Semantics 2 - Revision history

Gert: /* Models in Carnap */

2021-02-03T12:07:47Z

Models in Carnap

← Older revision		Revision as of 12:07, 3 February 2021
Line 53:		Line 53:


	[[Semantics\|Unit 1]] Unit 2 [[Semantics_3\|Unit 3]]		[[Semantics\|Unit 1]]     Unit 2     [[Semantics_3\|Unit 3]]

Gert: /* Models in Carnap */

2021-02-03T12:06:21Z

Models in Carnap

← Older revision		Revision as of 12:06, 3 February 2021
Line 53:		Line 53:


			[[Semantics\|Unit 1]] Unit 2 [[Semantics_3\|Unit 3]]


Line 146:		Line 146:
	F(f) = 6<br>		F(f) = 6<br>
	-->		-->

	~~[[Semantics\|Unit 1]] Unit 2 [[Semantics_3\|Unit 3]]~~

	~~Semantics~~

Gert at 12:05, 3 February 2021

2021-02-03T12:05:03Z

← Older revision		Revision as of 12:05, 3 February 2021
Line 146:		Line 146:
	F(f) = 6<br>		F(f) = 6<br>
	-->		-->

			[[Semantics\|Unit 1]] Unit 2 [[Semantics_3\|Unit 3]]

			Semantics

Gert at 08:32, 29 January 2021

2021-01-29T08:32:35Z

← Older revision		Revision as of 08:32, 29 January 2021
Line 50:		Line 50:
	I hope this information is enough to allow you to complete the exercises! If you encounter problems, then please write a message into the forum and I will help!		I hope this information is enough to allow you to complete the exercises! If you encounter problems, then please write a message into the forum and I will help!

			'''Important:''' Note that Carnap's terminology is sometimes different from what we have used in class. In particular, what we have called ''denotation'' is called ''extension'' by Carnap. So, for example, if you have used a referent as the denotation of the name or part of the denotation of a predicate, but forgot to add it to the domain of the model, you get the feedback that "The extension of ... is not contained in the domain."


Line 63:		Line 63:





	~~[[File:Model-at-the-outset.JPG \| 1000px]]~~

Gert: /* Models in Carnap */

2021-01-28T09:09:19Z

Models in Carnap

← Older revision		Revision as of 09:09, 28 January 2021
Line 48:		Line 48:
	m Maria		m Maria

			I hope this information is enough to allow you to complete the exercises! If you encounter problems, then please write a message into the forum and I will help!


Line 54:		Line 55:



	~~[[File:Model-0.JPG \| 1000px]]~~

Gert: /* Models in Carnap */

2021-01-28T09:07:34Z

Models in Carnap

← Older revision		Revision as of 09:07, 28 January 2021
Line 45:		Line 45:
	## Each name is already assigned a denotation. At first, all names denote the individual 0. Since I don't allow for 2 names to refer to the same individual, you must give each name a different denotation (counting from 0 upwards). Of course, if you introduce denotations other than 0 for names, you must add these denotations to the domain.		## Each name is already assigned a denotation. At first, all names denote the individual 0. Since I don't allow for 2 names to refer to the same individual, you must give each name a different denotation (counting from 0 upwards). Of course, if you introduce denotations other than 0 for names, you must add these denotations to the domain.
	## Each constant is listed with its arity shown in parentheses. That tells you whether its extension is a set of individuals or a set of ordered pairs.		## Each constant is listed with its arity shown in parentheses. That tells you whether its extension is a set of individuals or a set of ordered pairs.
	# To make things easier on you, I give a key over each model that gives the intended interpretation of single letters. For instance, the key contains the pair		# To make things easier on you, I give a key over each model that gives the intended interpretation of single letters. For instance, the key contains the pair below which means that the model's name for Maria is "m".
	m Maria		m Maria
	~~which means that the model's name for Maria is "m".~~

Gert: /* Models in Carnap */

2021-01-28T09:06:55Z

Models in Carnap

← Older revision		Revision as of 09:06, 28 January 2021
Line 45:		Line 45:
	## Each name is already assigned a denotation. At first, all names denote the individual 0. Since I don't allow for 2 names to refer to the same individual, you must give each name a different denotation (counting from 0 upwards). Of course, if you introduce denotations other than 0 for names, you must add these denotations to the domain.		## Each name is already assigned a denotation. At first, all names denote the individual 0. Since I don't allow for 2 names to refer to the same individual, you must give each name a different denotation (counting from 0 upwards). Of course, if you introduce denotations other than 0 for names, you must add these denotations to the domain.
	## Each constant is listed with its arity shown in parentheses. That tells you whether its extension is a set of individuals or a set of ordered pairs.		## Each constant is listed with its arity shown in parentheses. That tells you whether its extension is a set of individuals or a set of ordered pairs.
			# To make things easier on you, I give a key over each model that gives the intended interpretation of single letters. For instance, the key contains the pair
			m Maria
			which means that the model's name for Maria is "m".

Gert: /* Models in Carnap */

2021-01-28T09:03:27Z

Models in Carnap

← Older revision		Revision as of 09:03, 28 January 2021
Line 37:		Line 37:
	# Lower case letters are names. So, instead of "maria'" you need to write "m".		# Lower case letters are names. So, instead of "maria'" you need to write "m".
	# Upper case letters are n-place constants (the arity is not part of the name). So, instead of "Frau'" you need to write "F".		# Upper case letters are n-place constants (the arity is not part of the name). So, instead of "Frau'" you need to write "F".
	# You do not have to write sets in terms of curled brackets. Just list the members of the set separated by commas. Make sure that after the last member of the set, there are ~~not~~ further symbols, including spaces! As I found out that leads to an error message.		# You do not have to write sets in terms of curled brackets. Just list the members of the set separated by commas. Make sure that after the last member of the set, there are no further symbols, including spaces! As I found out that leads to an error message.
	# Ordered pairs are written with the symbols "<" and ">". So, <4,3> is the ordered pair of 4 and 3.		# Ordered pairs are written with the symbols "<" and ">". So, <4,3> is the ordered pair of 4 and 3.
	# Unfortunately, Carnap is also sparse in allowing only whole positive integers as members of the domain. One way to think about that is that the models just give each individual its own number.		# Unfortunately, Carnap is also sparse in allowing only whole positive integers as members of the domain. One way to think about that is that the models just give each individual its own number.

Gert: /* Models in Carnap */

2021-01-28T09:02:35Z

Models in Carnap

← Older revision		Revision as of 09:02, 28 January 2021
Line 31:		Line 31:
	F(p) = 0		F(p) = 0
	F(m) = 1		F(m) = 1

			Here are important rules for formulating models in Carnap:

			# Only single upper and lower case letters are permitted as non-logical constants.
			# Lower case letters are names. So, instead of "maria'" you need to write "m".
			# Upper case letters are n-place constants (the arity is not part of the name). So, instead of "Frau'" you need to write "F".
			# You do not have to write sets in terms of curled brackets. Just list the members of the set separated by commas. Make sure that after the last member of the set, there are not further symbols, including spaces! As I found out that leads to an error message.
			# Ordered pairs are written with the symbols "<" and ">". So, <4,3> is the ordered pair of 4 and 3.
			# Unfortunately, Carnap is also sparse in allowing only whole positive integers as members of the domain. One way to think about that is that the models just give each individual its own number.
			# I have put the constraint on the models that every name has to denote a different entity from the domain as all the other names.
			# When Carnap displays a model at first, it already puts some information into the model, as follows:
			## the domain already contains the entity 0
			## Each name is already assigned a denotation. At first, all names denote the individual 0. Since I don't allow for 2 names to refer to the same individual, you must give each name a different denotation (counting from 0 upwards). Of course, if you introduce denotations other than 0 for names, you must add these denotations to the domain.
			## Each constant is listed with its arity shown in parentheses. That tells you whether its extension is a set of individuals or a set of ordered pairs.

Gert: /* Models in Carnap */

2021-01-28T08:45:19Z

Models in Carnap

← Older revision		Revision as of 08:45, 28 January 2021
Line 23:		Line 23:
	In the standard format, this model would be written as follows:		In the standard format, this model would be written as follows:

	M = <D, F> such that		M = <D, F> such that

	D = {0, 1}		D = {0, 1}
Line 29:		Line 29:
	F(M) = {0}		F(M) = {0}
	F(L) = {<0,1>}		F(L) = {<0,1>}

	F(p) = 0		F(p) = 0

	F(m) = 1		F(m) = 1