THE SEMANTICS OF VALUE-RANGE NAMES AND FREGE’S PROOF OF REFERENTIALITY

In this article, I try to shed some new light onGrundgesetze§10, §29–§31 with special emphasis on Frege’s criteria and proof of referentiality and his treatment of the semantics of canonical value-range names. I begin by arguing against the claim, recently defended by several Frege scholars, that the first-order domain inGrundgesetzeis restricted to value-ranges (including the truth-values), but conclude that there is an irresolvable tension in Frege’s view. The tension has a direct impact on the semantics of the concept-script, not least on the semantics of value-range names. I further argue that despite first appearances truth-value names (sentences) play a distinguished role as semantic “target names” for “test names” in the criteria of referentiality (§29) and do not figure themselves as “test names” regarding referentiality. Accordingly, I show in detail that Frege’s attempt to demonstrate that by virtue of his stipulations “regular” value-range names have indeed been endowed with a unique reference, can plausibly be regarded as a direct application of the context principle. In a subsequent section, I turn to some special issues involved in §10. §10 is closely intertwined with §31 and in my and Richard Heck’s view would have been better positioned between §30 and §31. In a first step, I discuss the piecemeal strategy which Frege applies when he attempts to bestow a unique reference on value-range names in §3, §10–§12. In a second step, I critically analyze his tentative, but predictably unsuccessful proposal (in a long footnote to §10) to identify all objects whatsoever, including those already clad in the garb of value-ranges, with their unit classes. In conclusion, I present two arguments for my claim that Frege’s identification of the True and the False with their unit classes in §10 is illicit even if both the permutation argument and the identifiability thesis that he states in §10 are regarded as formally sound. The first argument is set out from the point of view of the syntax of his formal language. It suggests though that a reorganization of the exposition of the concept-script would have solved at least one of the problems to which the twin stipulations in §10 give rise. The second argument rests on semantic considerations. If it is sound, it may call into question, if not undermine the legitimacy of the twin stipulations.

What does the 5S rRNA multigene family tell us about the origin of the annual Triticeae (Poaceae)?

We have investigated the complex relationships among the annual genera within the tribe Triticeae through phylogenetic analyses of the 5S rRNA multigene family. Cloned sequences were assigned to groups of orthologous sequences, called unit classes, that were subjected to several analyses including BLAST (Basic Local Alignment Search Tool) searches to assess possible ancestral relationships with perennial genera; phylogenetic analyses using parsimony (Pars), maximum likelihood (ML), and Bayesian methods; and minimum reticulation networks from the Pars, ML, and Bayesian trees. In this study, we included genera with both annual and perennial species, such as Dasypyrum, Hordeum, and Secale. BLAST pointed to Pseudoroegneria (carrier of the St genome) and possibly Thinopyrum (carrier of the J genome) as the potential next of kin. However, Thinopyrum and Pseudoroegneria have never fallen together on the individual trees with the former generally associated with Crithopsis, Aegilops, Triticum, and Dasypyrum, while the latter is usually associated with the rest of the genera within Triticeae. The “long” unit classes placed Dasypyrum breviaristatum together with Dasypyrum villosum, whereas the “short” unit classes put them far apart on the trees. None of the gene trees alone was able to summarize the complex relationships among the genera, in line with previous results in the Triticeae. However, the application of tools designed to display phylogenetic networks was able to depict the complex links among the genera based on the short and the long gene trees, including the close link between Thinopyrum and Pseudoroegneria suggested by the phylogenetic analyses. In addition, our analyses provide support for the hypothesis that at least some annual Triticeae taxa are derived from their perennial relatives.

Phylogenetic relationships among the polyploid and diploid Aegilops species inferred from the nuclear 5S rDNA sequences (Poaceae: Triticeae)

Phylogenetic inferences of the polyploid Aegilops taxa were drawn based upon the analysis of 909 nuclear 5S rDNA sequences obtained from 15 Aegilops polyploid taxa (531 sequences new to this paper) and 378 sequences from our previous study on the diploid taxa. The 531 sequences can be split into two orthologous groups (unit classes), the long AE1 and short AE1 previously identified in the diploid set. An examination of the relationships between unit classes and their associated haplomes suggests that U haplome sequences found in Ae. umbellulata are the closest to the T sequences found in Amblyopyrum muticum and that sequences of the polyploid species expected to be the M type found in Ae. comos are more similar to the T haplome sequences, except in the three hexaploids Ae. glumiaristata, Ae. juvenalis, and Ae. vavilovii and the tetraploid Ae. crassa where they are found to be similar to the M haplome sequences. These three hexaploid taxa likely originated from the tetraploid Ae. crassa (DM), while the closest taxon to the fourth hexaploid, Ae. recta, is the tetraploid Ae. neglecta (UM). Based upon the distribution of the unit classes, several reticulate phylogenies depicting evolutionary relationships among diploid, tetraploid, and hexaploid taxa were constructed; however, none of these widely used methods could depict the expected reticulate relationship as previously drawn from cytogenetic analyses in this group of allopolyploid species. These results suggest that evolutionary relationships derived from models based upon the assumption of bifurcating species require careful interpretation when these same models are applied to species with reticulate evolution.

Differences Between South American H Haplome Diploids and I Haplome Diploids from the Perspective of the 5S rDNA Gene in the Genus Hordeum

Twelve South American diploid Hordeum species belonging to the H genome and three diploid species belonging to the I genome (including cultivated barley) were investigated for their 5S rDNA sequence diversity. The 374 sequenced clones were assigned to classes called “unit classes” which were further assigned to haplomes. Two unit classes were found to be present in each haplome. These were labelled to reflect the haplomes, viz. the long H1 and short I1 unit classes for the I haplome diploids, and the long H2 and long Y2 unit classes for the South American H genome diploids. The aligned sequences were subjected to a series of Maximum Likelihood analyses and various tests, including molecular clock, which are presented and discussed. The divergences among the unit classes suggest that the genus Hordeum might be of paleopolyploid origin.  

Elimination of 5S DNA unit classes in newly formed allopolyploids of the genera Aegilops and Triticum

Two classes of 5S DNA units, namely the short (containing units of 410 bp) and the long (containing units of 500 bp), are recognized in species of the wheat (the genera Aegilops and Triticum ) group. While every diploid species of this group contains 2 unit classes, the short and the long, every allopolyploid species contains a smaller number of unit classes than the sum of the unit classes of its parental species. The aim of this study was to determine whether the reduction in these unit classes is due to the process of allopolyploidization, that is, interspecific or intergeneric hybridization followed by chromosome doubling, and whether it occurs during or soon after the formation of the allopolyploids. To study this, the number and types of unit classes were determined in several newly formed allotetraploids, allohexaploids, and an allooctoploid of Aegilops and Triticum. It was found that elimination of unit classes of 5S DNA occurred soon (in the first 3 generations) after the formation of the allopolyploids. This elimination was reproducible, that is, the same unit classes were eliminated in natural and synthetic allopolyploids having the same genomic combinations. No further elimination occurred in the unit classes of the 5S DNA during the life of the allopolyploid. The genetic and evolutionary significance of this elimination as well as the difference in response to allopolyploidization of 5S DNA and rDNA are discussed.

Codependence of repetitive sequence classes in genomes: phylogenetic analysis of 5S rDNA families in Hordeum (Triticeae: Poaceae)

To complete our study of the genus Hordeum and to elaborate a phylogeny of species based upon 5S rDNA sequences, we have cloned and sequenced PCR amplicons from seven American polyploid species to generate 164 new 5S rRNA gene sequences. These sequences were analysed along with the more than 2000 5S rDNA sequences previously generated from the majority of species in Hordeum to provide a comprehensive picture of the distribution (presence or absence) of 5S rDNA unit classes (orthologous groups) in this genus as well as insights into the phylogeny of Hordeum. Testing of substitution models for each unit class based upon the consensus sequences of all the taxa as well as for each unit class within the genus found that the general best fit was TPM3uf+G, from which a maximum-likelihood tree was calculated. A novel application of cophylogenetic analysis, where relationships among unit classes were treated as host–parasite interactions, depicted some significant pair links under tests of randomness indicative of nonrandom codivergence among several unit classes within the same taxon. The previous classification of four genomic groups is reflected in combinations of unit classes, and it is proposed that current taxa developed from ancient diploidized paleopolyploids and that some were subjected to gene loss, i.e., unit class loss. Finally, separate phylogenetic analyses performed for the tetraploid and hexaploid species were used to derive a working model describing the phylogeny of the polyploid taxa from their putative diploid ancestry.

Loss of 5S rDNA units in the evolution of Agropyron, Pseudoroegneria, and Douglasdeweya

We have investigated relationships among the three closely related genera Agropyron , Pseudoroegneria , and Douglasdeweya. Based upon grouping of 330 5S rDNA sequences into unit classes, we found that Douglasdeweya, with the genomic constitution PPStSt, has 2 unit classes, the long P1 and short S1, and Pseudoroegneria, with the genomic constitution StSt or StStStSt, has the long S1 and short S1 unit classes. In contrast, only the long P1 unit class was found in species of the genus Agropyron (PP). Having a single unit class is unique among all the genera of the tribe Triticeae investigated so far and may reflect gene loss or lineage sorting during its genesis. The presence of the short S1 and long P1 unit classes confirms the amphiploid origin of Douglasdeweya.

Molecular diversity of the 5S rRNA gene and genomic relationships in the genus Avena (Poaceae: Aveneae)

The molecular diversity of the rDNA sequences (5S rDNA units) in 71 accessions from 26 taxa of Avena was evaluated. The analyses, based on 553 sequenced clones, indicated that there were 6 unit classes, named according to the haplomes (genomes) they putatively represent, namely the long A1, long B1, long M1, short C1, short D1, and short M1 unit classes. The long and short M1 unit classes were found in the tetraploid A. macrostachya , the only perennial species. The long M1 unit class was closely related to the short C1 unit class, while the short M1 unit class was closely related to the long A1 and long B1 unit classes. However, the short D1 unit class was more divergent from the other unit classes. There was only one unit class per haplome in Avena, whereas haplomes in the Triticeae often have two. Most of the sequences captured belonged to the long A1 unit class. Sequences identified as the long B1 unit class were found in the tetraploids A. abyssinica and A. vaviloviana and the diploids A. atlantica and A. longiglumis . The short C1 unit class was found in the diploid species carrying the C genome, i.e., A. clauda, A. eriantha , and A. ventricosa , and also in the diploid A. longiglumis, the tetraploids A. insularis and A. maroccana , and all the hexaploid species. The short D1 unit class was found in all the hexaploid species and two clones of A. clauda. It is noteworthy that in previous studies the B genome was found only in tetraploid species and the D genome only in hexaploid species. Unexpectedly, we found that various diploid Avena species contained the B1 and D1 units. The long B1 unit class was found in 3 accessions of the diploid A. atlantica (CN25849, CN25864, and CN25887) collected in Morocco and in 2 accessions of A. longiglumis (CIav9087 and CIav9089) collected in Algeria and Libya, respectively, whereas only 1 clone of A. clauda (CN21378) had the short D1 unit. Thus there might be a clue as to where to search for diploids carrying the B and D genomes. Avena longiglumis was found to be the most diverse species, possibly harboring the A, B, and C haplomes. The long M1 and short M1 are the unit classes typical of A. macrostachya. These results could explain the roles of A. clauda, A. longiglumis, and A. atlantica in the evolution of the genus Avena. Furthermore, one clone of the tetraploid A. murphyi was found to have sequences belonging to the short D1 unit class, which could indicate that A. murphyi might have been the progenitor of hexaploid oats and not, as postulated earlier, A. insularis. The evolution of Avena did not follow the molecular clock. The path inferred is that the C genome is more ancient than the A and B genomes and closer to the genome of A. macrostachya, the only existing perennial, which is presumed to be the most ancestral species in the genus.