futile activities.
When Schliemann were looking for Troy he was pretty much convinced that Troy existed though it might have been otherwise. And even if he happened to set foot on the hill of Hissarlik (now presumed to be the site of Troy along with Mycenae), he’d not be interested in that little hill at all unless he had found out that this is the site of Troy.
Hence the type of an entity to which the seeker is related is either a construction, or an intension. The seeker wants to find out which object if any is the product of the construction or the value of the intension.
Seek/() or Seek*/(n)

4. a) De dicto, intensional: Seek/()
The seeker aims to find out what is the value of the -intension
Success = finding, hence: Find/()
Tom seeks a unicorn
wt [0Seek1wt 0Tom 0Unicorn], Seek1/(())
Police seeks the murderer of JFK
wt [0Seek2wt 0Police wt [0Murdererwt 0JFK]], Seek2/().
Police found the murderer of JFK
wt [0Find2wt 0Police wt [0Murdererwt 0JFK]], Find2/().
The constructions 0Unicorn, wt [0Murdererwt 0JFK] occur de dicto.
Existence of the sought object is not presupposed.
The seeker can seek non-existent objects (unicorns, Pegasus, …); then he/she cannot find them

5. a) De dicto, intensional: Find/()
Is the existence of the sought object presupposition of finding?
Police found the murderer of JFK |= the murderer of JFK exists
Police did not find the murderer of JFK |= ???
Failure in seeking can be due to two reasons:
The murderer does not exist
Police did not work well, the murderer is well hidden, …
But survival under (narrow-scope) negation is the most important test for presupposition;
Hence, finding after foregoing search merely entails the existence of the sought object but does not presuppose it; in other words, the existence of the sought object is a necessary but not sufficient condition for finding
Hence, finding after foregoing seeking cannot be a relation to the value of the sought intension; rather, it must be a relation to the intension itself: ()

6. Seeking and Finding; ambiguities
The term ‘seeking’ is ambiguous;
There is another kind of seeking. The seeker does not have to aim at finding out who/what holds an office or has a property.
Consider this
Donald Trump is looking for Melania Trump.
Here ‘looking for’ denotes the relation between two individuals, Donald and Melania. Hence, the types are:
Look-for/(); Donald, Melania/
And the literal analysis of the sentence comes down to
wt [0Look-forwt 0Donald 0Melania]
Well, but what then does Donald want to find out? Certainly not who is Melania; the identity of his wife is well known to him.
Presumably he does not know where is Melania right now. Hence, he is looking for the location of Melania.

7. Seeking/finding/locating
We explicate this kind of seeking as the relation to the office that can be occupied by locations (positions, places, …) of individuals rather than individuals.
Let Loc be an empirical function that associates each individual with its position, place where it occurs.
For the sake of simplicity, let  be the type of a place of occurrence (it can be specified by GPS coordinates, or relatively with respect to another individual, …).
Loc/()
Hence, such kind of looking for can be explicated as the relation of two individuals x, y such that x is seeking the location of y, Seek3/():
0Look-for = wt xy [0Seek3wt x wt [0Locwt y]]

8. Seeking/finding/locating
“Donald Trump is looking for Melania Trump.”
wt [0Look-forwt 0Donald 0Melania] =
wt [0Seek3wt 0Donald wt [0Locwt 0Melania]].
Types. Look-for/(); Donald, Melania/; Seek3/(); Donald, Melania/. Loc/().
“Police seeks the murderer of JFK”
is ambiguous between de dicto and de re reading.
de dicto (who is the murderer of JFK?)
wt [0Seek2wt 0Police wt [0Murdererwt 0JFK]], Seek2/()

9. Seeking/finding/locating
de re (where is the – existing, known – murderer of JFK?).
If Lee Oswald really was the murderer of Kennedy, then another scenario is possible. Oswald did not have to be shot during the transport for interrogation but he could have escaped police. Then police in Dallas would announce “Lee Oswald, the murderer of JFK, is wanted for questioning”, and would want to find out where this individual is.
wt [0Look-forwt 0Police wt [0Murdererwt 0JFK]wt] =
wt [xy [0Seek3wt x wt [0Locwt y]] 0Police wt [0Murdererwt 0JFK]wt] =
Mind ! We must not apply -reduction by name:
wt [0Seek3wt 0Police w’t’ [0Locw’t’ w”t” [0Murdererw”t” 0JFK]wt]  drawing extensional (de re) occurrence of w”t” [0Murdererw”t” 0JFK]wt into the intensional -generic context of w’t’ cancels de re
wt [0Seek3wt 0Policie [0Sub [0Tr wt [0Murdererwt 0JFK]wt] 0y 0[wt [0Lokwt y]]]]
Look-for/(); Seek3/()

10. Seeking/finding/locating
Now both principles de re are valid
a) Existential presupposition:
If wt [0Murdererwt 0JFK]wt is v-improper (the murderer does not exist), then the Composition
[0Tr wt [0Murdererwt 0JFK]wt] is also v-improper, hence also
[0Sub [0Tr wt [0Murdererwt 0JFK]wt] 0y 0[wt [0Locwt y]]] and its Double Execution are v-improper, and also
[0Seek3wt 0Policie 2[0Sub [0Tr wt [0Murdererwt 0JFK]wt] 0y 0[wt [0Locwt y]]]] or its negation are v-improper; partiality is propagated up
b) Substitution of v-congruent constructions.
Assume that Lee is the murderer of JFK, wt [0Vrahwt 0JFK]wt = 0Lee. Then
[0Seek3wt 0Policie 2[0Sub [0Tr wt [0Murdererwt 0JFK]wt] 0y 0[wt [0Locwt y]]]] =
[0Seek3wt 0Policie 2[0Sub [0Tr 0Lee] 0y 0[wt [0Locwt y]]]] =
[0Seek3wt 0Policie 20[wt [0Locwt 0Lee]]] =
[0Seek3wt 0Policie [wt [0Locwt 0Lee]]]

11. Seeking & finding, summary
Seeking of empirical objects comes in two basic variants
De dicto: the seeker wants to find out who, what is the value of -intension () in the world w and time t of seeking
Most frequently (), (())
De re: the seeker wants to find out where does a sought individual occur; seeking its location ()
Finding after foregoing search is an entity of the same type as the respective seeking
Existence of the sought object is a necessary but not sufficient condition of its finding

12. More on Finding de dicto
Police keeps seeking but not finding the murderer of JFK
wt [0Seek2wt 0Police wt [0Murdererwt 0JFK]]  [0Find2wt 0Police wt [0Murdererwt 0JFK]]
Seek2/(); Find2/().
Can be true if the unique murderer does not exist; hence, existence is not a presupposition of finding, it is merely entailed.
Assume that the police eventually succeeded and found the murderer of JFK who happens to be also the world champion in shot put. Does it entail that the police found the world champion in shot put? Of course not. By seeking and finding the police is related to the role of the murderer rather than the shot-put champion.

13. More on Finding Hence, Identify / ():
Anyway, if the police succeeded, in addition to the existence of the murderer we can infer that the police knows who the murderer is (or where that villain is in case of locating)
Furthermore, if the murderer is Lee Oswald, then the police identified Oswald as the murderer.
Hence, identifying the respective individual as the murderer is a requisite of finding.
Could Identify (something as something else) be of type ()? If it were so, then if the murderer of JFK is also the world champion in shot put, then the police would identify Lee Oswald as the world champion in shot put, which is of no sense.
Hence, Identify / ():
The relation-in-intension between an individual (the finder who identified), another individual (whom identified) and an individual office (as what has been identified).

14. Requisites of Finding
Identifying and existence are requisites of finding:
[0Req1 0Identify 0Find] = wt [xr [[0Findwt x r]  [0Truewt wt [0Identifywt x rwt r]]]]
[0Req2 0Exist 0Find] = wt [xr [[0Findwt x r]  [0Existwt r]]]
Req1/(()()); Req2/(()()); Find/(); Exist/(); Identify/(); x  ; r  .
Gloss. Necessarily, if x found out what/who plays the role r, then x identified the individual who plays the role and the role is occupied

15. Rules for finding [0Findwt x r] (I)  [0Identifywt x rwt r]
Since the first occurrence of r in the consequent is extensional (de re), both the principles de re are valid:
[0Identifywt x rwt r], [rwt = r’wt] [0Identifywt x rwt r]
(IIa)  (IIb) 
[0Identifywt x r’wt r] [0Existwt r]
By transitivity we have
(III) 
[0Existwt r]
None of these rules is valid in case of a fail in the foregoing search, of course

16. Rules for finding
Example. It is true that Schliemann found the place where the antient Troy was situated:
wt [0Find3wt 0Schliemann [wt [0Locwt 0Troywt]]]
Find3/(); Troy/.
Hence we can infer that Troy existed and if Hissarlik is the location of Troy
wt [= 0Hissarlik [wt [0Locwt 0Troywt]]wt]
then Schliemann identified Hissarlik as the place where Troy was situated:
wt [0Identwt 0Schliemann 0Hissarlik [wt [0Locwt 0Troywt]]]

17. Coincidental, accidental finding
Imagine that by walking Tom kicks a little piece of metal on a path, and on his coming home he finds out that it is the most valuable coin in the history of numismatic.
„Tom found the most valuable coin“.
This time it is not a relation to the role of the most valuable coin because Tom was not looking for it; rather, Tom has been simply related to the individual playing this role: Find4/()
wt [0Find4wt 0Tom wt [0Mostwt [0Valuable 0Coin]wt]wt]
where wt [0Mostwt [0Valuable 0Coin]wt]   is the construction of the role of most valuable coin occurring with de re supposition.
Types. Most/(()): the function that dependently on state-of-affairs picks out one individual from the set of individuals, namely the most valuable one; Valuable/(()()): the modifier of a property; Coin/().

18. Coincidental, accidental finding
wt [0Find4wt 0Tom wt [0Mostwt [0Valuable 0Coin]wt]wt]
Since the meaning of the most valuable coin occurs extensionally (de re), both principles de re are valid.
For instance, if 1933 US Mint Gold Double Eagle is the most valuable coin, then Tom found the 1933 Double Eagle.
And, of course, there is an existential presupposition (rather than mere commitment – entailment, as it is in case of finding after the foregoing search) that there is just one most valuable coin.

19. Hyperintensional seeking
Tilman is seeking the last decimal of 
Tilman is seeking something
where something is restricted type-theoretically, so that the conclusion states that Tilman is seeking something of one particular type of a construction.
wt [0Seek*wt 0Tilman 0[0Last_Dec 0]]

wt [0*c [0Seek*wt 0Tilman c]]
Seek*/(n); */((n)); Tilman/; Last_Dec/(): the function that associates a number with its last decimal digit; /; c/2 v 1.

20. Hyperintensional seeking
Tilman is seeking the last decimal of 
There is a number such that Tilman is seeking its last decimal
wt [0Seek*wt 0Tilman 0[0Last_Dec 0]]

wt [0x [0Seek*wt 0Tilman [0Sub [0Tr x] 0y 0[0Last_Dec y]]]]
Additional types: x, y/1 v ; /(()).

21. Hyperintensional seeking/finding
If Tilman is seeking the millionth digit of the decimal expansion of the number , he may succeed in his effort and identify that number. Thus we have another valid argument:
Tilman found the millionth digit of the decimal expansion of 
There is a number such that Tilman identified it as the millionth digit of the decimal expansion of 
wt [0Find*wt 0Tilman 0[0Mill_Dec 0]]

wt [0x [[x = [0Mill_Dec 0]]  [0Identwt 0Tilman x 0[0Mill_Dec y]]]]
Types: Find*/(n); : the type of naturals; Mill_Dec/(): the function that associates a real number with its millionth decimal digit; Ident/(n).

22. Hyperintensional seeking/finding
Suppose that Tilman is solving the equation (x2 + x – 2) = 0 and that his effort meets with success:
Tilman has solved the equation (x2 + x – 2) = 0
––––––––––––––––––––––––––––––––––––––––––
There is something that Tilman has solved
wt [0Solvedwt 0Tilman 0[x [x2 + x – 2] = 0]]
––––––––––––––––––––––––––––––––––––––––
wt [0c [0Solvedwt 0Tilman c]]
If Tilman has solved the equation x2 + x – 2 = 0 then there is an ()-object (in this case the set {1, –2}) satisfying the equation, and Tilman has identified this set as the product of the construction [x [x2 + x – 2] = 0]. Thus we have (variable s v ()):
–––––––––––––––––––––––––––––––––––––––––––
wt [0s [[s=[x [x2 + x – 2] = 0]]  [0Identwt 0Tilman s 0[x [x2 + x – 2] = 0]]]]